book of abstracts final - Université libre de...

CONTENTS

INFORMATION ABOUT THE IMT10 CONGRESS

ORGANIZING COMMITTEE

PROGRAMME

ORAL PRESENTATIONS

Monday, June 4th

Morning session.

Session Chair: Simone Wiegand

Afternoon session: Near critical region; Mutlicomponent mixtures.

Session Chair: Manfred Luecke

Tuesday, June 5th

Morning session: Experimental; Microgravity related

Session Chair: Mounir Bou Ali

Afternoon session: Simulations, Janus particles

Session Chair: Guillaume Galliéro

Wednesday, June 6th

Morning Session: Convection and vibrational phenomena

Session Chair: Tatyana Lyubimova

Thursday, June 7th

Morning session: Convection (mutlicomponent, ferrofluids)

Session Chair: Boris Smorodin

Afternoon session: Soret and diffusion

Session Chair: Prof. A. Mojtabi and M. Papalexandris (Poster

session)

Friday, June 8th

Morning session: porous media, industrial applications

Session Chair: Valentina Shevtsova

POSTER SESSION

LIST OF PARTICIPANTS

2

INFORMATION ABOUT THE IMT10 CONGRESS

The sequence of the past IMT conferences is:

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3

SCIENTIFIC ADVISORY BOARD

Spain

France

USA

France

Germany

Germany

France

France

Belgium

USA

Germany

ORGANIZING COMMITTEE

Chair

Phone:

Email:

4

10th International Meeting on Thermodiffusion Brussels, ULB, June 4-8, 2012

Final Program

Monday, June 4th

ROOM: Salle Dupree (S)

Morning session. Chair Simone Wiegand

8:30 – 9:45 Registration, Coffee

9:45 – 10:00 Opening

10:00 – 11:00 Konstantin Morozov (Technion, Israel)

Microscopic theory of the Soret effect in binary liquid mixtures

11:00 – 11:20 Coffee break

11:20 – 11:40 Eric Bringuier (Université de Paris 7, France)

Simple ideas about thermodiffusion in a binary liquid mixtures

11:40 – 12:00 Thomas Sottmann (University of Cologne, Germany)

On the size and structure dependence of the Soret coefficient studied in nonionic microemulsions

12:00 – 12:20 Kirill Glavatskiy ( NTNU, Trondheim, Norway)

The membrane surface heat of transfer and the enthalpy of adsorption

12:20 – 12:40 Mingcheng Yang (Forschungszentrum Jülich, Germany)

Langevin equation in non-isothermal suspensions

12:40 – 13:50 Lunch

Monday afternoon session: Near critical region; Mutlicomponent mixtures;


14:00 – 15:00 Abbas Firoozabadi (Yale University, USA)

Framework to Study Complexities from the Combined Effect of Thermal, Pressure and Fickian Diffusions in Multi-components

15:00 – 15:20 Jose M. Ortiz de Zarate (University of Complutense de Madrid, Spain)

Thermal fluctuations of the concentrations in a ternary mixture

15:20 – 15:40 Fabrizio Croccolo (Université de Fribourg, Suisse)

Observing the Soret effect in a different direction

15:40 – 16:00 Aliaksandr Mialdun (Université Libre de Bruxelles, Belgium)

Analysis of ternary mixtures with one wave length interferometer.


16:30 – 16:50 Thomas Triller (Universität Bayreuth, Germany)

A multicolor interferometer for the simultaneous measurement of contrast factors

6

16:50 – 17:10 Ilie Hodor (National Institute for R&D of Isotopic and Molecular Technologies, Cluj-Napoca, Romania)

The Universal Theory of the Separation Column as Applied to Thermodiffusion in Multicomponent Mixtures

17:10 – 17:30 Philipp Naumann (Forschungszentrum Jülich, Germany)

Development of an interferometric contactless detection system for a µ-thermogravitational column with transparent windows

18:30-20:30 RECEPTION at Museum of Musical Instrument http://www.mim.be/architecture

Tuesday, June 5th


Morning session: Experimental; Microgravity related


9:00 – 10:00 Werner Koehler (Bayreuth University, Germany)

Soret effect of small and large molecules - an experimentalist’s view

10:00 – 10:20 David Alonso de Mezquia (Mondragon Unibertsitatea, Spain)

Determination of the Molecular Diffusion coefficient in binary n-Alkane Mixtures

10:20 – 10:40 Flaminio Cordido (CEIF, Applied Optics Laboratory, Venezuela)

Measurement of the Soret coefficient in organic/water mixtures by thermal lens spectrometry


11:00 – 11:20 G. Salloum Abou Jaoude (Aix-Marseille Univ, France)

Influence of diffusion on the mushy zone evolution in a fixed temperature gradient

11:20 – 11:40 O. Fedorov (Space Research Institute Kyiv, Ukraine)

Directional solidification of transparent substances

11:40– 12:00 V. Shevtsova (Université Libre de Bruxelles, Belgium)

Experimental evidence of symmetry-breaking dynamical patterns in vibration-induced flows.

12:00 – 12:20 Q. Galand (Université Libre de Bruxelles, Belgium)

Preliminary Results of the DCMIX Experiment: Measurements of Thermodiffusion and Diffusion Coefficients in Ternary Liquid Systems

12:20 – 12:40 Stefan Van Vaerenbergh (Université Libre de Bruxelles, Belgium)

Soret and molecular diffusion of ternary systems in microgravity: evolution of the DCMIX experiments

12:40 – 14:00 Lunch

7

Tuesday afternoon session; Simulations, Junus particles


14:00 – 15:00 Bernard Rousseau (Université Paris-Sud, France)

Computing Soret coefficient for real systems from molecular dynamics. Motivations and difficulties

15:00 – 15:20 Frank Roemer (Imperial College London, London )

Alkali Halide aqueous solutions under temperature gradients: A non equilibrium molecular dynamic study

15:20 – 15:40 Rachid Hannaoui (Université de Pau et des Pays de l’Adour, France)

Molecular dynamics simulation of thermodiffusion in atomistic micro pores

15:40 – 16:20 Coffee break and POSTER WATCHING

16:20 – 16:45 Frank Cichos, Leipzig, Germany

Thermophoretic trapping and steering of Janus particles

16:45 – 17:10 Marisol Ripoll (Forschungszentrum Jülich, Germany)

Simulations of thermophoretic colloids and nanoswimmers

17:10 – 17:35 Natsuhiko Yoshinaga (Tohoku University, Japan)

Active Motion of Janus Particle by Self-thermophoresis

18:00 DCMIX ESA TT Session (for members)

Wednsday, June 6th



Chair: Tatyana Lyubimova

9:00 – 10:00 Alexander Nepomnyashchy (Haifa, Israel)

Onset of Marangoni Convection in Binary Solutions

10:00 – 10:20 Denis Melnikov (Université Libre de Bruxelles, Belgium) DNS of Soret driven diffusion in a three-dimensional rectangular domain

10:20 – 10:40 Isabel Mercader (Universitat Politecnica de Catalunya, Barcelona, Spain)

Convectons and drifting convectons in binary mixtures


11:00 – 11:20 Boris L. Smorodin (ICMM, Perm, Russia)

Binary mixture convection under high-frequency vertical vibration

11:20 – 11:40 Tatyana Lyubimova (ICMM, Perm, Russia)

Vibration influence on instability of binary fluid with negative Soret effect in square cavity heated from above

11:40 – 12:00 Marie Catherine Charrier-Mojtabi (University of Toulouse, France)

Action of acoustic streaming on species separation in a binary mixture: analytical and stability analysis

8

12:00 – 12:20 Xavier Ruiz (Universitat Rovira i Virgili, Tarragon, Spain )

On the accuracy of the interdiffusion coefficient measurements of high temperature binary mixtures under ISS real conditions

12:20– 12:40 Tatyana Lyubimova (ICMM, Perm, Russia)

Vibration effect on a stability of convective flows of multicomponent mixtures in vertical layer

12:40 – 21:00 Sandwich Lunch

Buses to Visit “La Brasserie Cantillon” http://www.cantillon.be/

Dinner at Royal Museums of Art and History, 18:00-21:00

http://en.wikipedia.org/wiki/Royal_Museums_of_Art_and_History

Thursday, June 7th


Morning session: convection (mutlicomponent, ferrofluids)

Session Chair: Boris Smorodin

9:30 – 10:30 Alois Würger (LOMA, France)

Is Soret an equilibrium effect?

10:30 – 10:50 Ilya I. Ryzhkov (Siberian Branch RAS, Krasnoyarsk, Russia)

Rayleigh-Benard instability in multicomponent fluids with the Soret effect

10:50 – 11:20 Coffee break and Poster watching

11:20 – 11:40 Dmitry Zablotsky (Institute of Physics, Latvia)

Convective stability of photoinduced microstructures in ferrofluid layers

11:40 – 12:00 Lisa Sprenger (Institute of Fluid Mechanics, TU Dresden)

Thermodiffusion in Ferrofluids regarding Thermomagnetic Convection

12:00 – 12:20 Miren Larrañaga (Mondragon Unibertsitatea, Spain)

Thermodiffusion Coefficient in Toluene-normal Alkane Binary Mixtures

12:20 – 12:40 Odalys Sanchez (Universitat Politecnica de Catalunya, Barcelona, Spain)

Secondary Flows in a Laterally Heated Horizontal Cylinder

12:40 – 14:00 Lunch


Session Chair: Prof. A. Mojtabi and M. Papalexandris (Poster session)

14:00 – 14:30 Dr. Moritz Kreysing (Systems Biophysics, Ludwig-Maximilians-Universitat Munchen, Germany)

Thermophoresis to detect and evolve biological functionality

14:30 – 14:50 Alain Martin (Mondragon Unibertsitatea, Spain)

Numerical and Experimental Analysis on Microfluidic Separation Process

9

14:50 – 15:10 Zilin Wang (Forschungszentrum Jülich, Germany)

Thermal diffusion of nucleotides

15:10 – 15:30 Ana C.F. Ribeiro (University of Coimbra, Coimbra, Portugal)

Ternary mutual diffusion coefficients in systems containing ion nickel

15:30 – 15:50 V. Sechenyh (Université Libre de Bruxelles, Belgium)

Design and development of a new instrument for measurements of diffusion in liquid mixtures


16:10 – 17:50 Oral presentation of Posters (2-3 slides and max 3 minutes, incl speaker change)

18:00 – 20:00 Belgian beer and Poster watching (sponsored by QinetiQ Space)

Award ceremony for the best Poster

Friday, June 8th


Morning session: porous media, industrial applications


9:00 – 10:00 Francois Montel (Total, France)

Pressure and Compositional Gradients in Petroleum Reservoirs

10:00 – 10:20 Jean Claude Legros (MRC, ULB)

Kinetic of thermo diffusion in binary liquids approaching critical point. Towards KIBILI experiment

10:20 – 10:40 Henri Bataller (Université de Pau, France)

Thermodiffusion of the Tetrahydronaphtalene and Dodecane mixture under high pressure and in porous medium.


11:20 – 11:40 Matthias Augustin (University of Kaiserslautern, Germany)

On convection patterns of binary fluid mixtures in porous media

11:40 – 12:00 Denis S. Goldobin (ICMM, Perm, Russia)

Thermal Diffusion and the Accumulation of Methane Bubbles in Deep-Water Sediments

12:00 – 12:20 Abdelkhalek Cheddadi (Univ. Mohamed V-Agdal, Rabat, Morocco)Stability of the Gradient Zone of a Solar Pond with Salt Gradient Taking into Account Soret Effect

12:20 – 13:00 Discussion on future IMT11

13:00 Lunch and Adjourn

10

Monday, June 4th


Morning session. Chair Simone Wiegand

8:30 – 9:45 Registration, Coffee 9:45 – 10:00 Opening 10:00 – 11:00 Konstantin Morozov (Technion, Israel) Microscopic theory of the Soret effect in binary liquid mixtures

11:00 – 11:20 Coffee break 11:20 – 11:40 Eric Bringuier (Université de Paris 7, France) Simple ideas about thermodiffusion in a binary liquid mixtures

11:40 – 12:00 Thomas Sottmann (University of Cologne, Germany) On the size and structure dependence of the Soret coefficient studied in

nonionic microemulsions

12:00 – 12:20 Kirill Glavatskiy ( NTNU, Trondheim, Norway) The membrane surface heat of transfer and the enthalpy of adsorption

12:20 – 12:40 Mingcheng Yang (Forschungszentrum Jülich, Germany) Langevin equation in non-isothermal suspensions

12:40 – 13:50 Lunch

11

Microscopic theory of the Soret effect in binary liquid mixtures

Konstantin I. Morozov1

1Department of Chemical Engineering, Technion - Israel Institute of Technology,

Haifa 32000, Israel [email protected]

Calculation of the Soret coefficient of binary liquid mixture is a long-standing problem of statistical

mechanics. The point is that thermal diffusion is a bizarre combination of two types of effects – kinetic

and thermodynamic ones. The former dominate in gaseous mixtures where the Soret effect is determined

by molecular collisions [1]. The latter stem from interparticle interactions and are expressed via spatial

variation of appropriate equilibrium thermodynamic potential of the mixture [2]. Just this mechanism

prevails in liquid mixtures. There is an experimental evidence in favor of the thermodynamic mechanism.

These are the data of Ref. [3] where similarly to property of thermodynamical potentials the additivity

of different contributions to the Soret effect has been found.

Recently [4], we proposed a thermodynamic approach where the gradient of partial pressure of mix-

ture’s components was considered as a driving force of the Soret effect. The approach represents a

development of the early idea of Bearman and Kirkwood. Its important part was the usage of the modern

solvation theory. It has been shown that the chemical contribution to the Soret coefficient can be written

in two different ways: (i) in accordance with the nature of intermolecular forces or (ii) via the defect of

mixture volume. The second representation allows determination of the main trend of the composition

dependence of the Soret coefficient of many non-polar as well as polar liquids what is important in ap-

plications. Moreover, calculated values of the Soret coefficient of benzene-cyclohexane mixture are in a

good agreement with experimental data [3].

Lately, we successfully generalized our approach to the case of chemically similar liquids whose

molecules differ in their masses and moments of inertia (isotope Soret effect) [5]. Surprisingly, the

isotope Soret effect proves to be a quantum effect at room temperatures stemming from librational and

vibrational motions of the molecules. Another amazing feature of the phenomenon is that the isotope

contribution can be the dominating effect as it has been demonstrated for mixtures CCl4-C6H6 and CCl4-

C6H12. Thus it appears that isotope Soret effect is most pronounced in these two non-isotope mixtures.

The resulting value of the Soret coefficient is equal to the sum of chemical and isotopic contributions.

The property is well satisfied for homologous series of halobenzenes in toluene and cyclohexane [5].

[1] Bringuier, E., Physica A, 390, pp. 1861-1875, 2011.

[2] Piazza, R. and Parola, A., J. Phys.: Condens. Matter, 20, pp. 153102(18), 2008.

[3] Debuschewitz, C. and Kohler, W., Phys. Rev. Lett., 87, pp. 055901(4), 2001.

[4] Morozov, K.I., Phys. Rev. E, 79, pp. 031204(11), 2009.

[5] Hartmann, S., Kohler, W. and Morozov, K.I., Soft Matter, DOI: 10.1039/C1SM06722B, 2012.

12

Simple ideas about thermodiffusion

in a binary liquid mixture

Eric Bringuier Matériaux et Phénomènes Quantiques, UMR 7162 du CNRS, Université de Paris 7, 5 rue Thomas Mann, 75205 Paris Cedex 13, France, [email protected]

The simplest system where the microscopic physical nature of thermodiffusion can be

understood theoretically is a binary mixture of non-reacting components. In a gaseous binary mixture,

thermodiffusion had been predicted theoretically by Enskog and Chapman prior to observation, and

their theory is quantitatively successful for monatomic gases. In the present contribution, the case of a

liquid mixture is considered, starting from the equilibrium state such as described by thermodynamics.

Under constant temperature, the gradients of composition and/or pressure bring about a non-

equilibrium state where enthalpy is not minimum and/or entropy is not maximum. The gradients of

enthalpy and entropy define thermodynamic forces which are shown to drive composition and

pressure diffusions (i.e. ordinary diffusion and barodiffusion). The thermodynamic forces considered

in this contribution have the physical dimension of a force, they are defined per particle, they are

invariant under gauge transformations of enthalpy and entropy and lastly they obey Newton's third law

[1].

Under a non-constant temperature, it is shown that neither the enthalpic force nor the entropic

force can account for thermodiffusion in a binary mixture. The force driving thermodiffusion is of a

non-thermodynamic essence in that it cannot be obtained from the thermodynamic functions of the

mixture. The thermodiffusive force requires to go beyond the approximation of local equilibrium. An

explicit kinetic expression of that force is obtained for mixtures of monatomic molecules in connection

with studies of thermodiffusion in gases, based upon two-body collision events. The absolute value of

the thermal-diffusion ratio is then calculated to be of the order of unity and it involves microscopic

scattering features. The irrelevance of three- and many-body collision events is addressed.

It is found that the thermodiffusive force depends on the internal degrees of freedom of the

molecules making up the mixture. Any model of thermodiffusion reducing polyatomic molecules to

point particles is expected to fail by typically 50 % [1] or more [2]. Whether the mixture is gaseous or

liquid, the microscopic theory of thermodiffusion cannot ignore the internal structure of molecules. In

short, there is no universality. This conclusion is checked against published experimental data.

[1] Bringuier, E., Physica A, 390, pp. 1861-1875, 2011. [2] Bringuier, E., Physica A, 389, pp. 4545-4551, 2010.

13

On the size and structure dependence of the Soret coefficient

studied in nonionic microemulsions

Bastian Arlt1), Sascha Datta2), Philipp Naumann1), Nils Becker2), Thomas Sottmann2) and Simone Wiegand1)

1) Forschungszentrum Jülich GmbH, ICS - Soft Matter, D-52425 Jülich, Germany2) University of Cologne, Department of Chemistry, Luxemburger Str. 116, D-50939 Cologne, Germany.

In this work we studied the thermal diffusion behavior of microemulsion systems of the type H2O/n-alkane/C12E5 (pentaethylene glycol monododecyl ether) using the n-alkanes n-octane, n-decane, n-dodecane and n-tetradecane. In order to determine the thermal diffusion behavior of these microemulsion droplets, the infrared thermal diffusion forced Rayleigh scattering (IR-TDFRS) setup was used. We measured the Soret coefficient (ST) as function of the type of the structure upon approaching the emulsification failure boundary (efb) and as a function of the radius of the spherical (o/w)-microemulsion droplets close to the efb. Thereby the chain length of the oil component was varied to obtain droplets of different sizes at the same temperature. SANS experiments were performed to determine the size and to examine in detail the shape of the microemulsion droplets, as the droplets are known to change shape with increasing temperature to elongated and network-like aggregates at the near critical boundary (ncb). Close to the efb the scattering curves could be quantitatively described by a combination of a spherical core-shell form factor and sticky hard sphere structure factor. Combining the results from the IR-TDFRS and SANS experiments an almost linear size dependence of the Soret coefficient was found for microemulsion droplets indicating that they can be regarded as solid particles. The findings are compared with literature results which indicate either a linear [1,2] or quadratic size dependence [3] of the Soret coefficient as function of the radius of the solute particles.

[1] Vigolo, D., Brambilla, G. and Piazza, R., Phys. Rev. E, 75, 040401, 2007. [2] Braibanti, M., Vigolo, D. and Piazza, R., Phys. Rev. Lett., 100, 108303, 2008. [3] Duhr S. and Braun D., Phys. Rev. Lett., 96, 168301, 2006.

14

The membrane surface heat of transfer and the enthalpy of

adsorption

Kirill Glavatskiy1) and Signe Kjelstrup2)

1) Department of Chemistry, NTNU, Trondheim, N-7491, Norway,[email protected]

2) Department of Chemistry, NTNU, Trondheim, N-7491, Norway, [email protected]

The heat of transfer, the ratio between the heat flux and the mass flux in the absence of a temperature difference, defines the magnitude of thermodiffusional phenomena, in particular, in the case of membrane transport. In that case, one heat of transfer is found for the membrane surfaces, and another one for the membrane interior [1]. The heat of transfer can be expressed by the thermal diffusion coefficient and the interdiffusion coefficient. Membranes are frequently chemically active substances, which interact with the component transported. The most important interactions take place at the boundary of the membrane, for instance when pure fluid (gas) is being adsorbed into the membrane. A large enthalpy of adsorption will affect the fluid transport through the membrane as it is related to the heat of transfer. In this work we study how the heat of transfer depends on the enthalpy of the phase change between the fluid inside and outside of the membrane.

For a surface that is described as a series of resistivites, it was shown [1] that the heat of transfer is a fraction k of the partial enthalpy difference of the phases next to the surface. The fraction depends on the nature of the chemical interactions in the membrane. For a membrane made of ion-exchange material, it depends on the nature of the water interactions with the ionic sites in the membrane. This is different for hydrophobic and hydrophilic membranes. The nature of the membrane can therefore affect the sign of k. Kinetic gas theory gives the value of this proportionality coefficient of -0.2 for the liquid-vapor transition of hard spheres. Modelling [2] the system within non-equilibrium thermodynamic approach, we have tested the effect of a varying membrane hydrophobicity on the overall performance of the membrane. This problem is relevant for polymer electrolyte fuel cells.

An interesting question to answer is how system variables are affected by the heat of transfer (the coupling of heat and mass transfer) at the interface. We show that neglect of coupling leads to 10 % difference in water fluxes, increasing in magnitude as the membrane becomes thinner.

Fig.1 The value of the pressure drop across the membrane at a given flux with (k = 0.2) and without (k = 0) coupling

[1] Kjelstrup, S. and Bedeaux, D., Non-equilibrium Thermodynamics of Heterogeneous Systems.,Ch.8, World Scientific, 2008.[2] Glavatskiy, K., Pharoah, J. and Kjlelstrup, S., preprint, 2011.

15

Langevin equation in non-isothermal suspensions

Mingcheng Yang1 and Marisol Ripoll

1Theoretical Soft Matter and Biophysics, Institute of Complex Systems,

Forschungszentrum Julich Julich 52425, Germany

[email protected]

The self-diffusion coefficient Ds of particles in a suspension with a temperature gradient is position-

dependent. This inhomogeneity has a significant influence in the dynamics of the particles. When

applying the standard overdamped Langevin equation (LE) to such a system, the position-dependent Ds

leads to an ambiguity related to multiplicative noise, namely, the results depend on the convention chosen

to evaluate the noise - the so called Ito-Stratonovich dilemma. In this work, we show that the ambiguity

can be solved by considering the force balance condition, so that the overdamped LE needs to be revised.

The obtained results are valid in systems far from equilibrium. With the revised LE, the expressions of

drift velocity and particle flux are obtained. Computer simulations confirm the theoretical predictions.

16

Monday afternoon session: Near critical region;

Mutlicomponent mixtures


14:00 – 15:00 Abbas Firoozabadi (Yale University, USA)Framework to Study Complexities from the Combined Effect of Thermal,

Pressure and Fickian Diffusions in Multi-components

15:00 – 15:20 Jose M. Ortiz de Zarate (University of Complutense de Madrid, Spain)Thermal fluctuations of the concentrations in a ternary mixture

15:20 – 15:40 Fabrizio Croccolo (Université de Fribourg, Suisse)Observing the Soret effect in a different direction

15:40 – 16:00 Aliaksandr Mialdun (Université Libre de Bruxelles, Belgium) Analysis of ternary mixtures with one wave length interferometer.

16:00 – 16:30 Coffee break 16:30 – 16:50 Thomas Triller (Universität Bayreuth, Germany) A multicolor interferometer for the simultaneous measurement of contrast

factors

16:50 – 17:10 Ilie Hodor (National Institute for R&D of Isotopic and Molecular Technologies, Cluj-Napoca, Romania) The Universal Theory of the Separation Column as Applied to

Thermodiffusion in Multicomponent Mixtures

17:10 – 17:30 Philipp Naumann (Forschungszentrum Jülich, Germany) Development of an interferometric contactless detection system for a µ-

thermogravitational column with transparent windows

18:30-20:30 RECEPTION at Museum of Musical Instrument http://www.mim.be/architecture

17

Framework to Study Complexities from the Combined Effect of

Thermal, Pressure and Fickian Diffusions in Multi-components

Abbas Firoozabadi1,2)

1) Reservoir Engineering Research Institute, Palo Alto, CA, U.S.A., [email protected]

2) Yale University, New Haven, CT, U.S.A.

When multi-components or even two-components are subjected to gradients of temperature, pressure and composition, the movement and segregation of different molecules become fascinating. The combined effect of the three diffusion processes --thermal, pressure and Fickian-- are important in a number of natural and industrial processes. The study of past climate changes from ice core data is facilitated by the combined effect of three diffusions in the furn over the ice column. The estimation and production of hydrocarbons in some of the most prolific fields in the world is also related to modeling from the combined effect of the three diffusion processes in multi-components. Long-term fate of CO2 sequestration in saline aquifers may depend on all the diffusions.

In some of the above applications, the fluid state is near the critical region. Fluctuations in the near-critical region add further complexity to the understanding of diffusions.

In this presentation, I will start with a brief review of a framework to formulate the multi-component diffusions in the critical region and away from the critical region. And then move on to the modeling based on molecular dynamics to explore insight into molecular motion and clustering in the critical region.

18

Thermal fluctuations of the concentrations in a ternary mixture

Jose M. Ortiz de Zarate1 and Jan V. Sengers2

1Departamento de Fısica Aplicada I. Universidad Complutense. Madrid, Spain [email protected] for Physical Science and Technology. University of

Maryland. College Park, Maryland, USA [email protected]

We present expressions for the spatial and temporal spectra of concentration fluctuations in a ternary

liquid mixture in both equilibrium and nonequilibrium. Our approach is based on Landau’s fluctuating

hydrodynamics [1]. For a ternary mixture in equilibrium our results agree with those found by Bardow [2]

by a different approach. For a ternary mixture subjected to a temperature gradient our results are new.

Thermal fluctuations in equilibrium systems can be theoretically modeled by two different meth-

ods. One is based on fluctuating hydrodynamics [1], and consists in introducing random contributions

to the dissipative fluxes and adopting a fluctuation-dissipation theorem (FDT). Then, stochastic equa-

tions have to be solved and the statistical properties of the fluctuating fields calculated from the known

correlation functions of the random dissipative fluxes [3, 4]. Alternatively, one can use an approach,

pioneered by Mountain [5] and adopted in the books of Boon and Yip [6] or Berne and Pecora [7], that

consists in solving deterministic (with no random contributions) hydrodynamic equations with arbitrary

initial conditions. One then averages over these initial conditions and obtains the dynamic correlation

function 〈δc(t) · δc(0)〉 from a knowledge of the static correlation(s) 〈δc(0) · δc(0)〉 which is obtained

from equilibrium statistical physics. Both approaches are fully equivalent for fluctuations in equilibrium

systems [4].

However, unlike the Mountain approach, fluctuating hydrodynamics can be extended to also deal

with fluctuations in systems in nonequilibrium, as previously shown and experimentally confirmed for

one-component and binary fluid mixtures [4]. Thermal fluctuations in ternary liquid mixtures have the-

oretically been investigated so far only by the arbitrary initial condition approach. Therefore, a first

necessary step in developing the theory of nonequilibrium fluctuations in these systems is to re-derive

the equilibrium results on the basis of fluctuating hydrodynamics.

In our derivation we adopt some approximations that are adequate for mixtures in the liquid state.

The physical meaning of the nonequilibrium static and dynamic structure factors for the concentration

fluctuations in a ternary mixture will be elucidated.

[1] L. D. Landau, E. M. Lifshitz, Fluid Mechanics, Pergamon, London, 1959, 2nd revised English version, 1987.

[2] A. Bardow, Fluid Phase Equilib., 251, pp. 121–127, 2007.

[3] R. F. Fox, G. E. Uhlenbeck, Phys. Fluids, 13, pp. 1893–1902, 1970.

[4] J. M. Ortiz de Zarate, J. V. Sengers, Hydrodynamic Fluctuations in Fluids and Fluid Mixtures, Elsevier, Ams-

terdam, 2006.

[5] R. D. Mountain, Rev. Mod. Phys., 38, pp. 205–214, 1966.

[6] J. P. Boon, S. Yip, Molecular Hydrodynamics, McGraw-Hill, New York, 1980, Dover edition, 1991.

[7] B. J. Berne, R. Pecora, Dynamic Light Scattering, Wiley, New York, 1976, Dover edition, 2000.

19

Observing the Soret effect in a different direction

Fabrizio Croccolo1), Henri Bataller2) and Frank Scheffold3)

1) Université de Fribourg, Dept. de Physique, Ch. du Musée 3, CH-1700, Fribourg, Suisse, [email protected]

2) Université de Pau et des Pays de l’Adour, Laboratoire des Fluides Complexes et leurs Réservoirs, Allée du Parc Montaury, F-64600, Anglet, France, [email protected]

3) Université de Fribourg, Dept. de Physique, Ch. du Musée 3, CH-1700, Fribourg, Suisse, [email protected]

Observing a horizontal slab of a binary mixture parallel to the vertical stressing thermal gradient, non equilibrium fluctuations can be analyzed by means of Dynamic Shadowgraph. By the analysis of the wave vector dependent static power spectrum and temporal correlation function the Soret and the mass diffusion coefficient are derived. An experiment is performed on the binary mixtures of the Fontainebleau benchmark which results confirm the literature data.

Most of the techniques used to measure the Soret coefficient are based on the horizontalobservation of the concentration profile while the fluid mixture is stressed by a vertical temperaturegradient. For example, in the beam deflection technique [1] a beam crosses the sample horizontallybeing deflected by the refractive index gradient due to the temperature and the concentration profiles. The analysis of the vertical displacement of the beam at certain distance from the cell allows measuring the Soret and mass diffusion coefficients once the so-called contrast factors are known.

Here we describe how the Soret and mass diffusion coefficients can be measured by careful investigation of the static and dynamic spectra of non equilibrium fluctuations (NEFs) by means of dynamic Shadowgraph [2]. This is obtained by sending a probe beam parallel to the temperature and concentration gradients without knowledge of the values of the contrast factors. NEFs are tiny (in intensity) but giant (in lateral size) fluctuations of the temperature or the concentration which appear as soon as a gradient is applied to a fluid [3].

The temporal correlation function of NEFs for wave vectors larger than a critical value follows

an exponential decay with time constant

cq

21 Dqq in which is the mass diffusion coefficient

and is the fluctuation wave vector. From the time constants a precise measurement of the diffusion

coefficient can be obtained. Conversely, the time constants below show a quadratic behavior

due to the buoyancy effect of gravity on larger fluctuations [4]. The critical value is the

wave vector at which gravity and diffusion play the same role and depends on the Soret coefficient:

D

q

cq

2q cq

4

1

1

D

ccSTgq ooT

c

in which is the mass expansion coefficient, g the gravitational acceleration, the temperature

gradient, the average concentration of the denser component and

T

oc the kinematic viscosity of the

mixture. By measuring the critical wave vector one is able, upon knowledge of the fluid parameters

and , to get a measurement of the Soret coefficient. Results will be presented concerning the application of method to three binary mixtures of the Fontainebleau benchmark. These mixtures are a calibration standard for the development of thermodiffusion cells [5].

[1] Giglio, M., and Vendramini, A., Phys. Rev. Lett., 34, pp. 561-564, 1975. [2] Croccolo, F., et al., Phys. Rev. E, 76, pp. 41112-1-9, 2007. [3] Vailati, A., and Giglio, M., Nature, 390, pp. 262-265, 1997, Weitz, D.A., Nature, 390, pp. 233-235,1997[4] Croccolo, F., et al., Ann. New York Acad. Sci., 1077, pp. 365-379, 2006. [5] Platten, J.K., et al., Philosophical Magazine, 83, pp. 1965-1971, 2003.

20

Analysis of the ternary mixtures with one wave length interferometer

Alexander Mialdun, Alexander Nepomnyashchy, Valentina Shevtsova1

1MRC, ULB, EP - CP165/62, Dept. Chemical Physics,

B1050, Brussels, Belgium [email protected]

The liquids appearing in nature and industrial applications are essentially multicomponent. In mix-

tures, the diffusive mass transport of a given component is induced not only by its compositional gradient

(main or principal diffusion), but also by the compositional gradients of the other components (cross-

diffusion) and the temperature gradient (thermodiffusion, also called Soret effect). Although several

theoretical approaches have been presented in the literature there is no unambiguous theory for thermal

diffusion in liquids. So, advanced experimental techniques and accurate data on transport coefficients

are of great importance for further theoretical developments and applications.

Among the existing methods for measurement of thermodiffusion coefficients in binary mixtures, the

modern optical techniques play an important role. They require accurate knowledge of refractive index

derivatives (contrast factor) with respect to concentration and temperature. Moving to ternary mixtures

the success of the experiments depends not only on contrast factors of individual components but on the

matrix (2×2) composed by ∂nλj/∂ci, i, j = 1, 2. There is a serious obstacle in practical implementation

of optical techniques because the matrix can be ill-conditioned. There are two equivalent ways to choose

optimal experimental conditions: by choosing a concentration set or by choosing a proper wave length.

In the case of interest for some specific liquids one should search for proper light sources while for

the prescribed wavelengths not all compositions are suitable [1]. To find the proper pair of lights or

substances is not always possible.

We have developed mathematical approach which allow to determine the Soret coefficient from the

experiments with one wave length interferometer. However, this approach require knowledge of mass

diffusion coefficients. For this purpose an independent technique to measure mass diffusion coefficients

is under development [2].

[1] Shevtsova V., Sechenyh V., Nepomnyashchy A., Legros J.C., Analysis of the application of optical two-

wavelength techniques to measurement of the Soret coefficients in ternary mixtures, Philosophical Magazine,

91(26), pp.3498-3518 (2011)

[2] V. Sechenyh, J. C. Legros, V. Shevtsova, Design and development of a new instrument for measurements of

diffusion in liquid mixtures, Abstract of IMT10

21

A multicolor interferometer for the simultaneous measurement of

contrast factors

Andreas Koniger, Thomas Triller, Werner Kohler1

1Physikalisches Institut, Universitat Bayreuth, 95440 Bayreuth, Germany,

[email protected]

During the last years thermodiffusion in ternary fluid mixtures has been a subject of increasing in-

terest. Currently, optical experiments are performed both in a microgravity environment on board of the

international space station (ISS) using an interferometric device (SODI) and on ground using the optical

beam deflection (OBB) technique [1].

For analysis of the experimental data, precise knowledge of the so called contrast factors ( ∂n∂ci

)p,T,cj 6=iand

( ∂n∂T )p,ci

is essential. Monte Carlo simulations have shown that a reliable measurement of the contrast

factors is even more critical than a precise measurement of the Soret-induced refractive index changes.

For reliable values of the Soret coefficients it is therefore necessary to keep refractive index errors as low

as 10−5.

As a step to reach such precision we present a setup which is currently being built by our group. Using

the basic outline of a Michelson interferometer (FIG. 1), we want to measure concentration series of

ternary mixtures with five different wavelengths simultaneously, to have a consistent data set of contrast

factors for microgravity and ground experiments. Later, we are planning to equip the instrument also

with a cell for multicolor ∂n/∂T -measurements.

FIG. 1: Schematic of a multicolor interferometer for refractive index measurements.

[1] Koniger, A., Wunderlich, H. and Kohler, W., J. Chem. Phys, 132, 174506, 2010.

22

The Universal Theory of the Separation Column

as Applied to Thermodiffusion in Multicomponent Mixtures

Ilie Hodor National Institute for R&D of Isotopic and Molecular Technologies, Cluj-Napoca, Romania, [email protected]

Over many years, this author has developed the theory of separation column that is universal and abstract. The theory is called universal, as it is applicable to every separation process, as distillation, chemical exchange, ultra-centrifugation, thermodiffusion, and so on. It is called abstract because the concrete column images are substituted by axioms that are self-evident truths for every separation process.

In the present paper, the universal theory is extended, for the first time, to mixtures with more than two components. The theory is presented as applied to the thermodiffusion/thermogravitational column for the following reasons: (1) the transparency of the theory is greater if it is explained on a particular process; (2) as a particular process it is chosen the thermodiffusion column because this separation process is very much studied in literature. Because the volume of the work is too large, only the final results are presented and explained in this paper. The intention is that the actual theory be treated in future publications.

Geometrically, the theory covers: (1) the flat plate geometry, (2) cylindrical column with annular section, and (3) cylindrical column with arbitrary cross-section. For all geometries, the theory leads to the same form of the species transport through the column,

( )z

wKKH�w�

j

j dijcijiii∂

∂+−+= � 1...2,1, −= �ji

But the expressions for iH , cijK , and dijK depend on geometry.

Of course, the present theory covers although the flat plate case studied by Haugen and Firoozabadi [1]. But the application of the universal theory to any particular case is characterized by a maximum simplicity and rigor.

�� !�� "#�� $%�&'())*��+�� % �% ��'� ��, � �# �!!��%��-�. ��*&/�� 01'02 �

�

23

Development of an interferometric contactless detection system for a

µ-thermogravitational column with transparent windows

Philipp Naumann ([email protected]),1 Hartmut Kriegs,1 Simone Wiegand

([email protected]),1 Alain Martin ([email protected]),2

Miren Larranaga,2 and M. Mounir Bou-Ali ([email protected])2

1Institute for complex systems - Soft Matter,

Forschungszentrum Juelich, Juelich, Germany2Manufacturing Department, MGEP Mondragon Goi Eskola Politeknikoa,

Loramendi 4 Apartado 23, 20500 Mondragon

Using a Mach-Zehnder interferometer in combination with a thermogravitational column with trans-

parent windows we determine thermal diffusion coefficients of several binary mixtures. The used µ-TG

column has a very small sample volume of less than 50 µL and transparent windows in the direction

of the temperature gradient. The time dependence of concentration difference between two points at

different heights is measured by an interferometer with active phase control. From the concentration

difference we can determine the thermal diffusion coefficient, DT, using the refractive index increment

with concentration, which has to be determined independently. We studied the three binary mixtures of

dodecane (DD), isobutylbenzene (IB) and 1,2,3,4-tetrahydronaphthalene (TH) with a concentration of

50wt% at a temperature of 25◦C. The thermal diffusion coefficients agree within a few percent with the

proposed benchmark values [1]. In addition we investigated also the binary mixture n-hexane/toluene

and compare with literature values. Beside the benchmark systems we investigated also the mixture

toluene/n-hexane, which has been studied by various groups [2–4] with convective free and convective

methods. For the investigated mixtures the typical measurements times were between 30 minutes and 2

hours.

FIG. 1: Comparison of the determined DT Values with literature results

[1] J. K. Platten, M. M. Bou-Ali, P. Costeseque, J. F. Dutrieux, W. Kohler, C. Leppla, S. Wiegand, and G. Wittko,

Philos. Mag. 83, 1965 (2003).

[2] W. Kohler and B. Muller, J. Chem. Phys. 103, 4367 (1995).

[3] K. J. Zhang, M. E. Briggs, R. W. Gammon, and J. V. Sengers, J. Chem. Phys. 104, 6881 (1996).

[4] M. M. Bou-Ali, O. Ecenarro, J. A. Madariaga, C. M. Santamaria, and J. J. Valencia, J. Phys.: Condens. Matter

10, 3321 (1998).

24

Tuesday, June 5th


Morning session: Experimental;

Microgravity related


9:00 – 10:00 Werner Koehler (Bayreuth University, Germany) Soret effect of small and large molecules - an experimentalist’s view 10:00 – 10:20 David Alonso de Mezquia (Mondragon Unibertsitatea, Spain) Determination of the Molecular Diffusion coefficient in binary n-Alkane Mixtures 10:20 – 10:40 Flaminio Cordido (CEIF, Applied Optics Laboratory, Venezuela)Measurement of the Soret coefficient in organic/water mixtures by thermal lens spectrometry10:40 – 11:00 Coffee break 11:00 – 11:20 G. Salloum Abou Jaoude (Aix-Marseille Univ, France) Influence of diffusion on the mushy zone evolution in a fixed temperature gradient 11:20 – 11:40 O. Fedorov (Space Research Institute Kyiv, Ukraine) Directional solidification of transparent substances 11:40– 12:00 V. Shevtsova (Université Libre de Bruxelles, Belgium) Experimental evidence of symmetry-breaking dynamical patterns in vibration-induced flows 12:00 – 12:20 Q. Galand (Université Libre de Bruxelles, Belgium) Preliminary Results of the DCMIX Experiment: Measurements of Thermodiffusion and Diffusion Coefficients in Ternary Liquid Systems 12:20 – 12:40 Stefan Van Vaerenbergh (Université Libre de Bruxelles, Belgium) Soret and molecular diffusion of ternary systems in microgravity: evolution of the DCMIX experiments 12:40 – 14:00 Lunch

25

Soret effect of small and large molecules - an experimentalist’s view

Werner Kohler1

1Universitat Bayreuth, D95440 Bayreuth, Germany, [email protected]

The understanding of the Soret effect of binary mixtures of simple molecular liquids has made consid-

erable progress during the recent decade. Reliable experimental techniques – such as thermogravitational

columns, Soret cells with optical beam deflection, transient holographic gratings and digital holography

– are nowadays available and have been validated against the Fontainebleau benchmark systems. Thus,

the Soret effect of almost any binary fluid can successfully be studied under laboratory conditions.

Despite the progress made from the theoretical side and from molecular dynamics simulations, we are

still facing a situation where it is not possible to predict the Soret and thermal diffusion coefficients for

an arbitrary system. In order to advance our understanding and provide a solid basis for the development

of theories it is important to perform well-structured and well-planned experiments that address specific

aspects of the mixtures. Only from such systematic experiments it is possible to discover trust-worthy

patterns in the experimental data that can serve as a solid basis for the development of theoretical models.

In my contribution I will focus on experimental observations that show general patterns and, possi-

bly, point to common microscopic mechanisms. One example is the isotope Soret effect that was first

discovered between isotopic mixtures of the same molecule. Later, it has also been observed in isotopic

mixtures of different compounds, and the generalized description in terms of differences of molecu-

lar mass and moment of inertia now even proofs to be applicable to different but chemically similar

molecules.

In order to be in the liquid state at room temperature, the size of the molecules cannot easily be varied

to a large extent. One possible scenario, where the transition from small molecules to very large entities

can be studied, are solutions of synthetic polymers. While very short polymer chains, behave ‘as erratic’

as small molecules, most molecular details get lost and only universal properties of both the solvent and

the polymer survive in the limit of long polymer chains in dilute solution.

Still largely unanswered and controversially discussed questions are linked to the computation of

the Soret and thermal diffusion coefficients from equilibrium properties of the mixtures and/or from

properties of the pure compounds. Closely related is the question, whether simple additivity exists. To

address in particular the last problem, we have started to build a data base with the Soret coefficients of all

possible binary mixtures of a constantly growing number of compounds. Based on these now available

data for non-polar and weakly polar systems, it is clear that ST cannot be split into simple additive

contributions. But after factoring out the so-called thermodynamic factor, which is a pure equilibrium

property that can be obtained from a suitable equation of state, heats of transfer can uniquely be assigned

to every compound. Once these single-component-heats of transfer are known, the Soret coefficient of

arbitrary symmetric mixtures can readily be calculated without requiring any nonequilibrium properties

of the mixture. Based on these results, it seems feasible to construct an ‘equivalent of the electrochemical

series’ for the Soret effect. Although this concept gives a very good agreement with experiments for

equimolar mixtures, the treatment of different concentrations is still an open question.

26

Determination of the Molecular Diffusion coefficient in binary n-Alkane

Mixtures

David Alonso de Mezquia,1 M. Mounir Bou-Ali,1 Miren

Larranaga,1 Jose Antonio Madariaga,2 and Carlos Santamarıa2

1MGEP Mondragon Goi Eskola Politeknikoa,

Mechanical and Industrial Manufacturing Department, Loramendi 4 Apartado 23,

20500 Mondragon, Spain [email protected] of Applied Physics II, University of Basque Country, Apdo. 644, 48080 Bilbao, Spain

A concentration gradiente within a liquid mixtures causes a transport of matter. This phenomenon,

known as molecular diffusion, has been widely studied due to its influence in several fields as can be

medicine and phisiology [1].

In this work the Sliding Symmetric Tubes (SST) (Fig. 1) technique [2] has been used for the de-

termination of the molecular diffusion coefficient of 25 normal alkane binary mixtures at 298 K. This

coefficient has been determined in nC6 − nCi, nC10 − nCi and nC12 − nCi series at 50 wt %. Addi-

tionally, a study of nC12 − nC6, nC12 − nC7 and nC12 − nC8 binary mixtures in the whole range of

concentration has been done.

Figura 1: Left: Image of the Sliding Symmetric Tubes set-up; Right: Comparison between experimental results and

those obtained by the correlation developed.

The obtained results show how, for the studied mixtures, there exits a relation between the molecular

diffusion coefficient and the dynamic viscosity of the mixtures. These observations have been used to

develop a new correlation that is able to determine the molecular diffusion coefficient in normal alkane

binary mixtures at any concentration using the data of the molecular weight of the components and

the dynamic viscosity of the mixture. It has been checked the good agreement between the analytically

obtained data and the experimentally obtained one (Fig. 1).

[1] Cussler, E., Cambridge Univesity Press, 1997.

[2] Alonso de Mezquia, D., Bou-Ali, M.M., Larranaga, M., Madariaga, J.A., and Santamarıa, C., Journal of

Physical Chemistry B, (acepted).

27

Measurement of the Soret coefficient in organic/water mixtures by

thermal lens spectrometry

Humberto Cabrera,1 Flaminio Cordido,1 Maximo Garcıa-Sucre,1 Ana

Velasquez,1 Eloy Sira,1 Pablo Moreno,1 and Santos A. Lopez-Rivera2

1IVIC, CEIF - CP5101, Applied Optics Laboratory,

Merida, Venezuela [email protected] Andes University, Applied Physics Laboratory,

CP5101, Merida, Venezuela, [email protected]

In previous work the Soret coefficient of organic/water mixtures has been determined by a thermal

lens technique [1, 2]. In a stationary situation the total thermal lens signal is related to the Soret coeffi-

cient as follows [1, 2]

Stotal(z, t) = Sth − Ss =Peαlπ

kλp2

[

∂n

∂T−

∂n

∂xST x0(1− x0)

]

, (1)

Equation (1) provides a simple relation between the total signal Stotal and the Soret coefficient

ST . Measuring the total signal, the Soret coefficient can be obtained if the rest of the parameters are

known [2]. The Soret coefficient for binary mixture can be obtained also from the ratio of the Soret

signal and the pure thermal lens signal

ST =∂n∂T

∂n∂x

x0(1− x0)

Ss

Sth

, (2)

Using equation (2) there is no need for the use of cobalt nitrate which allowed more easy experimental

determination of the absorption coefficient. We can obtain the Soret signal Ss as the difference between

the final steady-state total signal Stotal and the value of the pure thermal lens signal Sth obtained extrap-

olating the fit of the thermal lens contribution of the Eq.(1) in the 0-400 ms range (see Fig. 1). Finally

the Soret coefficient ST can be calculated according to Eq. (2). Using this method we have obtained

the values of the Soret coefficient for ethanol/water, acetone water, and propanol/water mixtures. This

values agree well with previous results obtained from the use of another procedure [1, 2] .

FIG. 1: The time evolution of the experimental total signal for acetone molar fraction x0 = 0.8. The thin yellow

line represents the best fit to the experimental data using Eq. (1)

[1] Cabrera, H., Sira, E., Rahn K. and Garcıa-Sucre, M., Appl. Phys. lett., 94, pp. 051103(1)-031106(3), 2009.

[2] Cabrera, H., , Marti-Lopez L., Sira, E., Rahn K. and Garcıa-Sucre, M., J. Chem. Phys., 131, pp. 031106(1)-

031106(3), 2009.

28

Influence of diffusion on the mushy zone evolution in a fixed

temperature gradient

G. Salloum Abou Jaoude1) 2), G. Reinhart1) 2), H. Nguyen-Thi1) 2), H. Combeau3), M. Zaloznik3),T. Schenk3), T. Lafford4)

1) Aix-Marseille Univ & 2)CNRS, IM2NP UMR 6242, Campus Saint-Jérome Case 142, 13397 Marseille Cedex 20, France3) IJL, Department SI2M, UMR CNRS 7198, Lorraine University, Ecole des Mines de Nancy, Parc de Saurupt CS 14234, F-54042 Nancy Cedex, France 4) ESRF, 6 rue Jules Horowitz, BP 220, 38048 Grenoble Cedex 9, France

A mushy zone (MZ) is a region that is formed when solidification proceeds with the development of dendrites. The MZ is the partially solid/liquid zone composed of dendritic solid networks and the remaining melt. The purpose of this work is to characterize the time-evolution of a MZ in a fixed temperature gradient, when solidification is stopped during the MZ formation. We aim to determine the key physical diffusion mechanisms that control its evolution, namely Temperature Gradient Zone Melting (TGZM), coarsening phenomena, solute diffusion in inter-dendritic liquid channels [1] and solute diffusion in the melt.

This presentation describes a series of experiments performed at BM05 at the European Synchrotron Radiation Facility (ESRF), dedicated to the analysis of a MZ evolution in a fixed temperature gradient. It has been recently shown that synchrotron X-ray radiography is a powerful technique, perfectly adapted for such a study [2]. Experiments were performed using an experimental furnace described elsewhere [2], which enables the control of the main parameters of solidification (cooling rate and temperature gradient), and allows the continuous recording of X-ray radiographs on a FReLoN CCD camera. We chose to investigate the MZ for an Al - 4 wt% Cu alloy. A good contrast was obtained due to the difference of absorption between the two elements. Thin samples (40 mm 6 mm 0.2 mm) were first directionally solidified with a power-down method. As soon as the MZ was formed in the field of view, solidification was stopped and the evolution of the MZ was analyzed.

Our results exhibit the successive evolution regimes of the MZ. In a first phase, solidification leads to the MZ formation (Fig.1a, end of solidification phase). Immediately following the solidification end, regress of the mush-liquid interface is observed, due to the dendrite tip remelting provoked by the solute diffusion in the liquid phase from the inside part of the MZ towards the top of the MZ. Concomitantly, solute migration in the MZ induces the formation of an Al-enriched solid layer at the bottom of the MZ. Fig.1b and Fig.1c show the effect of these two phenomena on the MZ morphology. After the solid-mush and mush-liquid interfaces merge the MZ disappears and the solid-liquid interface moves upward again due to the diffusion of the solute in the melt. Observations are analyzed with the help of existing models in order to characterize the main phenomena responsible for the MZ evolution. It is shown that several phenomena act simultaneously with an intensity depending on the location in the MZ.

1m

Fig.1. Radiographs of the time evolution of the mushy zone in an Al-4wt%Cu experiment

[1] Combeau, H., Appolaire, B. and Seiler, J.M., Nuc. Eng. Des., 240, pp. 1975–1985, 2010[2] Nguyen Thi, H., et al, J. of Crystal Growth, 310, pp. 2906-2914, 2008

29

DIRECTIONAL SOLIDIFICATION OF TRANSPARENT

SUBSTANCES

O. Fedorov1), V.Demchenko2), I.Shuba2)

1) Space Research Institute/ Institute/ Institute for Metal Physics,

National Academy of Sciences of Ukraine, Kyiv, Ukraine [email protected]

2) Paton Welding Institute, National Academy of Sciences of Ukraine, Kyiv, Ukraine

The aim of this work is the direct study of the solid-liquid interface evolution in bulk (3-dimensional) samples under directional solidification. The interface stability and growth pattern development are studied experimentally and using calculations of heat and mass transfer in the melt. The effect of low-frequency vibration is discussed.

Applications of transparent substances for the study of solidification is the promising experimental approach for better understanding of crystal growth dynamics due to direct data on the interface and melt flow during material production. Bridgman-type of experimental technique is used both for 3-dimensional and 2-dimensional samples of succinonitrile. The installation provides observation and recording of crystallization front and adjacent crystal regions directly during growth process through the molten zone. Optical unit consists of TV pickup camera, image focusing system and illuminators.

The morphology of crystallization front was investigated under different growth conditions and crystallographic orientations of seed crystals in cylinders and plane samples, fig1. The oscillations of mean cellular spacing and other peculiarities of non steady-state growth were noted. The comparisons of the evolution of nodes and cells, their interaction under different growth rates in bulk and plane preparations are demonstrated.

The theoretical analysis of non steady-state solidification used the following models: (i) study of heath transfer in the sample under gradient of temperature; (ii) non steady-state crystallization ofbinary alloy in no stirred melt (plane sample); (ii) determination of convective flow pattern and heath transfer under directional solidification of cylindrical sample. The influence of low-frequency vibration on convective pattern is presented.

For different growth conditions and alloy compositions the following features were identified:(i) dynamics of impurity damping near the interface; (ii) peculiarities of crystallization temperatures changes during the growth process; (iii) period of steady-state growth as the function of thermalconditions. The comparison of theory and experiment for non steady-state growth is presented.

a b

c d

Fig1. The development of non steady-state interface morphology in 3-dimensional (a,b) and 2-

dimensional (c,d) samples

30

Experimental evidence of symmetry-breaking dynamical patterns in

vibration-induced flows.

Valentina Shevtsova, Vitaliy Sechenyh, Yuri Gaponenko, Denis Melnikov, Alexander Mialdun1



We report on a new nonlinear dynamics occurring in rigid-walled container subjected to translational

vibration of non–uniformly heated fluid with Soret effect in microgravity. The results were obtained in

the frame of IVIDIL experiment on the ISS.

The theory of thermovibrational convection in single fluid in weightlessness has been developed

a few decades ago and the direct experimental proof of this type of motion was recently obtained in

short duration low gravity experiments (parabolic flight experiments)[1], [2]. The mean flow structures

previously reported in numerical studies was confirmed. The transition from four–vortex structure to the

pattern with one large vortex and two small vortices were observed in the transient state.

For a binary mixture with inhomogeneous concentration, along with vibrational fields appears an

additional dissipative mechanism caused by diffusion (and thermodiffusion). The convective flow in

binary system is controlled by vibrational parameters as well as the by properties of the mixture: the

separation ratio, ψ = C0(1− C0)STβC/βT , the Schmidt number Sc = ν/D and Lewis number Le =

D/χ; where ST is the Soret coefficient, βC and βT are the solutal and thermal expansion,D is the mass

diffusion coefficient , χ is the thermal diffusivity and ν is the kinematic viscosity.

The microgravity experiments under discussion were performed in a cubic cell filled with mixture

90% water-10% IPA with negative Soret effect which hasψ = −0.0285 , Sc = 1620 andLe = 6.7·10−3.

We present an experimental evidence of convection caused by translational vibration and breaking the

symmetric solutions due to temperature dependent physical properties of the mixture.

FIG. 1: Results of IVIDIL experiments:

(a) ∆T = 10K, f = 2Hz, A = 44mm; (Run 5) (b) ∆T = 15K, f = 2Hz, A = 48mm; (Run 19)

[1] Shevtsova V, Ryzhkov I., Melnikov D., Gaponenko Y., Mialdun A., Experimental and theoretical study of

vibration-induced thermal convection in low gravity, J. Fluid Mech., 648, 53-82 (2010).

[2] Mialdun A., Ryzhkov I., Melnikov D., Shevtsova V., Experimental evidence of thermovibrational convection

in low gravity, Phys. Rev. Lett., 2008, 101, 084501

31

Preliminary Results of the DCMIX Experiment: Measurements of

Thermodiffusion and Diffusion Coefficients in Ternary Liquid

Systems

Galand Quentin1), Stéfan Van Vaerenbergh2) and Christophe Minetti3)

1) MRC, ULB, EP - CP165/62, Dept. Chemical Physics, B1050, Brussels, Belgium, [email protected]



The first DCMIX experiment was conducted aboard the International Space Station in late 2011 and early 2012. The objective of this experiment is to obtain experimental measurement of thermodiffusion and diffusion coeffients in ternary liquid systems. Preliminary analysis of the obtained results is reported.

Multicomponent diffusion and thermal diffusion play a key role in a variety of natural systems and industrial processes, for instance to get a better understanding of the gravitational and thermal effects in hydrocarbon reservoirs.

The DCMix experiment (Diffusion Coefficients in Mixtures) has been proposed to minimize the effects of convection during measurements and so obtain reference values to calibrate ground measurement techniques. A ternary system composed of dodecane (C12) - isobutylbenzene (IBB) – tetrahydronaphtalene (THN) has been selected as it is representative of a hydrocarbon reservoir mixture.

The implemented experimental technique is based on the interferometric measurement of the variation of the composition field in a parallelipipedic liquid volume. The thermodiffusion coefficients are obtained by imposing a temperature gradient to the liquid. The temperature gradient is then removed and the molecular diffusion coefficients are determined by observing the relaxation of the composition gradient.

During the measurement campaign, around fifty experiments were performed. Six systems were investigated at two different temperatures (25°C and 35°C). The compositions of the studied systems are reported in table (Tab. 1).

SYSTEM COMPONENT MASS FRACTIONS (%) THN IBB C12

1 10 10 80 2 10 80 10 3 80 10 10 4 45 10 45 5 40 20 40 6 50 - 50

Tab.1 Composition of the DCMIX1 system (mass fractions)

The acquired experimental data were stored on hard drives and will be analyzed as soon as they are delivered to the ground. However, for each run, a few images were downloaded in order to monitor the functioning of the experiment. The analysis of this partial data already allows obtaining an estimate of the measured Soret and diffusion coefficients. The different steps of post processing are described and the values of the obtained coefficients are compared with literature data

32

Soret and molecular diffusion of ternary systems in microgravity:

evolution of the DCMIX experiments

Stefan Van Vaerenbergh1), Q. Galand1), N. Rahal1), C. Minetti1), F. Dubois1), V. Shevtsova1),A. Mialdun, 1), Ziad Saghir2) , Henri Bataller3), Marcus Dejmek4), Stefano Mazonni 5)

1) Microgravity Research Center, Université Libre de Bruxelles, CP165/62, B-1150 Bruxelles, Belgium, [email protected]

2) Ryerson University, 350 Victoria St, Toronto, ONT, M5B 2K3, Canada, [email protected] Laboratoire des Fluides Complexes et leurs Réservoirs - UMR 5150, Université de Pau et des Pays de l’Adour, BP 1155, F-64013 Pau Cedex, France, [email protected]

3) Laboratoire des Fluides Complexes et leurs Réservoirs - UMR 5150, Université de Pau et des Pays de l’Adour, BP 1155, F-64013 Pau Cedex, France, [email protected]

3) Canadian Space Agency, St-Hubert, Canada, [email protected] 4 European Space Agency, Nordwijk, The Netherlands, [email protected]

The diffusion and Soret coefficients long duration experiments can be performed in microgravity

conditions on the International Space Station. Two color interferometric technique is used and the set

up is designed to obtain the Soret and the isothermal diffusion coefficients. The mean temperature and

the temperature gradients can be adjusted in paralellipipedic cells, and modulated in time. This can

typically be used for Soret phases, followed by isothermal diffusion phase with the built composition

gradient. The set-up and its performances and limitations are now much better documented, and have

evolved with post processing developments. Evolutions of these capabilities are explained at the light

of the DSC-DCMIX experiment that was carried on the SODI facility in ISS end of 2011 beginning

2012.

The measurement of both Soret coefficients and isothermal diffusion coefficients in ternary systems molecular mixtures can be realized in experiments much like Kolodner experiments. A thermal gradient is applied to a layer, the composition gradient is build by Soret effect and once done, the thermal gradient is suppressed, thus allowing the observation of isothermal diffusion. In the DSC experiment proposed, the observation is realized with a full interferometric mapping of the refractive index field. In order to allow for the analysis of ternary molecular mixtures, two wavelengths are implemented. The way refractive indexes change with composition at the two wavelengths must be such that the ternary composition variations can be deduced from the refractive indexes changes. This usually limits the accuracy that can be obtained on the measurements in a way that depends strongly, for given optical wavelengths, on the system and the composition. However, the accuracy question is much linked also to the exceptionally high resolution of the interferometric mapping. Good results can so be obtained in most systems, and this was used first on ternary Dodecane, Tetrahydro-naphtalen, Isobutyl-benzen system. The experiment has been carried out in the Microgravity Science Glovebox of the International Space Station in the US module, from the November 2011 to January 2012. Systems have been studied at compositions selected by the DCMIX science team, and at mean temperatures of 25 and 35 °C. One run consists of a long enough Soret phase, where the thermal gradient (about 10°C) is applied, followed by a long enough phase where the mean temperature is the same, but the thermal gradient is absent. Durations are selected as large enough to allow for the process to be significantly developed. These runs are repeated to ensure the validity of the results and increase the accuracy on the claimed values of the coefficients. The set-up was so used for the first time, and its performances could be determined thanks to downloaded images. Although with the amount of data only preliminary results can be provided, we shall here detail the apparatus behavior in view of the forthcoming experiments. �

33

Tuesday afternoon session

Simulations, Janus particles


14:00 – 15:00 Bernard Rousseau (Université Paris-Sud, France) Computing Soret coefficient for real systems from molecular dynamics.

Motivations and difficulties

15:00 – 15:20 Frank Roemer (Imperial College London, London ) Alkali Halide aqueous solutions under temperature gradients: A non

equilibrium molecular dynamic study

15:20 – 15:40 Rachid Hannaoui (Université de Pau et des Pays de l’Adour, France)Molecular dynamics simulation of thermodiffusion in atomistic micro pores

15:40 – 16:20 Coffee break and POSTER WATCHING 16:20 – 16:45 Frank Cichos (Leipzig, Germany) Thermophoretic trapping and steering of Janus particles

16:45 – 17:10 Marisol Ripoll (Forschungszentrum Jülich, Germany) Simulations of thermophoretic colloids and nanoswimmers

17:10 – 17:35 Natsuhiko Yoshinaga (Tohoku University, Japan) Active Motion of Janus Particle by Self-thermophoresis

18:00 DCMIX ESA TT Session (for members)

34

Computing Soret coefficient for real systems from molecular dynamics.

Motivations and difficulties

Bernard Rousseau1

1Laboratoire de Chimie Physique, Universite Paris-Sud,

UMR 8000 CNRS, Orsay, France [email protected]

During the 1980s, many approaches based on irreversible thermodynamics and statistical mechanics

have been developed to compute the Sor et coefficient in binary mixtures using molecular dynamics

methods. The corresponding transport coefficients can be obtained either from Green–Kubo formula and

equilibrium molecular dynamics or synthetic nonequilibrium molecular dynamics. One can also mimic

a thermal diffusion experiment by modifying the conditions at the boundaries of the simulation box to

do boundary driven nonequilibrium molecular dynamics. A large amount of work has been devoted to

the validation and improvement of the different models. It appears that boundary driven nonequilibrium

molecular dynamics is the only method adapted to the study of associated mixtures, where significant

excess properties are observed.

In this contribution, I will present molecular dynamics simulation results concerning simple molec-

ular liquids, associated or not. I will put emphasis on difficulties related to quantitative predictions of

the Soret coefficient in these mixtures: methodological choices, forcefield and model limitations. I will

review the main motivations for studying molecular systems as opposed to simple Lennard-Jones fluids.

35

Alkali Halide aqueous solutions under temperature gradients:

A non equilibrium molecular dynamic study

Frank Romer1 and Fernando Bresme1

1Department of Chemistry, Imperial College London, London SW7 2AZ, UK

[email protected], [email protected]

We study the response of alkali halide aqueous solutions to a thermal gradient using non equi-

librium molecular dynamics simulations. Using an atomistic approach we examine the microscopic

mechanisms defining heat transpot and the thermal diffusion of the solution in terms of salt concen-

tration and composition, in an attempt to correlate transport with the solvation structure.

Aqueous solutions play an important role in nearly every aspect of our life. The properties and

behaviour are a focus of intense study by researchers in physics, chemistry, biology or engineering.

The response of an aqueous solution to a thermal gradient is relevant to understand heat- and mass

transport (the Ludwig-Soret effect [1, 2]) in a wide range of practical applications, e.g., in customized

refrigerant fluids for industrial processes. Lithium bromide solutions are for example often used in

simple absorption refrigeration systems which are common in large commercial plants [5]. Unfortunately

there is not yet available a full microscopic interpretation of the Ludwig-Soret effect [3]. Recent work

has also illustrated that water is not a passive solvent, and that can feature a sizable polarization as a

reponse to strong thermal gradients, which are achievable at micro and nanometer scales[6]. We have

also recently observed the possibility of orienting non polar molecular fluids with temperature gradients

and established a link with the Soret effect. Hence, a systematic study on solvent orientation effects is of

particular interest on ionic solutions given the competition between orientation and ion solvation.

To study aqueous solutions under a thermal gradient we utilized boundary driven non equilibrium

molecular dynamics (NEMD) simulations. The motion of a predefined set of water molecules located at

different regions in the simulation cell are restrained by a harmonic potential and thermalized to prede-

fined hot and cold temperatures, to induce a temperature gradient and heat flux. The water is modelled via

the rigid SPC/E model, whereas for the ions we use a combination of Lennard-Jones (LJ) and Coulombic

potential with parameters optimized to model electrolyte solutions [7, 8].

With this simulation set up we study the dependence of the Soret coefficient on concentration, thermal

gradient and the solution composition (charge, size, strength of dispersion interaction of the ions). The

contribution of the ions to the heat transport is analyzed at a microscopic level. The alignment of the

water molecules in the direction of the thermal gradient and the coupling of this thermopolarization with

the Soret effect is also analyzed.

[1] Ludwig, C., Sitzungsber. K. Preuss. Akad. Wiss., 20, pp. 539-539, 1856.

[2] Soret, C., Arch. Sci. Phys. Nat., Geneve, 3, pp. 48-61, 1879.

[3] Kincaid, J. and Hafskjold, B., Mol. Phys., 82, pp. 1099-1114, 1994.

[4] Hafskjold, B. and Ratkje, S., Entropy and Entropy Generation, Kluwer Academic, pp. 197-219, 1996.

[5] Sapali, S.N., Textbook Of Refrigeration And Air-Conditioning, PHI learning, pp. 258-260, 2009.

[6] Bresme, F., Lervik, A., Bedeaux, D. and Kjelstrup, S., Phys. Rev. Let., 101, 020602, 2008.

[7] Dang, L.X. and Garrett, B.C., J. Chem. Phys., 99, pp. 2972-2977, 1993.

[8] Smith, D.E. and Dang, L.X., J. Chem. Phys., 100, pp. 3757-3766, 1994.

36

Molecular dynamics simulation of thermodiffusion in atomistic

micro pores

Rachid Hannaoui, Guillaume Galliéro and Christian Boned

LFC-R (UMR5150 with CNRS and TOTAL), Université de Pau et des Pays de l’Adour, BP 1155, F-64013 Pau Cedex, France.

[email protected].

It is generally assumed that porous medium, through confinement and tortuosity, has a similar influence on the mass and thermal diffusion coefficients [1]. In order to test that assumption in very low permeability medium, following previous works [2, 3, 4], we have studied the mass and thermal diffusion of binary fluid mixtures confined in slit pore on a nanometer scale.

In this work, we perform a systematic study of the influence of the parameters used to describe a model slit pore on mass and thermal diffusion factor of simple binary mixtures. To represent realistically the adsorption and the fluid-solid contact, we have used a fully atomistic representation of the porous medium contrary to our previous work presented during the IMT9 [4]. Furthermore we have chosen to use a Grand-Canonical Ensemble rather than an Isothermal-Isobaric ensemble (NP//T)to compare in consistent manner results obtained for different pore width.

For this purpose, we have performed Non-Equilibrium Molecular Dynamics simulations of Lennard-Jones equimolar mixtures confined in atomistic walls of three adsorbent natures, various widths (5 to 35 times the size of a molecule) and in sub- and super-critical conditions. In previous works, it was difficult to separate the effect of the porous medium on the amplitude of thermal diffusion from an effect inducted by the selective/relative adsorption [2, 3]. So we employed “isotopic” mixtures because in such mixtures, the two components are completely equivalent in terms of thermodynamic and adsorption properties, which allows to focus on the influence on the thermodiffusion of the porous medium alone (confinement + molecular package). We also compared the values with thermal diffusion of corresponding bulk fluids.

The results indicate that, except for very narrow pore, the pore width has a negligible effect on the thermal diffusion factor, these differences remaining nearly within the error bars (down to 15%compared to bulk fluid in extreme case). However, the mass and thermal diffusion coefficients are largely influenced by the pore size and the presence of the rough solid surface (up to 60% compared to bulk fluid in extreme case) with important differences compared to what occurs in integrated smooth slit pore.

[1] Platten, J.K and Costesèque, P., Journal of Porous Media 7, 317-329, 2004.[2] Colombani, J., Galliero, G., Duguay, B., Caltagirone, J.P. and Montel, F., Bopp P.A., Philosophical

Magazine, 83, pp. 2087-2095, 2003. [3] Galliero, G., Colombani, J., Bopp, P.A., Duguay, B., Caltagirone, J.P. and Montel, F., Physica A,361, pp. 494-510, 2006. [4] Hannaoui, R., Galliéro, G., Ameur, D. and Boned, C., Chemical Physics, 389, pp. 53-57, 2011.

37

Thermophoretic trapping and steering of Janus particles.

A. Bregulla1), M. Selmke1), M. Braun1), D. Rings2), K. Kroy2) H. Yang3) and F. Cichos1)

1) Molecular Nanophotonics Group, Institute of Experimental Physics I, University Leipzig, 04103 Leipzig, GERMANY, [email protected]

2) Soft Condensed Matter Group, Institute of Theoretical Physics, University Leipzig, 04103 Leipzig, GERMANY

3) Department of Chemistry, Princeton University, Princeton, NJ 08544-2020, USA

The erratic motion of Brownian particles can be understood as a continuous interconversion of solvent thermal energy into particle kinetic energy and back, which is mediated by the viscous friction. It is expressed by a simple fluctuation dissipation relation known as the Stokes-Einstein relation. As all motion of small particles in liquids is determined by this random jittering motion, manipulation of particles on a nanoscale in liquid environments requires to beat Brownian motion.

Here we describe our efforts to manipulate Brownian motion by varying the local temperature as well as the local viscous friction around the diffusing particle. Our experiments employ gold nanoparticles and coatings as optically controlled heat sources. Spherically symmetric temperature profiles around these nanoparticles lead to enhanced diffusivity. This Hot Brownian motion is described by a new fluctuation dissipation relation [1] with effective temperatures for translational and rotational motion. Janus type particles with half spherical gold coating break the spherical symmetry of the temperature profile to cause a net directed transport of particles along the axis of the Janus particle. This directed motion is randomized by rotational Brownian motion but can be rectified with an optical feedback mechanism. This feedback mechanism allows the steering and trapping of individual Janus particles by stochastic thermophoretic activity.

�

[1] Rings, D., Schachoff, R., Selmke, M., Cichos, F. and Kroy, K., Phys. Rev. Lett. 105, pp. 090604, 2010.

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38

Simulations of thermophoretic colloids and nanoswimmers

Mingcheng Yang, Daniel Lusebrink and Marisol Ripoll1

1Theoretical Soft-Matter and Biophysics, Institute of Complex Systems,

Forschungszentrum Julich, 52425 Julich, Germany

[email protected]

The motion of a colloid induced by a temperature gradient is investigated by means of simulations.

We perform simulations a with a hybrid algorithm. The solvent is provided by the mesoscale simulation

method known as multiparticle collision dynamics (MPC) that has shown to properly include the effect of

hydrodynamic interactions in colloidal and polymeric systems, and to be able of sustaining temperature

inhomogeneities [1]. Colloidal interactions are considered with standard molecular dynamics (MD)

such that the effect of varying colloid-solvent interactions can be straightforwardly investigated [2].

The variation of the solvent colloid interaction from attractive to purely repulsive interestingly results

to change from a thermophobic to a thermophilic behavior. The thermophoretic force induced in the

colloid by the temperature gradient, results not only on a directed drift on the particle but also in a fluid

flow around the particle [3, 4] that we can also quantify in our simulations.

Recent experiments with a Janus particle have shown to display self-propelled motion due to ther-

mophoresis [5]. With a defocused laser, a half-metal coated colloidal sphere is heated. The higher heat

absorption of the metal side produces a temperature gradient on the non-metal side, what translates into

a self-propelled motion. We perform computer simulations [6] of two strongly bonded monomers which

are immersed in a hydrodynamic solvent. The heated bead, can have a temperature higher than the

surrounding fluid. If the average temperature of the system is kept constant, the surrounding solvent

will sustain a steady temperature gradient with radial symmetry. The non-heated bead can generate a

thrust due to thermophoresis, what will translate into a directed motion of the nanodimer along the bond

direction. In case the non-heated bead is thermophilic, it will tend to go to higher temperatures, and

the nanodimer will behave as a pusher. Reciprocally, in case the non-heated bead is thermophobic, the

nanodimer will behave as a puller.

[1] Lusebrink D. and Ripoll M. J. Chem. Phys. (In press) (2012)

[2] Lusebrink D., Yang M. and Ripoll M. J. Phys.: Cond. Matt. (submitted) (2012)

[3] Weinert F. M. and Braun D. Phys. Rev. Lett. 101, 168301 (2008)

[4] Leonardo R. D. and Ianni F. and Ruocco G. Langmuir 25, 4247 (2009)

[5] Jiang H. R., Yoshinaga N. and Sano M. Phys. Rev. Lett. 105, 268302 (2010)

[6] Yang M. and Ripoll M. Phys. Rev. E 84, 061401 (2011)

39

Active Motion of Janus Particle by Self-thermophoresis

Natsuhiko Yoshinaga,1, 2 Hong-Ren Jiang,3 and Masaki Sano4

1WPI Advanced Institute for Materials Research (WPI-AIMR),

Tohoku University, Japan [email protected] Institute, Tohoku University, Japan

3Institute Applied Mechanics, National Taiwan University, Taiwan [email protected] of Physics, the University of Tokyo [email protected]

Spontaneous motion or self-propulsion has been attracting attention in recent decades because of its

potential application to biological problems such as cell motility. These intensive studies have stemmed

from the fact that mechanical properties of cells can be measured thanks to recent developments in

visualization techniques. In addition, several model experiments showing spontaneous motion have been

carried out. These systems consisted of relatively simple components such as oil droplets in the water.

Nevertheless, the droplets give the impression of being alive in that they move spontaneously without

being pushed or pulled.

Here we consider active motion of Janus particle [1], whose surface is half coated by a different

material (Fig. 1 (A)). The asymmetric temperature distribution is realized by laser shinning on the

particle (Fig. 1 (B) and (C)). The particle is propelled by the asymmetric distribution that is a local

temperature gradient leading to thermophoresis [2]. The motion of this self-thermophoresis is fluctuating

and similar to the Brownian motion (Fig.1 (D)) due to rotational diffusion, but the diffusion constant is

enhanced by the propulsion.

We will also show the self-propulsion of a small droplet where in contrast to solid particle, there is

no a priori asymmetry in the system. In this case, the droplet exhibits transition between stationary and

moving states [3, 4].

(A)(C)

(D)

(B)

FIG. 1: (A) Janus particle of a silica beads half coated by gold. (B) The Janus particle in a defocused laser. (C)

Temperature distribution around the particle. (D) Trajectory of the Janus particle under laser radiation.

[1] Jiang, H.-R., Yoshinaga, N. and Sano, M., Phys. Rev. Lett., 105, 268302, 2010.

[2] Jiang, H.-R., Wada, H., Yoshinaga, N. and Sano, M., Phys. Rev. Lett., 102, 208301, 2009.

[3] Yabunaka, S., Ohta, T. and Yoshinaga, N., J. Chem. Phys., 136, 074904, 2012.

[4] Yoshinaga, N., Nagai, K. H., Sumino, Y. and Kitahata, H. (submitted).

40

Wednesday, June 6th



Chair: Tatyana Lyubimova

9:00 – 10:00 Alexander Nepomnyashchy (Haifa, Israel) Onset of Marangoni Convection in Binary Solutions

10:00 – 10:20 Denis Melnikov (Université Libre de Bruxelles, Belgium) DNS of Soret driven diffusion in a three-dimensional rectangular domain

10:20 – 10:40 Isabel Mercader (Universitat Politecnica de Catalunya, Barcelona, Spain) Convectons and drifting convectons in binary mixtures

10:40 – 11:00 Coffee break 11:00 – 11:20 Boris L. Smorodin (ICMM, Perm, Russia) Binary mixture convection under high-frequency vertical vibration

11:20 – 11:40 Tatyana Lyubimova (ICMM, Perm, Russia) Vibration influence on instability of binary fluid with negative Soret effect in

square cavity heated from above

11:40 – 12:00 Marie Catherine Charrier-Mojtabi (University of Toulouse, France)Action of acoustic streaming on species separation in a binary mixture:

analytical and stability analysis

12:00 – 12:20 Xavier Ruiz (Universitat Rovira i Virgili, Tarragon, Spain ) On the accuracy of the interdiffusion coefficient measurements of high

temperature binary mixtures under ISS real conditions

12:20– 12:40 Tatyana Lyubimova (ICMM, Perm, Russia) Vibration effect on a stability of convective flows of multicomponent mixtures

in vertical layer

12:40 – 21:00 Sandwich Lunch

Buses to Visit “La Brasserie Cantillon” http://www.cantillon.be/Dinner at Royal Museums of Art and History, 18:00-21:00 http://en.wikipedia.org/wiki/Royal_Museums_of_Art_and_History

41

Onset of Marangoni Convection in Binary Solutions

Alexander Nepomnyashchy,1 Sergey Shklyaev,2 and Alex Oron3

1Department of Mathematics, Technion - Israel Institute of Technology,

Haifa 32000, Israel [email protected] of Chemical Engineering, University of Puerto Rico - Mayaguez,

Mayaguez, PR 00681, USA [email protected] of Mechanical Engineering, Technion - Israel Institute of Technology,

Haifa 32000, Israel [email protected]

Spontaneous pattern formation is a striking but ubiquitous phenomenon. A paradigmatic example of

the pattern formation is the Benard convection in a liquid layer with a free surface heated from below.

The origin of hexagonal patterns first observed by Benard is a short-wave monotonic instability of the

mechanical equilibrium caused by the thermocapillary effect and buoyancy. The former effect prevails

under microgravity conditions and in thin layers which are especially important in modern microfluidic

technologies.

In the case where the heated liquid is a binary solution which is subject to the Soret effect, the

solutocapillary effect is activated. Due to the interaction of different kinds of the Marangoni effect, both

monotonic and oscillatory instabilities are possible. Also, longwave instabilities are possible when the

boundaries of the layer are poorly conducting or under microgravity conditions, when the deformations

of the free surface are not suppressed by gravity. While the pattern formation by monotonic short-wave

instabilities is a well studied subject, the cases of oscillatory and longwave instabilities are still less

explored.

The present talk is a review of recent developments on the onset of the nonlinear Marangoni convec-

tion in binary solutions, for any kinds of instabilities. While a monotonic instability creates typically

hexagonal patterns, the selection of wavy patterns generated by an oscillatory instability is a much more

intricate problem. Because of some specific features of the Boussinesq convection problem, generic pre-

dictions of the bifurcation theory are not fully applicable in the problem under consideration. We show

that a superposition of standing waves oscillating with a phase shift (alternating rolls) is selected on a

square lattice in the Fourier space. On a hexagonal lattice, the analysis needs the construction of fifth-

order amplitude equations. Under certain conditions, transitions between patterns are predicted which

correspond to a heteroclinic cycle. The theory is extended to the case where solute is a soluble surfac-

tant, which is present in both bulk and surface phases. The deformational Marangoni instability is also

discussed.

42

DNS of Soret driven diffusion in a three-dimensional rectangular domain

Denis Melnikov,1 Aliaksandr Mialdun,2 and Valentina Shevtsova3

1MRC, ULB, CP165/62, Dept. Chemical Physics,

B-1050, Brussels, Belgium [email protected], ULB, CP165/62, Dept. Chemical Physics,

B-1050, Brussels, Belgium [email protected], ULB, CP165/62, Dept. Chemical Physics,

B-1050, Brussels, Belgium [email protected]

In attempt to explain experimental observations, we perform three-dimensional numerical modeling

of Soret driven convection in a rectangular cell filled with a binary mixture with negative thermodiffu-

sion coefficient. The system is heated from above by imposing a constant temperature gradient. We

work under normal gravity conditions, which is a thermally stable RayleighBenard configuration. The

concentration and temperature fields are strongly coupled by the Soret effect that causes concentration

gradients in response to the applied temperature difference. Due to the negative Soret effect, the heavier

liquid is slowly accumulated on the top of the lighter one. It was shown that this unstable stratification

may result in an instability and the bulk flow is initiated [1]. The value of the critical Rayleigh number

Racr, at which motion starts, has been found very small (it is equal to only 27).

FIG. 1: Snapshots of the isoconcentration surface. Left: Ra = 8700; Right: Ra = 10800.

We analyze the transient behavior of the velocity, temperature and concentration fields. It was ob-

served that the flow in a cubic cell has a finger structure with the mass flux being the strongest near the

center line, (see Fig. 1). This columnar structure diffuses with time in the horizontal direction. The de-

velopment of the motion is shown through the evolution of three-dimensional flow patterns. The upward

or downward direction of the flow along the center line depends on the imposed temperature difference

[1].

[1] Melnikov, D., Mialdun, A. and Shevtsova, V., J. Non-Equilib. Thermodyn., 32, pp. 259-270, 2007.

43

Convectons and drifting convectons in binary mixtures

Isabel Mercader,1 Oriol Batiste,2 Arantxa Alonso,3 and Edgar Knobloch4

1Dep. Fısica Aplicada, Universitat Politecnica de Catalunya,

Barcelona, Spain. [email protected]. Fısica Aplicada, Univ. Politecnica de Catalunya, Barcelona, Spain. [email protected]

3Dep. Fısica Aplicada, Univ. Politecnica de Catalunya,

Barcelona, Spain. [email protected]. of Physics, University of California,

Berkeley, USA [email protected]

The onset of convection in a binary mixture with negative separation ratio heated from below takes

place via a subcritical Hopf bifurcation that leads to a rich dynamical behaviour near the threshold.

However, it is the presence of a strongly subcritical steady bifurcation of the conduction state beyond

the Hopf bifurcation which favors the presence of strongly nonlinear spatially localized states called

convectons. With midplane reflection symmetry convectons of odd and even parity lie on a pair of

intertwined branches [1, 2] that form the backbone of the snakes-and-ladders structure of the so-called

pinning region. These branches are connected by branches of asymmetric localized states that drift.

When the midplane reflection symmetry is broken, the odd parity convectons will necessarily drift (see

Fig. 1), greatly modifying the snakes-and-ladders structure of the pinning region. The resulting speed

depends on the magnitude of the symmetry-breaking and the convecton length. Head-on and follow-

on collisions between odd parity drifting convectons of different lengths are described and the results

compared with corresponding dynamics in a Swift-Hohenberg model studied in [3].

θ

σ= 7 τ= 0.01 S=−0.05 R=1768 Γ=14

C

0 140

600

x

tim

e

σ=7 τ=0.01 S=−0.05 Ra=1768 Γ=14

FIG. 1: An example of drifting convecton when the midplane reflection symmetry is broken. Left: Snapshot of the

temperature fluctuation θ and the corresponding concentration of the heavier component C . Right: An x-t plot of

the time evolution of the temperature fluctuation at mid-height.

[1] Batiste O., Knobloch E., Alonso A., Mercader I., J. Fluid Mech., 560, pp. 456-478, 2006.

[2] Mercader I., Batiste O., Alonso A., Knobloch E., J. Fluid Mech., 667, pp. 586-606, 2011.

[3] Houghton S.M. and Knobloch E., Physical Review E, 84, pp. 016204 1–10, 2011.

44

Binary mixture convection

under high-frequency vertical vibration

Bela I. Myznikova

1) and Boris L. Smorodin

2)

1) Institute for continuum mechanics, Urals branch of Russian Academy of Sciences, 1 Academician

Korolyov str., 614013 Perm, Russia

2) Perm State University, Physics of Phase Transitions Department, 15, Bukirev str., 614990, Perm,

Russia, [email protected]

he convective flow conditioned by the vibration, exists even in the weightlessness [1, 2]. In this

case the convective instability of the rest state is caused by the fluid stratification,, and its threshold as

well as nonlinear dynamic regimes are specified by the nondimensional vibration parameter

Gs ( ) / (2 )b h , which is also referred to as the Gershuni number [2] (here stands for

the thermal expansion, – the angular frequency, b – the amplitude of vibrations, and – the

kinematic viscosity and thermal diffusivity respectively, – the applied temperature difference, –

the length scale).

h

Vibrations provide the possibilities for managing the preferred mode of heat and

mass transfer, or destabilizing an undesirable convective regime [3].

The spatiotemporal evolution of steady and oscillatory convective roll patterns in the plane

horizontal layer subjected to the steady gravity and high-frequency vertical vibrations has been

investigated numerically through the use of laterally periodic convective cell with rigid, impermeable

horizontal boundaries,. Simulations have been performed for the parameter set adapted to laboratory

experiments with the ethanol-water mixture of negative Soret coupling between the temperature and

concentration fields. The following values were used: the Lewis number , the Prandtl

number , and the separation ratio

Le 0.01

Pr 10 0.25 .

The nonlinear dynamics of convective structures demonstrates different stable regimes, among

which are the weak- and strong-nonlinear traveling waves, amplitude- and phase-modulated traveling

waves, and steady convection. The characteristics of these patterns are found depending on the heat

intensity. To describe the spatiotemporal changes in the different oscillatory scenarios the Fourier

spectra of temporal oscillations and sideview fields of model variables have been studied. The

bifurcation map is plotted. The regions of the convective pattern occurrence are represented on the

plane “the Rayleigh number – the Gershuni number”.

[1] Gershuni, G.Z., Lyubimov, D.V. Thermal Vibrational Convection. Jonh Wiley & Sons. 1997.

[2] Mialdun, A., Ryzhkov, I.I., Melnikov, D.E., and Shevtsova, V. PRL, 101, 184501, 2008.

[3] Gershuni, G.Z., Kolesnikov, . ., Legros, J.C., and Myznikova, B.I. Int. J. Heat Mass Transfer, 42,

p. 547-553, 1999.

45

Vibration influence on instability of binary fluid with negative

Soret effect in square cavity heated from above

Tatyana Lyubimova1), Valentina Shevtsova2), Nadezhda Zubova1) and Denis Melnikov2)

1) Institute of Continuous Media Mechanics UB RAS, 614013, Perm, Russia, [email protected]


The paper deals with the investigation of vibration influence on instability of binary fluid with negative Soret effect heated from above. We consider square cavity completely filled with the viscous incompressible binary fluid, subjected to the gravity field and horizontal vibrations. The no slip and zero mass flux conditions are imposed at the boundaries. The horizontal boundaries are maintained at constant different temperatures and vertical boundaries are adiabatic.

The problem is solved numerically, by finite difference method, in terms of stream function and vorticity. The study is performed using both averaged equations of vibrational convection [1] and full non-averaged equations. The calculations are carried out for binary fluid water-isopropanol with 90% of water and 10% of isopropanol. The physical parameters of fluid and geometrical parameters conrrespond to [2].

Non-stationary problem on heat and mass transfer is studied. Initial conditions correspond to the uniform distribution of concentration of the components. The temperature of fluid initially is the same all over the volume, then the temperature of upper boundary is suddenly increased. As the result, the thermal wave propagates from this boundary and linear temperature distribution in vertical direction which corresponds to the heating from above is established in short time (in characteristic thermal time scale). Since the Soret effect for the binary fluid under consideration is negative, this leads to the raising up of heavy component and to the development of instability accompanied by sharp increase of the flow intensity and sharp lowering of difference in concentrations at hot and could walls. Such a behaviour was found for the cubic cavity filled with the binary mixture and heated from above, in the absence of vibrations in [3]. The results obtained in the present paper in the case when vibrations are absent are similar to [3]. The isolines of concentration obtained at different values of gravitational Grasgof number Gr (different gravity levels) show the “front distortion” and the development of fingers. With the decrease of Gr the time-interval from the beginning of the process to the “front distortion” and the wave length of perturbations which corresponds to the distance between the fingers increases.

The calculations in the presence of vibrations are performed for different gravity levels and different values of the vibrational Grasgof number Grv. Numerical data on temporal evolution of local characteristics and stream-function and concentration fields at different Gr and Grv, as well as the dependencies of time-interval from the beginning of the process to the “front distortion” on Gr and Grv are obtained.

The work was made under financial support of the Government of Perm Region (Contract number C-26/212).

[1] Gershuni G.Z., Lyubimov D.V. Thermal Vibrational Convection. Wiley: N.Y. et al., 1998. [2] Shevtsova V., Melnikov D., Legros J.-C., Yan Y., Saghir Z., Lyubimova T., Sedelnikov G., Roux B.

Phys. Fluids, 19, 017111, 2007. [3] Shevtsova, V.M., Melnikov D.E. and Legros J.C., Physical Review E, 73, 047302, 2006.

46

Action of acoustic streaming on species separation in a binary

mixture: analytical and stability analysis.

Marie Catherine Charrier-Mojtabi, Abdelkader Mojtabi

2 and Pierre Costeseque

2

1University of Toulouse, Laboratory PHASE, EA 3028,118 route de Narbonne, 31062 Toulouse Cedex 9 France.

2 IMFT, UMR CNRS/INP/UPS N°5502, University of Toulouse, 118 route de Narbonne, 31062, Toulouse cedex,

France

E-mail: [email protected]

Acoustic streaming describes a steady flow generated by an ultrasound wave propagating in a fluid.

The ultrasound waves at high frequency are shown to allow a reduction of convection and also to

affect the stability of the buoyant convection [1]. The coupling of convection and thermodiffusion

leads to species separation independently of the gravity direction [2].

The purpose of the present work is to study the influence of acoustic streaming on the species

separation which appears in a heated binary fluid layer either in weightlessness or in the gravity field.

A rectangular cavity (height H and length L with L>>H ) filled with an incompressible Newtonian

binary fluid is considered. The two impermeable horizontal walls are kept at different and constant

temperatures. A constant radiation pressure is generated in the x direction by an ultrasonic beam of

dimensionless width =Hb/H placed on the upper part of the wall x=0. (Fig. 1). The dimensionless

parameters which appear in this problem are the follows: the acoustic parameter, A, defined as: 232HVA a where is the spatial attenuation coefficient for ultrasound, Va the amplitude of the

acoustic velocity oscillation and the binary fluid cinematic viscosity, the normalized width, , the

Lewis number, Le, the Prandtl number, Pr, in microgravity. If we consider the action of the gravity

field, two other dimensionless parameters appear: the Rayleigh number, Ra, and the separation ratio, .

In microgravity (i.e. Ra=0) and in the presence of gravity, a closed form analytical solution is

obtained using the parallel flow assumption. Then the separation S, defined as the difference in mass

fraction of the denser component between the two ends of the cell (x=B and x=0) is studied. An

analytical relation S=mB function of A, Le, Pr, and Ra is given. The optimal separation S is obtained

for =1/2. A linear stability analysis of the monocellular flow is performed using both the Galerkin

method until the order N=12, and a finite element method for the determination of the critical

parameters corresponding to either stationary or Hopf bifurcation. The non linear regime of stationary

and oscillatory convection is investigated numerically. The critical parameters (Rac, Ac, wc ) obtained

are smaller than the one (Raopt, Aopt) leading to optimal separation. This work highlights the possibility

of increasing significantly the species separation for an optimal value of the beam width.

Z=H

X=0

absorbent wall

T=T1

Z

X

Binary fluid

T=T2

Hb : acoustic beam

Z=0

X=L

[1] Dridi W., Henry D. and Ben Hadid H. Physical Review E81.056309, 2010.

[2] Elhajjar B., Mojtabi A., Costeseque P.and M.C. Charrier-Mojtabi, IJHMT, Vol.53,pp4844-4851,

2010.

47

ON THE ACCURACY OF THE INTERDIFFUSION COEFFICIENT MEASUREMENTS OF HIGH TEMPERATURE BINARY MIXTURES UNDER ISS REAL CONDITIONS

N. Saez1, S. Cito1, X. Ruiz1,2, J. Pallarés3, V. Shevtsova4

(1) Dept. Química Física i Inorgànica, Universitat Rovira i Virgili, Tarragona. Spain. (2) The Institut of Cosmos Sciences, University of Barcelona. Barcelona. Spain. (3) Mechanical Engineering Department.Universitat Rovira i Virgili. Tarragona, Spain.(4) MRC, ULB, EP - CP165/62, Dept. Chemical Physics, B1050, Brussels, Belgium.

A real accelerometric signal from the IVIDIL experiment (Columbus module, ISS) [1]

has exhaustively been studied using digital signal analysis techniques. Firstly, the analysis

involved the determination of some basic statistical properties as the histogram of amplitudes,

the cross / auto correlations between the three different cartesian components and the power

spectra. After that, using higher order statistical analysis techniques we address another

interesting question, the Gaussian nature of the time series. Finally, analyzing the variations of

the power spectrum as a function of the window size, we also study the existence of random

components, equivalently noise, during the period of observation of the signal [2].

In parallel, a 3D shear cell computational model has been adjusted using the results

obtained from the above-mentioned analysis. Following recently published techniques [3] a

scalar percentage indicator %D(tend) has been used to quantify the degree of accuracy of the

measurements in the case of high temperature binary mixtures involving semiconductors as, for

instance, photovoltaic silicon or liquid metal alloys as, in particular, aluminum alloys.

Preliminary solutal results indicate that, in both mixtures, the interdiffusion

configuration is practically insensitive to the environmental conditions. But, this configuration

gives the highest quantitative value of the indicator if compared with the so-called centered or

lateral thick layer ones. All these results agree well with recently reported conclusions using a

simpler two-dimensional computational model [4].

______________________________________

[1] V. Shevtsova, IVIDIL accelerometric data, 2012.

[2] J. Ross Thomson, J. Casademunt, F. Drolet, J. Viñals, Coarsening of soli-liquid mixtures in a random

acceleration field, Phys. Fluids, 9 (1997) 1336- 1343.

[3] X. Ruiz, J. Pallarés, F.X. Grau, On the accuracy of the interdiffusion measurements at low and moderate solutal

Rayleigh numbers. Some computational considerations, International Journal of Heat and Mass Transfer, 53 (2010)3708-3720.

[4] X. Ruiz, J. Pallarés, On the accuracy of the diffusion coefficient measurements using different initial shear cell

configurations at low and moderate Rayleigh numbers. Some computational considerations, International Journal of Heat and Mass Transfer, 2012 (Submitted).

48

Vibration effect on a stability of convective flows of

multicomponent mixtures in vertical layer

Tatyana Lyubimova1), Dmitriy Lyubimov2) and Nikolay Lobov2)


2) Perm State University, 614990, Perm, Russia, [email protected]

Stability of convective flows of multicomponent mixtures in vertical layer subjected to the high frequency vibrations in the direction perpendicular to the layer boundaries is studied taking into account thermodiffusion effect. The layer boundaries are maintained at constant different temperatures. Zero mass flux through the boundaries is assumed. The problem under consideration has stationary solution which corresponds to plane-parallel flow in vertical direction with cubic velocity profile and linear temperature and concentration profiles. Investigation of linear stability of this flow leads to the spectral boundary-value problem which is solved numerically by differential sweep method. In limit case of zero separation ratio ε the problem is reduced to the problem on stability of the convective flow of single-component fluid in vertical layer subjected to high frequency vibrations [1]. In the other limit case of zero vibrational Grasgof number the problem on a stability of convective flow of multicomponent mixture in the absence of vibrations is obtained. For the case of binary mixture this problem was studied in [2]. We extent the results [2] by analyzing thermodiffusion effect on Prandtl number range where growing traveling perturbations exist. It is known that in the case of single-component fluid growing waves exist at any Prandtl number value larger than Pr* = 11.562. Thermodiffusion leads to the extension of Prandtl number range where growing traveling waves exist. Our calculations for positive Soret effect at Schimdt number equal to 676.6 show that with the growth of the separation factor the boundary of the domain of growing traveling wave existence is shifted to lower Prandtl number values, at ε = 0.263 additional domain of wavy instability appears at low Prandtl number values and at ε = 0.278 two wavy instability domains merge such that at even larger values of ε the wavy instability exists at any values of Prandtl number.

Investigation of high frequency vibration effect on the development of wave perturbations show that vibrations do not change the threshold value of Prandtl number. Stability of flow to traveling perturbations in the presence of vibrations is higher, and besides, in the case of strong vibrations quantitative characteristics approach asymptotic dependencies. It is also found that high frequency vibrations results in the “widening” of neutral curves which makes the perturbations with substantially different wave numbers to be nearly equally dangerous.

For the case of ternary mixture, stability of steady flow in plane vertical layer in the absence of vibrations was studied in [3] under long-wave approximation. It is found that there exist two long-wave instability modes: monotonous and oscillatory. Analysis shows that the high frequency transversal vibrations do not influence long-wave instability. In the present paper the influence of such vibrations on a stability of the convective flow of ternary mixture to the perturbations with finite wave-length is studied. The maps of stability to perturbations of different types are obtained.

The work was made under financial support of the Government of Perm Region (Contract C-26/212).

[1] Gershuni G.Z., Zhukhovitskii E.M., Sorokin L.E., Applied Mathematics and Mechanics, 46, 1, pp.66-71, 1982.

[2] Gershuni G.Z., Zhukhovitsky E.M. and Nepomnyashchy A.A., Stability of Convective Flows. Moscow, Nauka, 1989.

[3] Ryzhkov I.I. and Shevtsova V.M. Physics of Fluids, 21, 014102, 2009.

49

Thursday, June 7th


Morning session: Convection (mutlicomponent, ferrofluids)

Session Chair: Boris Smorodin9:30 – 10:30 Alois Würger (LOMA, France) Is Soret an equilibrium effect?

10:30 – 10:50 Ilya I. Ryzhkov (Siberian Branch RAS, Krasnoyarsk, Russia) Rayleigh-Benard instability in multicomponent fluids with the Soret effect

10:50 – 11:20 Coffee break and Poster watching 11:20 – 11:40 Dmitry Zablotsky (Institute of Physics, Latvia) Convective stability of photoinduced microstructures in ferrofluid layers

11:40 – 12:00 Lisa Sprenger (Institute of Fluid Mechanics, TU Dresden) Thermodiffusion in Ferrofluids regarding Thermomagnetic Convection

12:00 – 12:20 Miren Larrañaga (Mondragon Unibertsitatea, Spain) Thermodiffusion Coefficient in Toluene-normal Alkane Binary Mixtures

12:20 – 12:40 Odalys Sanchez (Universitat Politecnica de Catalunya, Barcelona, Spain) Secondary Flows in a Laterally Heated Horizontal Cylinder

12:40 – 14:00 Lunch

50

Is Soret equilibrium an equilibrium effect?

Alois Wurger 1

1LOMA, Universite de Bordeaux, France

[email protected]

Recent thermophoretic experiments on colloidal suspensions revived an old debate, namely whether

the Soret effect is properly described by thermostatics, or necessarily requires non-equilibrium thermo-

dynamics. Based on colloidal transport theory and entropy production, we discuss this question in view

of experiments on salt ions, colloidal macroions, polymers, and small molecules.

In the second part of the talk we show that thermophoresis of charged colloids is to a large extent

due to the Seebeck effect of the electrolyte solution. Piazza’s recent experiments on SDS micelles are

discussed in terms of ion-specific effects and the resulting Hofmeister series.

Finally we point out how the electrolyte Seebeck effect can be used for thermocharging of hot col-

loidal particles.

51

Rayleigh-Benard instability in multicomponent

fluids with the Soret effect

Ilya I. Ryzhkov

Institute of Computational Modelling SB RAS, 660036 Krasnoyarsk, Russia

[email protected]

Presently, multicomponent mixtures are widely investigated [1–4] due to the fact that many

liquids and gases used in applications are mixtures of various substances. The prediction of mass

transfer processes in such fluids greatly relies on the knowledge of transport properties. One of the

most established and frequently used configurations for measurement of diffusion and thermal

diffusion coefficients is represented by a horizontal layer, which is heated either from above or below

[5]. The main requirement in this method is a purely diffusive heat and mass transfer in the sample

mixture (i.e. a stable mechanical equilibrium state). In this respect, the stability analysis of equilibrium

state in a plane multicomponent fluid layer is an actual and important problem.

In this work, we consider the stability of a multicomponent fluid layer heated from above or

below in gravity field. The cross-diffusion and Soret effect are taken into account. In the basic state,

the motion is absent and temperature gradient induces compositional gradients due to the Soret effect.

The problem is a generalization of a classical Rayleigh-Benard problem for a single-component fluid.

The use of special transformations [4] allowed us to reduce the stability problem to that without cross-

diffusion. Several types of boundary conditions have been considered: 1) free, permeable boundaries

2) rigid, permeable boundaries 3) rigid, impermeable boundaries. The case of permeable boundaries

corresponds to constant values of concentration at the boundaries, while in the case of impermeable

boundaries the mass flux through them is zero. The theorems, which generalize the ‘exchange of

stability’ principle to multicomponent fluids, are proved for boundary conditions of type 1 and 2.

These results allow one to estimate the stability domains in the parameter space. An explicit formula

for critical Rayleigh numbers is obtained for boundary conditions of type 1. The stability problem for

boundary conditions of type 3 has been solved numerically for a ternary mixture. The neutral curves

and stability maps are constructed in a wide range of physical parameters. A comparison between

results for different types of boundary conditions is made.

The work is supported by the Russian Federation for Basic Research Grant 11-01-00283- .

Temperature

field

Concentration

field

(component 1)

Concentration

field

(component 2)

Fig.1 The structure of oscillatory critical perturbations in a ternary mixture heated from below. The

two principle components are lighter ones. They segregate to the cold side (negative Soret effect).



[3] Ryzhkov I.I. and Shevtsova V.M. Physical Review E, 79, 026308, 2009.

[4] Ryzhkov I.I. and Shevtsova V.M. Microgravity Science and Technology, 21, p. 37–40, 2009.

[5] Platten J.K. Journal of Applied Mechanics, 73 (5), P. 5–15, 2006.

52

Convective stability of photoinduced microstructures in ferrofluid

layers

Dmitry Zablotsky1), Ansis Mezulis1) and Elmars Blums1)

1) Institute of Physics of University of Latvia, 32 Miera str., LV-2169 Salaspils, Latvia

The microeffects concerning the transfer of heat and colloidal particles attract the scientific attention by their cooperative nature. Ferrofluids are colloidal suspensions of magnetic nanoparticles and as such they possess superparamagnetic properties and an additional control parameter - the magnetic field.

We will consider a periodic concentration grating induced in a thin layer of ferrofluid by interfering laser beams ([1, 2]) under the action of externally applied uniform magnetic field. The application of the external field causes the appearance of the internal demagnetizing field within the layer and the magnetic forces due to the nonuniform distribution of concentration owing to the absorption of the incident radiation and the strong Soret effect characteristic for colloidal solutions. The induced magnetic forces enhance the diffusivity of the ferroparticles along the direction of external field due to the magnetophoretic contributions to the concentration flux and cause the appearance of the parasitic microconvection within the layer ([3]).

(a) Problem setup (b) Experiment

Fig.1: (a) Concentration maxima of the optically induced concentration grating within the ferrofluid layer under the action of the applied uniform magnetic field. The transversal convective currents are incited by the magnetic forces, (b) Holographic image of the optically induced concentration grating

We describe a stationary system of periodic convective rolls emerging within the photoinducedconcentration grating under the external field. The parasitic microconvection attempts to either suppress or enhance the induced grating depending on the orientation of the magnetic field. Wedetermine the critical parameters of the instability of the primary system of convective rolls in the first approximation via a combined crossroll-square type perturbation. The critical period of the lateral perturbation is approximately twice as large as the period of the primary grating. These results correlate well with the experimental observations by direct visualization of the grating.

As the mean diameter of ferroparticles is 20…50 times smaller than exciting wavelength, theexperiments with the grating are Forced Rayleigh scattering (FRS) type. We induce 1D sinusoidalpattern by interference of two green Nd:YAG laser beams. Used for reading a low power He-Ne red laser beam represents the holographic amplitude-phase image of the grating.

This work is supported by ERDF, Project 2DP/2/1/1/1/0/10/APIA/VIAA/007 and the European Social Fund within the project Support for Doctoral Studies at University of Latvia.

[1] J. C. Bacri, A. Cebers, A. Bourdon, G. Demouchy, B. M. Heegaard, B. Kashevsky, and R.Perzynski, Phys. Rev. E, 52, pp. 3936-3942, 1995. [2] J. Lenglet, A. Bourdon, J.-C. Bacri, G. Demouchy, Phys. Rev. E, 65, pp. 3936-3942, 2002.[3] D. Zablotsky, E. Blums, Phys. Rev. E, 84, 2011.

53

Thermodiffusion in Ferrofluids regarding Thermomagnetic Convection

Lisa Sprenger, Adrian Lange, and Stefan OdenbachInstitute of Fluid Mechanics, Chair of Magnetofluiddynamics, TU Dresden,

01062 Dresden Germany [email protected]

Thermodiffusion in ferrofluids, a binary system of magnetic nanoparticles dispersed in a carrier

liquid, can be magnetically influenced in the way that the direction of the separation is changed in

the presence of high magnetic fields. A magnetic field dependent Soret coefficient is numerically

obtained by solving the diffusion equation compiled by the ferrofluid-dynamics theory (FFD). This

Soret coefficient is then used to investigate the onset of thermomagnetic convection.

Thermomagnetic convection denotes a transport phenomenon in ferrofluids due to a temperature gra-

dient and a magnetic field. Convection sets in when a critical Rayleigh number is reached. This process

could be influenced by thermodiffusion which itself is magnetic field dependent. Recent experimental

results [1] motivated further investigations of the mutual influence of the two processes. Thermodiffusion

is characterised by a rather general partial differential equation of the FFD [2] describing the diffusion

driven by gradients of the concentration, temperature, and magnetic field.

To solve this diffusion equation a solver code was developed using the finite differences method. Experi-

ments to validate the numerics are carried out with a horizontal layer of fluid subjected to a perpendicular

temperature gradient with a cell design based on [3]. The separation process of the fluid is detected by

two fluid reservoirs whose changes in concentration are determined by sensor coils.

The figures below show on the left hand side the behavior of the magnetic Soret coefficient as calcu-

lated numerically and on the right hand side experimentally and numerically obtained scaled separation

curves.

FIG. 1: a) run of the magnetic Soret coefficient for a magnetic field parallel/perpendicular to the temperature

gradient; b) separation rates: grad(T)=1 K/mm; ”calc.”=calculated, ”exp.”=experimental

The numerical determination of the magnetic field dependent Soret coefficient in ferrofluids show a

change in the direction of the separation process starting with a positive Soret coefficient for small mag-

netic fields changing to a negative one in a high field regime. This is the basis for a linear stability

analysis of the convection problem suggesting a hinderance of the onset of convection.

[1] Engler, H., Parametric Modulation of the thermomagnetic Convection in Ferrofluids (in German), PhD Thesis,

2010.

[2] Lange, A., Phys Rev. E, 70, 046308, 2004.

[3] Voelker, T., Odenbach, S., Phys. Fluids, 17, 037104, 2005.

54

Thermodiffusion Coefficient in Toluene-normal Alkane Binary

Mixtures

Miren Larrañaga1), M. Mounir Bou-Ali1), Estela Lapeira1), Carlos J. Santamaría2), Joseba A. Madariaga2) and Jean K. Platten1)

1) MGEP Mondragon Goi Eskola Politeknikoa, Mechanical and Industrial Manufacturing Department, Loramendi 4 Apdo. 23, 20500 Mondragon, Spain, [email protected] .

2) Department of Applied Physics II, University of Basque Country, Apdo. 644, 48080 Bilbao, Spain

A temperature gradient within a liquid mixture causes a transport of matter known as thermal diffusion. This phenomena, together with the molecular diffusion, has a great importance in many fields.

In this work, the thermogravitational technique [1] has been used for measuring the thermal diffusion coefficient in 24 binary mixtures of toluene and normal Alkanes (n-hexane, n-octane, n-decane, n-dodecane, n-tetradecane and n-hexadecane), with different mass concentrations of toluene (20%, 40%, 60% and 80%). The measurements of the stationary separation along the thermogravitational column have been determined at 25ºC (Fig. 1), as well as all the corresponding thermophysical properties (density, mass expansion coefficient, thermal expansion coefficient and dynamic viscosity).

The objective of this work is to analyze experimentally the effect of the different parameters (molecular weight, viscosity and shape and size of molecules) on the variation of the thermal diffusion coefficient.

Fig.1: Stationary separation along the thermogravitational column of the toluene-n-

alkane analyzed mixtures.

The obtained results specially point out the effect of the viscosity and the molecular weight on the thermodiffusive behavior of these binary mixtures.

[1] Blanco P., Bou-Ali M.M., Platten J.K., Madariaga J.A., Urteaga P. and Santamaría C.J., J. Non-

Equilib. Thermodyn., 32, 2007.

55

Secondary Flows in a Laterally Heated Horizontal Cylinder

Odalys Sanchez1), Isabel Mercader2) and Oriol Batiste3)

1) Dep. Física Aplicada, Universitat Politècnica de Catalunya, 08034 Barcelona, Spain. [email protected].

2) Dep. Física Aplicada, Universitat Politècnica de Catalunya, 08034 Barcelona, Spain. [email protected]) Dep. Física Aplicada, Universitat Politècnica de Catalunya, 08034 Barcelona, Spain. [email protected]

Numerical results for the natural convection in a horizontal cylindrical enclosure with constant but different end temperatures, and an adiabatic lateral wall, are presented. Most of the previous research activities have addressed natural convection in enclosures such as rectangles [1] or cylinders [2, 3], due to its relevance in many engineering applications, i.e. crystal growth of semiconductors. In this later problem, undesirable defects like striations can be generated by the convective motion of the fluid. For a single fluid contained in a differentially heated horizontal cylindrical cavity, convection always exists, but above a critical temperature difference between the end walls of the cavity, the flow changes from the stationary symmetric basic flow (three reflection symmetries [3]), to either a secondary flow, steady or oscillatory, that breaks two reflection symmetries of the basic flow and maintains other, or an oscillatory flow that maintains all the symmetries of the basic flow. This passage from one state to another could affect the quality of grown crystal due to the complex structure of the flow.

In this work, we use the Navier-Stokes equations in the Boussinesq approximation to analyse numerically the stability of the primary flow and characterize the saturated solutions once the basic flow has became unstable. We have chosen aspect ratios (length/diameter) ,2 and typical values

of the Prandtl number for liquid metals and molten semiconductors 1Pr .

1/10 2/10 3/10 4/10 5/10

6/10 7/10 8/10 9/10 1

Fig.1 One period sequence of isosurfaces (level = max,v5.0 z ) of the perturbation with respect the basic flow

of the axial component of the velocity. Pr = 0.00715 and Rayleigh = 2500.

[1] Lyubimova, T. P., Lyubimov, D. V., Morozov, V. A., Scuridin, R. V., Ben Hadid, H., Henry, D. Journal of Fluid Mechanics, 635, pp. 275–295, 2009. [2] Mercader, I., Batiste, O., Alonso, A., Computers and Fluids, 39, pp. 215-224, 2010. [3] Vaux, S., Ben Hadid, H., Henry, D., Journal of Crystal Growth, 290, pp. 674-682, 2006.

56


Session Chair: Prof. A. Mojtabi and M. Papalexandris (Poster session)

14:00 – 14:30 Dr. Moritz Kreysing (Systems Biophysics, Ludwig-Maximilians-Universitat Munchen, Germany) Thermophoresis to detect and evolve biological functionality

14:30 – 14:50 Alain Martin (Mondragon Unibertsitatea, Spain) Numerical and Experimental Analysis on Microfluidic Separation Process

14:50 – 15:10 Zilin Wang (Forschungszentrum Jülich, Germany) Thermal diffusion of nucleotides

15:10 – 15:30 Ana C.F. Ribeiro (University of Coimbra, Coimbra, Portugal) Ternary mutual diffusion coefficients in systems containing ion nickel

15:30 – 15:50 V. Sechenyh (Université Libre de Bruxelles, Belgium) Design and development of a new instrument for measurements of diffusion

in liquid mixtures

15:50 – 16:10 Coffee break 16:10 – 17:50 Oral presentation of Posters (2-3 slides and max 3 minutes, incl speaker change) 18:00 – 20:00 Belgian beer and Poster watching (Sponsored by QinetiQ Space nv) Award ceremony for the best Poster

57

Thermophoresis to detect and evolve biological functionality

Moritz Kreysing, Simon Lanzmich, Christof Mast,

Susanne Seidel, Christoph Wienken and Dieter Braun1

1Systems Biophysics, Ludwig-Maximilians-Universitat Munchen,

Germany [email protected]

We summarize recent insights in the relevance of the thermophoretic effect for the field of biochem-

istry: on the application side thermophoresis allows the marker free quantification of affinities between

biological binding partners. Exemplary studies presented here demonstrate the compatibility of this

method with complex environments such as blood serums. Secondly, the drift of molecules in hetero-

geneous temperature fields also facilitates a local reduction of entropy in biochemical systems. This

solves the concentration problem of the origin of life, a prerequisite of many molecular evolution sce-

narios. Furthermore, we discuss if thermophoresis can affect the fitness of early replicators to trigger a

Darwinian selection step.

Selectivity in biochemical systems, such as biological cells or entire organisms, is predominantly

reflected in binding affinities. Because the mutual binding of biomolecules usually changes their Soret

coefficients, thermophoresis can be used to detect and quantify these interactions. For this an infra red

laser beam is used to locally heat microliter sized volumes of solutions with potential binding partners.

Monitoring the depletion of one of these partners from the heated zone while varying the concentration

of the other, allows the accurate determination of binding constants. Examples are the interaction of

proteins with other proteins, DNA, membrane peptides or pharmaceutical compounds [1–4]. As we

show, this approach has several advantages over surface binding methods: first, it allows to measure

in complex, biologically relevant environments, like blood serums [1]. Second, there is practically no

limit to the size of the substances screened. Binding of ions as well as macromolecules can be observed.

Results recently obtained with this method indicate a strong potential for drug screening applications as

well as basic research[5].

A second aspect of the thermophoretic behaviour of biomolecules discussed in this talk, connects

to the question how biomolecules can form complex structures that are far away from equilibrium. In

particular, we focus on the accumulation, lifetime and replication rate of thermally driven, self-replicating

molecules inside hydrothermal vents. Here, replicating molecules (i.e. DNA or RNA) are trapped in

pores of volcanic rock that form thermo-gravitational columns [6, 7]. We are exploring the possibility,

that based on their thermo-diffusive properties, larger molecules could have had an increased fitness,

giving rise to a selection bias in favour of more complex structures.

[1] Wienken, Ch., Baaske, Ph., Rothbauer, U., Braun, D., and Duhr, S. Nature Communication, 1, 100, 2010.

[2] Jerabek-Willemsen, M., Wienken, Ch., Braun, D., Baaske, Ph., and Duhr, S. ASSAY and Drug Development

Technologies, 9, pp.342-353, 2011.

[3] Wang, X., Corin, K., Baaske, Ph., Wienken, Ch., Jerabek-Willemsen, M., Duhr, S., Braun, D., and Zhang, S.,

PNAS, 108, pp.9049-9054, 2011.

[4] Corin, K., Baaske, Ph., Ravel, B., Song, J., Brown, E., Wang, X., Geissler, S. Wienken, Ch., Jerabek-

Willemsen, M., Duhr, S., Braun,D., and Zhang, S. PLoS One, 6, 23036, 2011.

[5] Scientific and technological insight into the field of micro-scale thermophoresis also provided the basis to

found NanoTemper Technologies.

[6] Baaske, Ph., Weinert, M., Duhr, S., Lemke, K., Russell, M. and Braun, D. PNAS, 104, 93469351, 2007.

[7] Mast, Ch., and Braun, D. PRL, 104, 188102, 2010.

58

Numerical and Experimental Analysis on Microfluidic Separation

Process

Alain Martin1) and M.Mounir Bou-Ali1)

1) MGEP Mondragon Goi Eskola Politeknikoa, Mechanical and Industrial Manufacturing Department, Loramendi 4, Apdo. 23, 20500 Mondragon, Spain, [email protected]

This paper presents the design, construction and numerical and experimental validation of a µdevice for the biological fluids separation. The geometry is based on another device [1] used for the DMSO (dimethyl sulfoxide) separation /cleaning from red blood cells previously cryopreserved by molecular diffusion. The separation of DMSO from red blood cells by molecular diffusion effect has attracted considerable interest since it does not damage globular tissue, as happens with current techniques [2-3].

In previous work [4] has been shown numerically that the Soret effect improves the separation of DMSO up to 32%. As continuation, in this paper, we analyze experimentally the possibility of optimizing this separation process by molecular diffusion through the temperature gradients application. For this purpose, the separation process by molecular diffusion of this new µdevice is validated numerically and experimentally by H2O-Isopropanol at 50% of mass fraction mixture.

Once the new µdevice is experimentally validated under a purely diffusive regime, the separationprocess of DMSO is studied, where a good agreement with numerical results is achieved. Finally thepossibility of improving the removal of DMSO by the temperature gradient application is discussed.

The experimental tests were performed using a pressure controller and three flowmeters (MFCS and Flowell, FLUIGENT), with flow rates from 25 µlitres/ min and 700 µlitres/ min (Fig. 1). While the numerical analysis was performed using the numerical simulation software Ansys-Fluent 13.0.

Fig. 1: Experimeltal dispositive.

[1] Mata, C., Longmire, E.K., McKenna, D.H., Glass, K.K., Hubel, A., Microfluid Nanofluid , 5,pp.529–540, 2008. [2] Antonenas V, Bradstock K, Shaw P., Chtotherapy, 4, pp. 16, 2002. [3] Cesare G. Perotti, Claudia Del Fante, Gianluca Viarengo, Pietro Papa, Loretta Rocchi, Paola Bergamaschi, Laura Bellotti, Andrea Marchesi, Laura Salvaneschi, Transfusion, 44 (6), pp. 900–906, 2004. [4] Martin, A., Bou-Ali, M. M., Barrutia, H., Alonso de Mezquia, D., C. R. Mecanique , 339 pp. 342–348, 2011.

59

Thermal diffusion of nucleotides

Zilin Wang1 and Simone Wiegand1

1Institute of Complex Systems, Forschungszentrum Julich GmbH, Germany,

[email protected] and [email protected]

We investigated the thermal diffusion behavior of aqueous solutions of nucleotides with the infrared

thermal diffusion forced Rayleigh scattering (IR-TDFRS) setup. Two cyclic nucleotides adenosine- and

guanosine- monophosphate, 5’-adenosine- and 5’-cytidine-monophosphate and also adenosine diphos-

phate have been studied. Some nucleotides have similar molecular weight but their structures differ as

well as some physical properties such as acidity, solubility and melting point. We compared the thermal

diffusion behavior of nucleotides, which have the same base or the same sugar and phosphate part. We

found a general trend that the Soret coefficient increases with increasing temperature, except at around

50 ◦C the Soret coefficient slightly drops and then increase again. This non-monotonic behavior might

be related to conformational changes in the molecule. Additionally, we measured also the viscosity and

thermal expansion coefficient of the nucleotide solutions in the investigated temperature and concentra-

tion range. While there is a clear correlation between the structure and the thermal diffusion behavior for

alkanes[1], the situation is much more complicated for the nucleotides. Nevertheless, as in the case of

the alkanes[1] and monoscaccharides[2] we find a correlation between the thermal diffusion coefficient

with the ratio of the thermal expansion coefficient and the kinematic viscosity. We discuss the physical

principles, which connect the thermal diffusion behavior with other thermophysical properties and the

structure of the different bases.

FIG. 1: Structure of the investigated nuclotides

[1] Blanco, P., Polyakov, P., Bou-Ali, M. M.and Wiegand, S., J. Phys. Chem. B, 112, pp. 8340-8345, (2008).

[2] Blanco, P. and Wiegand, S., J. Phys. Chem. B, 114, pp. 2807-2813, (2010).

60

Ternary mutual diffusion coefficients in systems containing ion nickel

Ana C.F. Ribeiro1), Joselaine C. S. Gomes1), Cecilia I.A.V. Santos1), Marisa C.F. Barros1),

Victor M.M. Lobo1), Abílio J.F.N. Sobral1), Miguel A. Esteso2) and Derek G. Leaist3)

1)Department of Chemistry, University of Coimbra, 3004 - 535 Coimbra, Portugal Tel: +351-239-854460; Fax: +351-239-827703.

[email protected], [email protected], [email protected], [email protected]

2)Departamento de Química Física, Facultad de Farmacia, Universidad de Alcalá 28871. Alcalá de Henares (Madrid)

[email protected]

3)Department of Chemistry, St. Francis Xavier University, Antigonish, Nova Scotia, Canada B2G 2W5 [email protected]

The diffusion of electrolytes in aqueous solutions and its impact on biological systems is ofgreat interest not only for fundamental purposes, but also for many technical fields, such as studies ofcorrosion in biological systems, desalination, dissolution and crystallization [1]. However, to our knowledge, there are only a few publications devoted to the study of diffusion in aqueous electrolyte solutions. We have been particularly interested in data on this property for chemical systems involving nickel ions in different aqueous media [2,3]. This work has been motivated by the fact that the nickel ion is one of the most mobile and bioavailable heavy metal ions present in different sources (e.g., drinking water, food, active pharmaceutical ingredients and excipients, and dental casting alloys), and by the possibility that the diffusion of nickel salts could produce substantial coupled flows of other dissolved salts.In this work, Taylor dispersion is used to measure ternary mutual diffusion coefficients for systems NiCl2-caffeine-water at 298.15 K at concentrations from (0.00 to 0.05) mol dm-3 for each component. From these data, we have estimated some thermodynamic and transport parameters, such as activity coefficients, the limiting diffusion coefficient and ionic conductance at infinitesimal concentration, contributing this way to a better understanding of the structure of these systems and of their thermodynamic behaviour in aqueous solution at different concentrations. In conclusion, diffusion coefficients measured for aqueous solutions of NiCl2 provide transport data useful to quantify diffusion for several chemical and pharmaceutical applications.

Fig.1 Schematic representation of the Taylor dispersion technique

[1] Tyrrell, H.J.V. and Harris, K.R. Diffusion in Liquids, 2nd ed., Butterworths, London, 1984. [2] A Ribeiro, A.C.F., Gomes, J.C.S., Santos, C.I.A.V., V Lobo, V.M.M, Esteso, M.A. and Leaist, D.G., J Chem Eng Data, 56, pp. 4696-4699, 2011. [3] Ribeiro, A.C.F., Gomes, J.C.S., Barros, M.C.F., Lobo, V.M.M. and Esteso, M.A., J. Chem.

Thermodynamics, 43, pp.270–274, 2011.

61

Design and development of a new instrument for measurements of diffusion in

liquid mixtures

Vitaliy Sechenyh, Jean Claude Legros, Valentina Shevtsova1



The prediction of mass transfer processes in multicomponent systems greatly relies on the knowledge of

diffusion and thermodiffusion (also called Soret) coefficients, which appear in the equations describing these

phenomena. Presently there exist well established methods for measurement of thermodiffusion coefficients

in binary mixtures. Some of them measure thermodiffusion coefficients DT while others the Soret coefficient,

ST . For binary mixtures the relation between coefficients is simple ST = DT /D and, consequently, thermod-

iffusion and Soret coefficients have the same sign. The appearance of cross-molecular diffusion complicates

measurement of the coefficients in ternary and higher mixtures in comparison to that in binary mixtures. The

diffusive mass transport of a given component is induced not only by its compositional gradient (main or prin-

cipal diffusion), but also by the compositional gradients of the other components (cross-diffusion) and the

temperature gradient. The Soret coefficients in ternary mixture can be determined as [1]

ST 1 = −

DT 1D22 −DT 2D12

D11D22 −D12D21

, ST 2 = −

DT 2D11 −DT 1D21

D11D22 −D12D21

, (1)

It follows from Eq. (1) that the signs of the Soret coefficients depend not only on DT i but also can be

affected by the diffusion and cross-diffusion coefficients. The correctness of Soret coefficients strongly relies

on the accuracy of the measured diffusion coefficients.

The results presented here summarize our efforts on the design and development of a new instrument to

measure diffusion coefficients in binary and ternary mixtures. The working principle of the set-up is based on

Taylor dispersion technique. The initial conceptual design is shown in Fig.1 which is targeted to identify the

effective conditions of operations for future work. The primary tasks include establishing the laminar flow with

a low constant velocity, elaboration of high quality Gaussian peak of injected mixture, maintaining the constant

temperature inside and outside the dispersion tube and in the differential interferometer. The following target is

to measure diffusion coefficients in the ternary mixtures which are studied in DCMIX experiments on the ISS.

FIG. 1: An experimental set up.

[1] Shevtsova V., Sechenyh V., Nepomnyashchy A., Legros J.C., Analysis of the application of optical two-wavelength

techniques to measurement of the Soret coefficients in ternary mixtures, Philosophical Magazine, 91(26), pp.3498-

3518 (2011)

62

Friday, June 8th


Morning session: Porous media, industrial applications


9:00 – 10:00 Francois Montel (Total, France) Pressure and Compositional Gradients in Petroleum Reservoirs

10:00 – 10:20 Jean Claude Legros (MRC, ULB) Kinetic of thermo diffusion in binary liquids approaching critical point.

Towards KIBILI experiment

10:20 – 10:40 Henri Bataller (Université de Pau, France) Thermodiffusion of the Tetrahydronaphtalene and Dodecane mixture under

high pressure and in porous medium.

10:40 – 11:20 Coffee break 11:20 – 11:40 Matthias Augustin (University of Kaiserslautern, Germany) On convection patterns of binary fluid mixtures in porous media

11:40 – 12:00 Denis S. Goldobin (ICMM, Perm, Russia) Thermal Diffusion and the Accumulation of Methane Bubbles in Deep-Water

Sediments

12:00 – 12:20 Abdelkhalek Cheddadi (Univ. Mohamed V-Agdal, Rabat, Morocco) Stability of the Gradient Zone of a Solar Pond with Salt Gradient Taking into

Account Soret Effect

12:20 – 13:00 Discussion on future IMT11 13:00 Lunch and Adjourn

63

Pressure and Compositional Gradients in Petroleum Reservoirs

Francois Montel , TOTAL, CSTJF, Avenue Larribau 64018 Pau Cedex France

[email protected]

The search for the optimal development of a field involves proper knowledge of the composition of the fluids that impregnated reservoirs and the development scheme could be strongly affected by the connectivity between the different reservoir units. After their migration into the trap, the fluids are shaped by various forces, among them; gravity has the most striking effect and was widely studied. In many cases there is evidence for the contribution of other forces like thermal gradients. Taking into account all the phenomena in order to establish a consistent picture of fluids distribution in the field is an important challenge for the petroleum industry. Reciprocally the actual fluid distribution can be used to assess the connectivity of the different panels and layers. But in that case, all the possible compositional redistribution mechanisms have to be taken into account. Drawing on field examples, a methodology will be proposed for dealing with any kind of reservoir fluid systems. Once the model matches the observed compositional gradient and corresponding PVT properties, it allows reliable connectivity assessment and extrapolation to the whole reservoir fluid column In this presentation we will also show how tall trees help us to model compositional gradients in reservoirs and we will focus on gas shale and oil shale where the thermal gradient could possibly play an important role in the production mechanism at pore scale level. .

64

Kinetic of thermo diffusion in binary liquids approaching critical

point. Towards KIBILI experiment

J.C. Legros, V. Sechenyh, D. Van Merode and V. Shevtsova

1MRC, ULB, EP - CP165/62, Dept. Chemical Physics, B1050, Brussels, Belgium [email protected] 2MRC Lessius University College | Campus De Nayer, Association K.U.Leuven

J. De Nayerlaan 5, B-2860 Sint-Katelijne-Waver, Belgium

[email protected]

This project is collaboration between ULB and LESSIUS. ULB is responsible for the KIBILI experiment

while LESSIUS is responsible of the JULES platform in a CubeSat (QB50 project).

An effective way to solve the issue of the reduction of CO2 emissions is through its capture from

stationary sources of energy production. A large amount can be stored in depleted oil and gas reservoirs being

mixed with hydrocarbons in states close to the critical point. Accumulation of chemically active impurities near

the top of the cap rock could lead to some leakages. KIBILI aims using a CubeSat to study diffusion near critical

point.

Far away from the critical point, transport coefficients (D, ST) are slowly varying functions of temperature

and density. Very close to the critical point the universal scaling laws described the vanishing of the diffusion

coefficients. This asymptotic behavior is localized in a much smaller region than what is observed. The transport

coefficients in this crossover region cannot be described in terms of simple power laws and depend on the

physical system under consideration.

When there is a temperature gradient, the Soret separation starts as a localized increase of concentration of

one of the components near the hotter wall while the other component accumulates near the colder wall.

The KIBILI project will study the formation of the

concentration gradient by the Soret effect and will quantify this

behavior first near the walls and then in the whole volume,

while the diffusion is becoming smaller and smaller as

approaching the critical conditions. Two opposite walls of the

experimental cell are maintained at different temperatures and

thus at different distances from the critical point. The kinetic of

the establishment of the concentration gradients near these two

walls are expected to be different. This would be observed for

the first time, and would yields important information on this

physical phenomenon.

In 1959 Rutherford et al. [1] measured the Soret

coefficient in the methane/n-butane mixtures. The Soret

coefficient measured in [1] at three different temperatures is

shown in Fig.1 as a function of pressure for the system

methane/n-butane: mole fraction of methane is 0.4; Tcrit =

115°C and Pcrit = 80 bars.

A CubeSat is a miniaturized satellite (10x10x10 cm, weighing 1 kg) which offers all the standard

functions of a normal satellite (attitude determination and control, uplink and downlink telecommunications,

power by body-mounted solar panels, on-board data handling and storage by a CPU, They can even have

deployable solar panels, antennas or booms.

[1] Rutherford W.M. and Roof J.G. Thermal diffusion in methane-n butane mixtures in the critical region, J.

Phys. Chem. 63, 1506, 1959.

Fig.1 Behavior of the Soret coefficient

approaching to the critical point

65

Thermodiffusion of the Tetrahydronaphtalene and Dodecane

mixture under high pressure and in porous medium

Cédric Giraudet1), Fabrizio Croccolo2), Guillaume Galliero1) Gilles Pijaudier-Cabot1), Stefan Van Vaerenbergh3) Ziad Saghir4) François Montel5), Henri Bataller1)

1) Laboratoire des Fluides Complexes et leurs Réservoirs - UMR 5150, Université de Pau et des Pays de l’Adour, BP 1155, F-64013 Pau Cedex, France, [email protected]

2) Université de Fribourg; Dept. Physique, Ch. Du Musée 3, CH-1700 Fribourg, Switzerland, [email protected]

3) Microgravity Research Center, Université Libre de Bruxelles, CP165/62, B-1150 Bruxelles, Belgium, [email protected]

4) Ryerson University, 350 Victoria St, Toronto, ONT, M5B 2K3, Canada, [email protected]

5) TOTAL SA, Avenue Larribau, F-64018 Pau Cedex, France, [email protected]

After calibrating and validating our high pressure thermodiffusion cell with a porous medium at

atmospheric pressure, we have measured the Soret coefficient of the Tetrahydronaphtalene and

Dodecane mixture at 10 and 50 MPa. The tortuosity of the porous medium has been evaluated, too.

For both these quantities, a significant decrease has been observed as a function of pressure.

A high-pressure thermodiffusion cell, filled with porous medium, has been developed in our labs in order to investigate the thermodiffusion of binary mixtures in oil field conditions. At each extremities of the filling porous medium, two small volumes allow a laser beam pass trough the cell by crossing sapphire windows. The system involves also a filling circuit able to pressurize the cell up to 100 MPa. The cell is placed within a Mach-Zehnder interferometer allowing the detection of refractive index differences between the cold and hot sides of the cell. In two precedent works we have used this cell to measure the concentration derivative of the refractive index of a binary mixture at high

pressure and the temperature derivative of the refractive index of binary mixtures [1,2] at

atmospheric pressure.

Tpcn ,/

TpTn ,/

In this work, first we have performed a series of experiments at atmospheric pressure with two well characterized binary mixtures. The two samples are the Toluene + Hexane system at the iso-molar mass concentration c0 = 51.7% of the first component and the 1,2,3,4-Tetrahydronaphthalene + n-Dodecane system at the mass concentration c0 = 50%. The experiments have been performed at the mean temperature of 25°C. The procedure to measure the Soret coefficient is explained and its accuracy discussed. The tortuosity of the porous medium is also evaluated.

Second, we have performed thermodiffusion experiments on the 1,2,3,4-Tetrahydronaphthalene + n-Dodecane mixture in the same porous medium at 10 and 50 MPa, at the mean temperature of 25°C and with an imposed temperature difference of 10°C. A significant decrease of the Soret coefficient ST

as a function of the pressure has been observed. By using a Leffler-Cullinan relation [3] and the dynamic viscosity values measured at high pressure [4], we evaluated the molecular diffusion coefficient of the mixture. After that, the tortuosity of the porous medium has been derived at 10 and 50 MPa and a decrease of the tortuosity as a function of pressure has been observed, indicating a modification of the geometry of the porous medium. At the end, given the measured values of and

, the thermodiffusion coefficient could be obtained for the different pressure levels. The values

of are in good agreement with those measured by Bou-Ali’s group by means of a

thermogravitational column [5].

D

D

TS TD

TD

[1] Croccolo, F., Arnaud, M.A., Bégué, D., Bataller, H., J. Chem. Phys., 135, pp. 034901-1-8, 2011. [2] Croccolo, F., Plantier, F., Galliero, G., Pijaudier-Cabot, G., Saghir, Z., Dubois, F., Van Vaerenbergh, S., Montel, F., Bataller, H., Rev. Sci. Instrum., 82, pp. 126105-1-3, 2011. [3] Taylor, R., Krishna, R., Multicomponent Mass Transfer, p. 77 (Wiley, New York, 1993)[4] Bataller, H., Miqueu, C., Plantier, F., Daridon, J.-L., Jaber, T. J., Abbasi, A., Saghir, M.Z., Bou-Ali, M.M., J. Chem. Eng. Data, 54, pp. 1710-1715, 2009. [5] Urteaga, P., Bou-Ali, M.M., Plantier, F., Bataller, H., Blanco, P., Fourth International Conference on Thermal Engineering, Abu Dhabi, UAE, 2007.

66

On convection patterns of binary fluid mixtures in porous media

Matthias Augustin,1 Bjorn Huke,2 Manfred Lucke,3 and Rudolf Umla4

1University of Kaiserslautern, Department of Mathematics, P. O. Box 30 49,

D-67653, Kaiserslautern, Germany [email protected] des Saarlandes, Institut fur Theoretische Physik, P. O. Box 15 11 50,

D-66041 Saarbrucken, Germany [email protected] des Saarlandes, Institut fur Theoretische Physik, P. O. Box 15 11 50,

D-66041 Saarbrucken, Germany [email protected] Imperial College, Department of Earth Science and Engineering, SW7 2AZ,

South Kensington Campus, United Kingdom [email protected]

During the last decades, the study of fluid flow in porous media has become increasingly importantdue to its significance in natural as well as industrial applications, for example in geothermal reservoirs.Here, the flow of the fluid is not only driven by externally applied forces but also by temperature gradi-ents. Moreover, we cannot usually consider a pure, one-component fluid but have to take into accountmixtures of at least two components, so–called binary fluids. Thus, the fluid flow is additionally drivenby concentration gradients. Furthermore, in many cases concentration currents are driven by temperaturegradients, which gives rise to another coupling known as Soret effect.

In a series of three papers [1–3], we investigated theoretically different convection patterns of one-and two-component fluids in the well–known setup of the Rayleigh–Benard system filled with a porousmedium using a multi-mode Galerkin method. For fluids with a positive separation ratio, ideal straightrolls (ISR), also called steady overtuning convection (SOC), square and crossroll patterns, their bifurca-tion properties and the stability of these structures are analyzed. In the case of negative separation ratios,stationary roll convection, traveling wave structures and their bifurcation behavior are discussed.

In this talk, I will point out the similarities and differences between the Rayleigh–Benard system withand without a porous medium. This includes differences concerning the structures of the velocity fieldin the Soret regime, temperature and concentration currents in traveling waves, as well as new types ofoscillatory instability mechanisms appearing in the case of roll or square convection.

[1] Augustin, M., Umla, R., Huke, B., and Lcke, M., Phys. Rev. E, 82, pp. 056303, 2010.[2] Umla, R., Augustin, M., Huke, B., and Lcke, M., J. Fluid. Mech., 649, pp. 165-186, 2010.[3] Umla, R., Augustin, M., Huke, B., and Lcke, M., Phys. Rev. E, 84, pp. 056326, 2011.

67

Thermal Diffusion and the Accumulation of Methane Bubbles in

Deep-Water Sediments

Denis S. Goldobin1

1 Institute of Continuous Media Mechanics, UB RAS,

614013, Perm, Russia [email protected]

Highlights of the work:

• The molecular diffusion of aqueous methane in marine sediments is significantly non-Fickian, which

is not accounted for in current studies on the formation of marine methane hydrate deposits.

• Non-Fickian diffusion can support the formation of free-gas zones (independent of hydrates).

• Bottom simulating reflector can be independent of the hydrate stability zone, while it is commonly

treated as the indication of the base of the zone.

We consider a liquid bearing gas bubbles in a porous medium. In the absence of fractures, gas bub-

bles are immovably trapped in a porous matrix by surface tension forces, and, therefore, the dominant

mechanism of transfer of gas mass becomes the diffusion of gas molecules through the liquid. Essen-

tially, the gas solution is in local thermodynamic equilibrium with vapor phase all over the system, i.e.,

the solute concentration equals the solubility. When temperature and/or pressure gradients are applied,

diffusion fluxes appear and these fluxes are faithfully determined by the temperature and pressure fields,

not by the local solute concentration, which is enslaved by the former. We derive the equations govern-

ing such systems, accounting for thermodiffusion and gravitational segregation effects which are shown

not to be neglected for geological systemsmarine sediments, terrestrial aquifers, etc [1]. The results are

applied for the treatment of non-high pressure systems and real geological systems bearing methane or

carbon dioxide, where we find a potential possibility of the formation of gaseous horizons deep below a

porous medium surface (see Fig. 1). The reported effects are of particular importance for natural methane

hydrate deposits and the problem of burial of industrial production of carbon dioxide in deep aquifers.

0.0

0.2

0.4

0.6

0.8

1.0dep

thb

elo

wth

eseafl

oo

r,z

(km

)

0.0 0.5 1.0 1.5 2.0 2.5

depth of water body above sediments, H (km)

GHSZ

Sea

0.0

0.2

0.4

0.6

0.8

1.0dep

thb

elo

wth

eseafl

oo

r,z

(km

)

0.0 0.5 1.0 1.5 2.0 2.5

depth of water body above sediments, H (km)

GHSZ

Sea

FIG. 1: Position of the methane-gas accumulation zones significantly depends on the non-Fickian drift strength

β = −α + Mg/RG for both weak (left) and typical (right) ascending water flux uf/φ(0) in seabed sediments.

Here α is the thermodiffusion constant, M = −24.3 g/mol is the effective molar weight of methane dissolved in

water, g is the gravity, R is the universal gas constant, G is the geothermal gradient, Tsf is the temperature of the

water–sediment interface.

The work has been supported by Grant of The President of Russian Federation (MK-6932.2012.1).

[1] Goldobin, D. S. and Brilliantov, N. V., Phys. Rev. E, 84(5), 056328, 2011.

68

Stability of the Gradient Zone of a Solar Pond with Salt Gradient

Taking into Account Soret Effect

Abdelkhalek Cheddadi1)

, Abdelkader Mojtabi2)

and Abderrahim Oudra1)

1) Ecole Mohammadia d’Ingénieurs, Univ. Mohamed V-Agdal, Rabat, Morocco

2) IMFT – Univ. Paul Sabatier, Toulouse, France

[email protected]

Thermodiffusion or Soret effect is a phenomenon that may become important in double diffusive systems

such as solar ponds.

In this study, the stability of the Gradient Zone of a salt gradient solar pond is explored. An analytical study

is performed. The mathematical formulation of the problem has been described using the Navier-Stokes equations

within the Oberbeck-Boussinesq approximation. In the equation of thermal diffusion, the solar energy rate absorbed

by the pond per unit volume has been expressed as a decreasing exponential, based on a single extinction

coefficient.

In this study, the infinite extension layer is considered, with rigid and thermally insulated lateral boundaries.

The study is devoted to the determination of the critical conditions for the onset of convection in the Gradient Zone,

for steady situations and for different values of the separation factor. The influence of thermodiffusion and the

fraction of heat flux extracted on the stability of the Gradient Zone were examined.

It is noted that when the Soret effect (separation factor = 0) is not taken into account in our problem,

convection in the gradient zone (GZ) is delayed compared to the case where it is considered especially for large

values of . The influence of the fraction of the heat flux extracted, on the stability of (GZ), has also been

considered.

Fig.1: Critical thermal Rayleigh number as function of the salinity

for different values of the separation factor

69

POSTER SESSIONS

70

POSTER PRESENTATIONS

1. F. M. Dennery

“Towards an expanding and reacting Thermodiffusion”

Ecole Centrale de Paris, [email protected]

2. Alain Martin1), M.Mounir Bou-Ali1), Estela Lapeira1), Simone Wiegand2), Michael Klein2),

Philipp Naumann2)

“Development of a New Thermogravitational µColumn”

1MGEP Mondragon Goi Eskola Politeknikoa, Mechanical and Industrial Manufacturing Department,

Loramendi 4 Apartado 23, 20500 Mondragon, Spain [email protected] 2 Institute for complex systems - Soft Matter, Forschungszentrum Juelich, Juelich, Germany,

[email protected]

3. Miren Larrañaga1), M.Mounir Bou-Ali1), Daniel Soler1), Manex Martinez1), Aliaksandr Mialdun2), Valentina Shevtsova2)

Remarks on the analysis method for determining the diffusion coefficient in ternary mixtures 1MGEP Mondragon Goi Eskola Politeknikoa, Mechanical and Industrial Manufacturing Department,

Loramendi 4 Apartado 23, 20500 Mondragon, Spain [email protected] 2MRC, ULB, EP - CP165/62, Dept. Chemical Physics, B1050, Brussels, Belgium [email protected]

4. David Alonso de Mezquia1, M. Mounir Bou-Ali1, Jean K. Platten1, Jose Antonio Madariaga2, Carlos Santamaria2

Determination of Thermal Diffusion Coefficient in Binary and Ternary Hydrocarbon Mixtures by Thermogravitational Technique 1MGEP Mondragon Goi Eskola Politeknikoa, Mechanical and Industrial Manufacturing Department,

Loramendi 4 Apartado 23, 20500 Mondragon, Spain [email protected] 2Department of Applied Physics II, University of Basque Country, Apdo. 644, 48080 Bilbao, Spain

5. Haruka Shinohara, Rio Kita, Naoki Shinyashiki and Shin Yagihara

Thermal diffusion of aqueous solution of cyclodextrin as a function of temperature

School of Science, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan [email protected]

6. Elmars Blums1), Gunars Kronkalns1), Ansis Mežulis1) and Viesturs Sints1)

Non-isothermal separation of ferrofluid particles through grids: abnormal magnetic Soret

effect

1) Institute of Physics, University of Latvia, Miera 32, Salaspils LV-2169, Latvia, [email protected]

7. Loujaine Yacine1, Abdelkader Mojtabi1, Rachid Bennacer2, Ali Khouzam1

Species separation of binary fluid in a horizontal cavity subjected to cross heat fluxe”

1 IMFT, UMR CNRS/INP/UPS N°5502, Université de Toulouse, 118 route de Narbonne, 31062,

Toulouse cedex, France 2ENS-Cachan Dpt GC/ LMT /CNRS UMR 8535,61, Av du Président Wilson 94235 Cachan Cedex,

France [email protected]

71

8. Slavtcho Slavtchev1, Penka Kalitzova-Kurteva1 and Alex Oron2

Long-wavelength Marangoni instability in a binary-liquid layer with the nonlinear Soret effect: Nonlinear analysis for monotonic instability

1) Institute of Mechanics, Acad. G. Bontchev, Bl. 4, Sofia 1113, Bulgaria, [email protected] 2) Technion-Israel Inst. Techn., Dept. Mech. Engng, Haifa 32000, Israel, [email protected]

9. Yuki Kishikawa,1) Rio Kita,1) and Simone Wiegand2)

Temperature dependence of Ludwig-Soret effect for polysaccharide solutions 1)

Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, [email protected])

Forschungszentrum Juelich GmbH, IFF-Weiche Materie, D-52425 Juelich, Germany

10. Matthias Gebhardt, Andreas Koniger and Werner Kohler

“Measurement of thermodiffusion in ternary mixtures using the two-color optical beam deflection technique (2-OBD)”

Physikalisches Institut, Universitat Bayreuth, 95440 Bayreuth, Germany [email protected]

11. Fabrizio Croccolo1), Henri Bataller2) and Frank Scheffold3)

Soret coefficient measurements close to a critical point 1)

Université de Fribourg, Dept. de Physique, Ch. du Musée 3, CH-1700, Fribourg, Suisse [email protected] 2)

Université de Pau et des Pays de l’Adour, Laboratoire des Fluides Complexes et leurs Réservoirs, Allée du Parc Montaury, F-64600, Anglet, France, [email protected])

Université de Fribourg, Dept. de Physique, Ch. du Musée 3, CH-1700, Fribourg, Suisse [email protected]

12. Ilya I. Ryzhkov

Soret separation in a two-phase ternary system and its stability

Institute of Computational Modelling SB RAS, 660036 Krasnoyarsk, Russia, [email protected]

13. N. Delenda, S. C. Hirata, M. N. Ouarzazi1)

On the separation of a binary viscoelastic fluid in a porous horizontal cavity

Laboratoire de Mecanique de Lille, UMR 8107, Universit lille 1, Villeneuve d’ascq, 59650, France [email protected]

14. D. Lyubimov1), T. Lyubimova2) and D. Nikitin2)

“Stability and secondary flow regimes in a horizontal binary fluid layer subjected to the horizontal temperature gradient”

1) Perm State University, 614990, Perm, Russia, [email protected] 2) Institute of Continuous Media Mechanics UB RAS, 614013, Perm, Russia, [email protected]

72

15. Mialdun1) A., Yasnou1) V., Shevtsova1) V., Koeniger2) A., Koehler2) W., Alonso de Mezquia3) D., Bou-Ali M.M3)

Measurements of diffusion, thermodiffusion, and Soret coefficients in water-isopropanol mixtures by different techniques 1MRC, ULB, EP - CP165/62, Dept. Chemical Physics, B1050, Brussels, Belgium [email protected]

2)Lehrstuhl für Experimentalphysik IV Universität Bayreuth 95440 Bayreuth

[email protected] 3MGEP Mondragon Goi Eskola Politeknikoa, Mechanical and Industrial Manufacturing Department,

Loramendi 4 Apartado 23, 20500 Mondragon, Spain [email protected]

16. David Alonso de Mezquia1, M. Mounir Bou-Ali1, Michael Klein2, Simone Wiegand2

Determination of Soret Coefficient of Binary Mixtures Measured by different Experimental Techniques 1MGEP Mondragon Goi Eskola Politeknikoa, Mechanical and Industrial Manufacturing Department,

Loramendi 4 Apartado 23, 20500 Mondragon, Spain [email protected] 2Institute of Complex Systems, Forschungszentrum Julich GmbH, Germany,

[email protected]

17. Kousaku Maeda 1), Rio Kita1), Naoki Shinyashiki1) and Shin Yagihara1)

“Thermal Diffusion Behavior of Aqueous Solution of Non-ionic Surfactant C12E5Studied in Micellar Phase” Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan [email protected]

18. Juan F. Torres1,2), Atsuki Komiya3), Daniel Henry2), Shigenao Maruyama3)

Measurement of Soret Coefficients in Binary Solutions by Phase-Shifting Interferometry

1) Graduate School of Engineering, Tohoku University, 980-8577 (2-1-1) Sendai, Japan, [email protected]) Laboratoire de Mécanique des Fluides et d’Acoustique, UMR CNRS 5509, ÉcoleCentrale de Lyon, 36 avenue Guy-de-Collongue 69134EcullyCedex, France,[email protected], [email protected]) Institute of Fluid Science, Tohoku University, 980-8577 (2-1-1) Sendai, Japan, [email protected], [email protected]

19. Ivan N. Cherepanov and Boris L. Smorodin

Traveling wave convection and heat transfer in a nanofluid

Perm State University, Physics of Phase Transitions Department, 15, Bukirev str., 614990 Perm, Russia, [email protected]

20. O. Sanchez1), X. Ruiz2), O. Batiste1), I. Mercader1)

Computer generated Earth diffusion processes in liquid binary Al-Cu alloys

(1) Departament de Física Aplicada, Universitat Politècnica de Barcelona, UPC. Barcelona. Spain. (2) Institut d’Estudis Espacials de Catalunya, IEEC, Barcelona, Spain (also Departament Química Física i Inorgànica, Universitat Rovira i Virgili, URV. Tarragona, Spain)

73

Towards an expanding and reacting Thermodiffusion

F. M. Dennery, Hon. Prof. at

Ecole Centrale de Paris [email protected]

Abstract

Among developments included in the reference [1], it has been already shown on a previous

poster that thermodiffusion broke down to be linear whenever relaxations between actual and

equilibrium temperatures locally occurred.

But this result is not sufficient for setting up the various balances of molar set numbers

relevant to species involved in expanding reactions.

So it is necessary that isochoric and isothermic rate progresses of reactants defined by

Arrhenius be converted into Prigogine non-linear equations and generalized through involving

temperature increases and through linear couplings with possible other reactions and with

phase expansions in the simplified lack of thermoradiations or supplementary hysteresis.

As to the growth rate of local equilibrium temperature, it derives from the entropy balance

only linked to thermoconduction, expansion, diffusions and reactions when other hysteresis

and frictions are omitted.

But the aforesaid operative processes depend on chemical potentials mainly relevant to

equilibrium temperature besides molar number of species determined by balances initially

quoted for ending with looping the loop.

[1] Dennery, F. M., “Towards a tamed and rich main features of Thermodynamics”,

summarizing Abstracts, Bibliographies, Concepts, Developments, Equivalents and Figures

previously shown on the last IMT posters, (twelve pages available on request).

74

Development of a New Thermogravitational µColumn

Alain Martin

1), M.Mounir Bou-Ali

1), Estela Lapeira

1), Simone Wiegand

2), Michael Klein

2),

Philipp Naumann2)

1) MGEP Mondragon Goi Eskola Politeknikoa, Mechanical and Industrial Manufacturing Department,

Loramendi 4, Apdo. 23, 20500 Mondragon, Spain, [email protected]

2) Institute for complex systems - Soft Matter, Forschungszentrum Juelich, Juelich, Germany,

[email protected]

In this paper, the desing, construction and numeric validation a new thermogravitational µcolumn

adapted to an optical measuring system is presented [1]. This microdevice is considered ideal to study

the thermodiffusion in synthetic and biological dispersions, due to the low sample volume needed (

50µL) and due to fairly low relaxation times. In addition, its design (fig. 1a), particularly in respect to

the aspect ratio used for the internal cavity (Lx= 500µm, Ly= 3mm, Lz= 30mm), is considered to be

within the limits of validity of the FJO theory [2]. This allows the determination of the

thermodiffusion coefficient DT from stationary separation measures.

For the numerical validation of the thermogravitational µcolumn, the software Ansys-Fluent 13.0 is

used. In this study, the thermodiffusion coefficient is defined, analizing the separation along the

µcolumn (fig. 1b). The analized mixtures are toluene-nHexane, THN-IBB, THN-nC12 and IBB-nC12

at 50% of mass fraction. The results show a variation of less than 2% in the worst case compared to

literature [3-4].

a) b)

Fig. 1: a) Thermogravitational µcolumn. b) Concentration of toluene (stationary state) in the thermogravitational column for the mixture of toluene/n-hexane along the

microcolumn and in the GAP.

[1] Naumann, P., Kriegs, H., Wiegand, S., Martin, A., and Bou-Ali, M. M., proceedings IMT10,

Brussels – Belgium, 2012.

[2] Valencia, J.J., Bou-Ali, M.M., Ecenarro, O., Madariaga, J.A., Santamaría, C.M., Thermal

nonequilibrium phenomena in fluid mixtures, in: S. Wiegand, W. Köhler (Eds.), Lectures Notes in

Physics, vol. 584, Springer, Berlin, pp. 233–249, 2002.

[3] Köhler, W., Muller, B; Soret and mass diffusion coeficients of toluene/n-hexane mixtures, Journal

of Chemical Physics, 103, pp. 4367-4370, 1995.

[4] Platten, J. K.; Bou-Ali, M. M.; Costeseque, P.; Dutrieux, J. F.; Köhler, W.; Leppla, C.; Wiegand, S.;

Wittko, G. Philos. Mag., 83, pp. 1965–1971, 2003.

75

Remarks on the analysis method for determining the diffusion

coefficient in ternary mixturesMiren Larrañaga1), M.Mounir Bou-Ali1), Daniel Soler1), Manex Martinez1), Aliaksandr

Mialdun2), Valentina Shevtsova2)

1) MGEP Mondragon Goi Eskola Politeknikoa,Mechanical and Industrial Manufacturing Department, Loramendi 4 Apdo. 23, 20500 Mondragon, Spain, [email protected].

2)MRC, ULB, EP - CP165/62, Dept. Chemical Physics, B1050, Brussels, Belgium,[email protected]

The objective of this work is the determination of pure and crossed molecular diffusion coefficients in multicomponent mixtures, by the “Sliding Symmetric Tubes” technique [1]. The governing equations, based on Fick’s law and considering the boundary conditions of the SST technique, have been solved analytically. Additionally, the method of least squares has been used for fitting.

In general, fitting was done by use of Nelder-Mead algorithm, implemented in Optimization Toolbox of Matlab (fminsearch function). To understand the robustness of the fit, we have studied an effect of basic parameters of the function, like tolerances, on the fit result. The results show that the less the tolerancesare, the more correct is the solution mathematically; but physically it can be meaningless. This dangerous situation easily appears in cases when limited experimental dataset is fitted.

To investigate an effect of dataset size, two different ways of fitting had been tested; in first case the time dependences of two concentration differences are fitted (Fig.1.a), in second case time dependences of four concentration values are fitted simultaneously (Fig.1.b).

In first case, the fit provides unique but nonrealistic solution.In second case, pure and crossed diffusion coefficients that comply with the conditions of the molecular coefficients in ternary mixtures have been obtained [2, 3]. However, it has been observed that the solution is not unique.

Fig.1: a) Nelder-Mead fit. b) Simultaneous fit with fminsearch

b)a)

The analysis shows that it is necessary to increase the number of experimental data; furthermore, it is required to do more experiments started from different concentration points, in order to leak the results and achieve a unique solution for all the cases.

[1] Alonso de Mezquia, D., Bou-AliM.M., Larrañaga, M., Madariaga, J.A. and Santamaría, C. Journal of Phisical Chemistry B (Accepted). [2] Leahy-Dios, A., Bou-Ali, M.M., Platten, J.K. and Firoozabadi, A., Journal of Chemical

Physics, 122, 2005. [3] Mutoru, J.W., Firoozabadi, A., Journal of Chemical Thermodynamics, 43, 2011.

76

Determination of Thermal Diffusion Coefficient in Binary and Ternary

Hydrocarbon Mixtures by Thermogravitational Technique

David Alonso de Mezquia,1 M. Mounir Bou-Ali,1 Jean K.

Platten,1 Jose Antonio Madariaga,2 and Carlos Santamarıa2



20500 Mondragon, Spain [email protected] of Applied Physics II, University of Basque Country, Apdo. 644, 48080 Bilbao, Spain

Determination of transport properties, such as thermal diffusion, in liquid mixtures is important for

progress in areas such us oil industry [1]. In this field, great improvements have been done in binary

mixtures, where there exists huge number of analytical and experimental results, but results in multi-

component mixtures are still scarce.

In this work the thermal diffusion coefficient of four ternary mixtures and their corresponding binaries

have been determined. The measurements have been carried out using two thermogravitational columns

(Figure 1) in both configurations, plane and cylindrical, which have been successfully used in previous

studies [2].

Figura 1: Plane thermogravitational column (left) and cylindric thermogravitational column (right) used in this

study

The ternary mixtures studied are the ones corresponding to Tetrahydronaphtalene, Isobutilbencene

and n-Dodecane components at different mass concentrations. These ternary mixtures are going to be

studied both in ground conditions and in microgravity conditions at the ISS.

Additionally, the results obtained in the thermal diffusion coefficient for the ternary mixtures have

been compared with the ones determined by the correlation in [3], which is able of determining the ther-

mal diffusion coefficient in ternary mixtures from the data of their corresponding binaries. The obtained

results show that there exist a great agreement between the results obtained with this correlation and the

experimentally obtained ones.

[1] F. Montel, Entropie, 214, 1998.

[2] P. Blanco, M.M. Mounir Bou-Ali, J.K. Platten, P. Urteaga, J. Madariaga and C. Santamaria, Journal of Che-

mical Physics, 129, pp. 174504-174510, 2008.

[3] P. Blanco, M.M. Bou-Ali, J.K. Platten, D. A. De Mezquia, J.A. Madariaga and C. Santamaria, Journal of

Chemical Physics, 132, 2010.

77

Thermal diffusion of aqueous solution of cyclodextrin

as a function of temperature

Haruka Shinohara, Rio Kita, Naoki Shinyashiki and Shin Yagihara

School of Science, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan

[email protected]

We have studied the Ludwig-Soret effect of aqueous solutions of -, -, and -cyclodextrin in the

temperature range of 15 – 55 oC by means of thermal diffusion forced Rayleigh scattering

(TDFRS).Cyclodextrins are circular oligosaccharides composed of -(1-4) linked glucose. The

number of glucose residues of -, -, and -cyclodextrin are known as 6, 7, and 8, respectively. The

glucose residues are linked in a circular arrangement around a central cavity and cyclodextrinshave a

bucket-like shape with hydrophilic groups locating at the outside of molecules. Figure 1 shows the

Soret coefficients of 1.0 wt% -, -, and -cyclodextrin in water as a function of temperature. The

thermally induced sign inversion behavior is observed that the sign of the Soret coefficient is negative

in lower temperatureswhereas the sign is positive at higher temperatures. The Soret coefficient of

glucose is also plotted in Figure 1 [1]. It is found that the slope of the Soret coefficient against

temperature tends to increase with increasing

the number of glucose residues. The solid

curves are obtained by the equation

proposed by Piazza and coauthors [2]. The

temperature dependent behavior is fitted

well by the equation. In contrast, the thermal

diffusion coefficients increase linearly with

increasing temperature. The sign inversion

behavior of cyclodextrins could be

associated with the molecular interactions

through hydrogen-bondings in addition to

the effects of the mass and size of molecules.

The role of molecular interactions on thermal

diffusion of aqueous solution of

cyclodextrinwill be discussed.

ST /

10

-3 K

-1

T / oC

Figure 1.Soret coefficient of glucose ( ),

-cyclodextrin ( ), -cyclodextrin ( ) and

-cyclodextrin ( ) inwateras a function of

temperature. The concentration of solutions is 1.0

wt%.

[1] Kishikawa, Y., Shinohara, H., Maeda, K., Nakamura, Y., Wiegand, S., and Kita, R.,(to be

submitted).

[2] Iacopini, S., Rusconi,R., and Piazza, R., Eur. Phys. J. E, 19, pp. 59-67, 2004.

78

Non-isothermal separation of ferrofluid particles through grids:

abnormal magnetic Soret effect

Elmars Blums1), Gunars Kronkalns1), Ansis Mežulis1) and Viesturs Sints1)

1) Institute of Physics, University of Latvia, Miera 32, Salaspils LV-2169, Latvia, [email protected]

Results of experiments on particle transfer through non-isothermal ferrofluid layer are presented. It is established an unexpectedly high influence of transversal uniform magnetic field on translation mass transfer. The results are interpreted as microconvective particle transfer induced by nonmagnetic grains of permeable layer walls.

We have measured transient nanoparticle transfer through a thin non-isothermal ferrofluid layer formed by-two permeable walls. The walls consist of plastic nonmagnetic filaments which form a fine square shaped grid. Transient particle flux is determined from measurements of particle concentration difference in two fluid chambers attached on both sides to the layer and kept at different temperatures.The experiments are performed employing a ferrofluid sample of preliminary optically measured diffusion and thermodiffusion coefficients [1].

Due to nonisothermal mass transfer through the filtering layer there develops a difference of particle concentration in both fluid chambers. Theoretically predicted exponential law of separation dynamics is observed. Separation curves allow calculating the effective diffusion De and Soret Se

coefficients of the colloid. Figure 1 represents the dependence of both coefficients on homogeneous magnetic field B applied normally to the fluid layer. The obtained values of transport coefficients for B=0 agree well with results of optical grating experiments [1]. Contrarily, experiments performed in presence of a magnetic field give principally different results (see Fig. 1). Under field the effective diffusion coefficient De abnormally strongly decreases and Se reduces. At B>40 mT even a reversal of mass flux direction is observed (Fig. 1a). Such changes are significantly stronger than those predicted by hydrodynamic theory of magnetic Soret effect and obtained from direct Soret effect measurements [1]. We regard that the observed effects may be interpreted as manifestation of a specific microconvective mass transfer induced by nonmagnetic grid elements of permeable walls. The obtained experimental results qualitatively well agree with approximate analysis of magnetic Stokes problem together with calculations of concentration boundary layer near spatially fixed sphere which induces motion of surrounding fluid of nonuniform magnetization [2].

The work is supported by ERDF Project 0001/2DP/2.1.1.1.0/10/APIA/VIAA/007 and the European Social Fund within the project Support for Masters' Studies at University of Latvia.

[2] Mezulis, A., Blums, E., Phys. Fluids, 18, 107101, 2006.[3] Blums E., Eur. Phys. J., E - Soft Matter. 15 pp.271-276, 2006.

-0.02

0

0.02

0.04

0.06

0.08

0.1

0 25 50 75 100EFFE

CTI

VE

SOR

ET C

OEF

FIC

IEN

T

(1/K

)

MAGNETIC FIELD (mT)

0

100

200

300

0 20 40 60 80 100

EFF

EC

TIV

E D

IFFU

SIO

N

D´

10

11

(m2/s

)

MAGNETIC FIELD (mT)

Fig. 1a. Effective Soret coefficient Fig.1b. Effective diffusion coefficient

79

Species separation of binary fluid in a horizontal cavity subjected

to cross heat fluxes.

Loujaine Yacine1, Abdelkader Mojtabi1, Rachid Bennacer2, Ali Khouzam1

1 IMFT, UMR CNRS/INP/UPS N°5502, Université de Toulouse, 118 route de Narbonne, 31062, Toulouse cedex, France

2ENS-Cachan Dpt GC/ LMT /CNRS UMR 8535,61, Av du Président Wilson 94235 Cachan Cedex, France E-mail: [email protected]

Thermogravitational separation has, usually, been used in differentially heated vertical cells, called thermogravitational columns. Recently Elhajjar et al. [1] showed that it is possible to carry out the species separation of a binary mixture in the classical horizontal Rayleigh-Bénard cell heated from below. The optimal value of the specie separation in such horizontal cell remained equal to the one obtained in a vertical columns [2]. The natural convection in differentially heated binary mixture subjected to the Soret effect was also studied Bahloul et al.[3] without considering the species separation aspect and by by Bennacer et al. [4] in porous media.

The aim of the present work is to study the Soret-induced convection in horizontal cavity filled with a binary mixture and subjected to cross heat fluxes. All four plates are subjected to uniform heat fluxes, opposite plates being heated and cooled, respectively and are assumed impermeable. The governing parameters for the problem are the thermal Rayleigh number, Ra, the Lewis number, Le, the separation ratio, , the Prandtl number, Pr, the aspect ratio of the cavity A and the dimensionaless horizontal heat flux, a.

Analytical solutions for the velocity component, temperature and concentration fields are obtained using a parallel flow assumption in the core region of the cavity:

)1)(12(12

)()(,)( zzz

maRazuxzuV

)( zfaxT and )( zgmxC , where f(z) and g(z) denote the temperature and concentration

analytical polynomial (five degree) with coefficients depending on Ra, , Le, a and m. Numerical solutions of the full governing equations are obtained for a wide range of the governing parameters (fig. 1). A good agreement is observed between the analytical model and the numerical simulations. The optimal specie separation obtained using the present boundary conditions, is much higher than that obtained in classical thermogravitational columns.

Figure 1. Separation as function of lateral flux for Ra=10, Le=100 and

[1] Elhajjar B., Charrier-Mojtabi M.C. and Mojtabi A., Physical Review E77, pp. 1539-3755, 2008. [2] Platten JK, Bou-Ali MM and Dutrieux JF, J. Physical Chemistry, Vol. 107, pp.11763-11767, 2003. [3] Bahloul A.,Vasseur P. and Robillard L. J. Fluid Mech. Vol. 574, pp.317-342 ,2007[4] Bennacer R., Mahidjiba A., et al., Int. J. Num. Meth Heat Fluid Flow, Vol. 13, pp. 199-215, 2003

80

Long-wavelength Marangoni instability in a binary-liquid layer

with the nonlinear Soret effect:

Nonlinear analysis for monotonic instability

Slavtcho Slavtchev1, Penka Kalitzova-Kurteva1 and Alex Oron2

1) Institute of Mechanics, Acad. G. Bontchev, Bl. 4, Sofia 1113, Bulgaria, [email protected]

2) Technion-Israel Inst. Techn., Dept. Mech. Engng, Haifa 32000, Israel, [email protected]

The thermodiffusion or Soret effect in binary systems is called nonlinear when thethermodiffusive flux is proportional to the temperature gradient with a coefficient being a quadratic function of the solute concentration, instead being constant as in the case of the linear Soret effect. The nonlinear Soret effect is mostly pronounced in very dilute solutions and can be significant in some separation processes. This work deals with the long-wavelength Marangoni instability in a thin horizontal layer of a binary liquid mixture, subjected to a vertical constant temperature gradient. The layer is bounded by a rigid plate from below and a free non-deformable surface from above. It is heated from below and the free surface is considered to be poorly conducting which corresponds to the case of small Biot numbers. The monotonic and oscillatory instabilities of the binary–liquid layer with the nonlinear Soret effect have been analyzed in [1] and [2].

Here, the nonlinear evolution of the three-dimensional liquid system is studied in the case of monotonic instability. We apply the technique of asymptotic expansions to derive a set of nonlinear evolution equations which describe the spatiotemporal dynamics of the system. The solution of the dimensional equations of mass and momentum balances, heat transfer and mass diffusion is sought near the linear instability threshold in the form of series in a small parameter that measures the supercriticality above the threshold. Based on the first two approximations, a system of two evolution equations is obtained. The dynamic behavior of the system is studied for large Prandtl number and in the limit of large times. Nonlinear amplitude equations for patterns of three kinds: rolls, squares, and hexagons, are derived.

The bifurcation analysis of the amplitude equations reveals the conditions for the emergence of different patterns and of their stability. It is shown that the dynamic behavior of the equations in the presence of the nonlinear Soret effect is similar to that in the case of the linear Soret effect. In the limit of large inverse Lewis numbers, roll and square patterns bifurcate supercritically for all values of both the linear and nonlinear Soret numbers. The linear stability analysis of the solutions of the corresponding amplitude equations shows that the roll patterns are unstable whereas the square pattern is always stable. Two hexagonal patterns can also emerge. In the subcritical region, one of them is unstable whereas the other is stable. In the supercritical region, both patterns are stable.

[1] Slavtchev S., Kalitzova-Kurteva P., Oron A., J. Theor. Appl. Mech., Sofia, 39, No. 1, pp. 31-54, 2009.

[2] Kalitzova-Kurteva P., Slavtchev S., Oron A., J. Theor. Appl. Mech., Sofia, 39, No. 3, pp. 63-78, 2009.

81

Temperature dependence of Ludwig-Soret effect

for polysaccharide solutions

Yuki Kishikawa,1) Rio Kita,1) and Simone Wiegand2)

1) Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan

2) Forschungszentrum Juelich GmbH, IFF-Weiche Materie, D-52425 Juelich, Germany

[email protected]

Experimental results of the Ludwig-Soret effect for the binary systems of pullulan in water

and of dextran in water will be presented. Additionally, the binary system of pullulan in DMSO

and the ternary systems of dextran in urea/water mixed solvents will be reported. The Soret

coefficient ST, the thermal diffusion coefficient DT, and the translational diffusion coefficient D

are obtained in the temperature range of 15 – 55 oC by means of thermal diffusion forced

Rayleigh scattering (TDFRS). The sample concentrations used in this study are a dilute regime

around 5.0 g/L.

Figure 1 shows the Soret coefficient ST of pullulan and dextran solutions as a function of

temperature. In water the ST of pullulan and dextran has negative sign at lower temperatures and

show sign inversion behavior with increasing temperature. In contrast to the aqueous solution,

pullulan in DMSO shows positive ST and no temperature dependence. This implies that the

hydrogen-bondings play a dominant role on sign inversion behavior. For the ternary system of

dextran in the mixed solvent urea/water, ST increases with increasing the urea content. It is

considered that urea modifies the

structure of hydrogen-bondings which

leads to the increasing behavior of ST.

The result also indicates a significant role

of the interactions via hydrogen-

bondings.

Additionally, we will present the

result of molecular weight dependence of

polysaccharides to discuss the effects of

mass and size of solute molecules on

thermal diffusion. Figure 1. Soret coefficient of polysaccharide solutions as a function of temperature [1,2].

[1] Sugaya, R., Wolf, B. A., and Kita, R., Biomacromolecules 7, pp. 435-440, 2006. [2] Kishikawa, Y., Wiegand, S., and Kita, R., Biomacromolecules 11, pp. 740-747, 2010.

82

Measurement of thermodiffusion in ternary mixtures using the two-color

optical beam deflection technique (2-OBD)

Matthias Gebhardt, Andreas Koniger and Werner Kohler1

1Physikalisches Institut, Universitat Bayreuth, 95440 Bayreuth,

Germany, [email protected]

Thermodiffusion measurements in ternary mixtures are still difficult to handle and the feasibility and

analysis of these measurements are a matter of debate. We use an improved two-color optical beam

deflection technique (2-OBD) with laser wavelengths of 405 nm and 633 nm to obtain the transport co-

efficients as suggested by Haugen and Firoozabadi [1]. In particular by employing the 405 nm laser

wavelength we can take advantage of the increased refractive index dispersion due to its proximity to

the UV absorption lines of aromatic molecules. Our group also participates in the DCMIX project with

the aim to compare the Soret effect of ternary mixtures under microgravity conditions on board of the

International Space Station and on ground.

FIG. 1: Improved two colored optical beam de-

flection set up.

FIG. 2: Top: Beam deflection signal for 405 nm(blue) and 633 nm (red). Bottom: Applied tem-

perature gradient.

Following first measurements by A. Koniger et al. [2] on the benchmark system dodecane/isobutyl-

benzene/1,2,3,4-tetrahydronaphthalene, we have improved the experimental setup to eliminate artifacts

from the signal. As an example, temperature overshooting at short times has been suppressed by em-

ploying optimized lab-built temperature controllers. Now we take a closer look at the benchmark system

and, in particular, investigate the error propagation from different sources. As first results, we identify

and discuss the refractive index dispersion relations of the contrast factors (∂ni/∂cj)p,T,ck 6=j as relevant

and decisive quantities.

[1] Haugen, K. and Firoozabadi, J. Phys. Chem B, 110, pp. 17678-17682, 2006.

[2] Koniger, A., Wunderlich, H. and Kohler, W., J. Chem. Phys., 132, 174506, 2010.

83

Soret coefficient measurements close to a critical point

Fabrizio Croccolo1), Henri Bataller2) and Frank Scheffold3)

1) Université de Fribourg, Dept. de Physique, Ch. du Musée 3, CH-1700, Fribourg, Suisse,[email protected]

2) Université de Pau et des Pays de l’Adour, Laboratoire des Fluides Complexes et leurs Réservoirs, Allée du Parc Montaury, F-64600, Anglet, France, [email protected]

3) Université de Fribourg, Dept. de Physique, Ch. du Musée 3, CH-1700, Fribourg, Suisse,[email protected]

By investigating non equilibrium fluctuations in a critical mixture by means of Dynamic Shadowgraph the Soret and the mass diffusion coefficients can be derived. An experiment is performed at different average temperatures in the vicinity of the critical point.

The Soret and mass diffusion coefficients can be measured by careful investigation of the static and dynamic spectra of non equilibrium fluctuations (NEFs) by means of dynamic Shadowgraph [1]. This is obtained by sending a probe beam parallel to the temperature and concentration gradients. NEFs are tiny (in intensity) but giant (in lateral size) fluctuations of the temperature or the concentration which appear as soon as a gradient is applied to a fluid [2].

The temporal correlation function of NEFs for wave vectors larger than a critical value cq follows

an exponential decay with time constant ( ) ( )21 Dqq =t in which D is the mass diffusion coefficient

and q is the fluctuation wave vector. From the time constants a precise measurement of the diffusion

coefficient can be obtained. Conversely, the time constants below cq show a quadratic behavior 2qµt due to the buoyancy effect of gravity on larger fluctuations [3]. The critical value cq is the

wave vector at which gravity and diffusion play the same role and depends on the Soret coefficient:

( ) 4

1

1÷ø

öçè

æ×

-××Ñ××=

D

ccSTgq ooT

c ub

in which b is the mass expansion coefficient, g the gravitational acceleration, TÑ the temperature

gradient, oc the average concentration of the denser component and u the kinematic viscosity of the

mixture. By measuring the critical wave vector one is able, upon knowledge of the fluid parameters band u , to get a measurement of the Soret coefficient.Critical molecular mixtures have been widely investigated in the past, but only a few works take into account the behavior of the Soret coefficient of such systems in the vicinity of the critical temperature [4]. Recently some measurements have been performed with the Thermal Diffusion Forced Rayleigh Scattering technique on polymer blends [5], however further verification by modern techniques is worth to be done.In this work an aniline/cyclohexane mixture at the critical concentration has been stressed by temperature gradients at different average temperatures and the resulting Soret and mass diffusion coefficients have been measured. From these data the value of the thermodiffusion coefficient has been determined, too.

[1] Croccolo, F., et al., Phys. Rev. E, 76, pp. 41112-1-9, 2007.[2] Vailati, A., and Giglio, M., Nature, 390, pp. 262-265, 1997, Weitz, D.A., Nature, 390, pp. 233-235,1997.[3] Croccolo, F., et al., Ann. New York Acad. Sci., 1077, pp. 365-379, 2006.[4] Giglio, M., and Vendramini, A., Phys. Rev. Lett., 34, pp. 561-564, 1975.[5] Köhler, W., et al., Adv. Polym. Sci., 227, pp. 145-198, 2010.

84

Soret separation in a two-phase ternary system and its stability

Ilya I. RyzhkovInstitute of Computational Modelling SB RAS, 660036 Krasnoyarsk, Russia

[email protected]

The dynamics of fluid systems with interfaces remains a challenging problem of modern physics. In such systems, the variation of surface tension due to thermal or compositional gradient along the interface can cause convective flows in the bulk fluid. The systematic studies of interfacial convection in multilayer systems of pure fluids were summarized in [1]. Recently, the interest was shifted to systems where the interface separates two different phases of a given binary mixture [2].

In this work, we are interested in the ternary mixture of benzene-ethanol-water. This system has important industrial applications, such as dehydration of aqueous ethanol to high-purity alcohol for beverage and motor fuel uses and development of oxygenates to produce lead free gasoline.

The phase diagram of benzene-ethanol-water mixture at T0=25°C is shown in Fig. 1. The binoidal curve separates the full range of concentrations in two regions. Above the curve, the mixture components are fully miscible, while below the curve the system separates into two phases. The equilibrium concentrations of components in these phases are connected by the dotted lines.

Let us consider a two-layer system, where the horizontal layers are formed by conjugate phases of benzene-ethanol-water mixture. The layers are bounded by rigid walls from above and below. The equilibrium concentrations of benzene, ethanol and water correspond to points 1 and 2 in Fig. 1: C1b=0.978, C1e=0.02, C1w=0.002; C2b=0.006, C2e=0.23, C2w=0.764. Due to very low concentrations of water in layer 1 and benzene in layer 2 (in comparison with the other components), we can consider these layers as layers of binary fluids. Layer 1 is represented by the ethanol-benzene mixture and layer 2 – by ethanol-water mixture. In the presence of gravity, the less dense phase (ethanol-benzene) is situated above the denser one (ethanol-water). A fixed temperature difference �T is applied between the walls. In the presence of temperature gradient, one can expect a slight separation of binary mixtures due the Soret effect. At the given mean concentrations, the Soret effect in both mixtures in negative, i.e. the lighter component (ethanol) is enriched in the cold region. The interfacial tension is assumed to depend linearly on temperature and concentration C1e [4].

We have determined the distributions of temperatures and ethanol concentrations in the layers 1 and 2 at the state of mechanical equilibrium. Linear stability analysis of this state is performed. A number of possible configurations are investigated: 1) weightlessness / normal gravity conditions 2) heating from above/below 3) different ratios of layer thicknesses. The relative importance of gravitational and Marangoni instability mechanisms is discussed. The influence of Soret effect on the stability characteristics is investigated.

The work is supported by the SB RAS Fundamental Research Project 38 and Russian Foundation for Basic Research Grant 11-01-00283-a.

[1] Nepomnyashchy A.A., Simanovskii I.B. and Legros J.C. Interfacial convection in multilayer systems. Springer, 2006. [2] McFadden G.B., Coriell S.R., and Lott P.A. J. Fluid Mech., Vol. 647, pp. 105–124 (2010). [3] Bancroft W.D. and Hubard S.S. J. Amer. Chem. Soc. Vol. 64, pp. 347–353 (1942). [4] Ross S. and Patterson R.E. J. Chem. Eng. Data. Vol. 24, pp. 111–115 (1979). �

Fig. 1. Phase diagram of benzene-ethanol-water system at 25°C [3].

85

On the separation of a binary viscoelastic fluid in a porous horizontal

cavity

N. Delenda, S. C. Hirata, M. N. Ouarzazi1

1Laboratoire de Mcanique de Lille, UMR 8107, universit lille 1,villeneuve d’ascq, 59650, France [email protected]

In thermogravitational columns (TGC), coupling of thermodiffusion and convection is used to sep-

arate species of a two-component fluid. Many studies have been devoted to the improvement of the

separation process in vertical TGCs. Recently, Elhajjar & al. [1] showed that it is possible to carry out

the separation of species of a binary mixture in a horizontal porous cavity heated from below. In this

configuration, and for separation ratios greater than a certain value ψmono > 0, a stationary bifurcation

leads to a monocellular flow at the onset of convection, allowing separation of species between the two

ends of the cell. The monocellular flow obtained from the loss of stability of the rest state remains sta-

ble beyond the Rayleigh number corresponding to the optimal separation Raopt. Moreover, the optimal

Rayleigh number of the horizontal cell is larger than the one of the vertical configuration, which allows

to perform separation in a larger cell.

Soret-driven convective effects in viscoelastic fluids may play an important role in many industrial and

biological process, such as the separation of polymers and the polymerase chain reaction (performed to

amplify target nucleic acid sequences from genetic samples containing DNA or RNA [2]). Therefore, the

present contribution extends the work dealing with Newtonian fluis [1] to the case of viscoelastic binary

fluids. The linear stability analysis of the monocellular flow is performed, and the critical conditions

above which the flow becomes unstable are determined. The influence of the elasticity number λ1 and

the ratio Γ of the retardation time to the relaxation time on the linear properties of the instability is

quantified as a function of the separation ratio ψ. It is found that, depending on the parameters, the

monocellular flow may lose its stability via a Hopf bifurcation giving rise to transversal travelling rolls

or via a stationary bifurcation to fixed longitudinal rolls. In the two cases, it is shown that separation is

also possible in viscoelastic liquids, and the monocellular flow remains stable beyond Raopt.

0

5

10

15

20

25

30

35

0.05 0.075 0.1 0.125 0.15 0.175 0.2 0.225 0.25 0.275 0.3

Rac2

ψ

RacsRaopt

Γ 0.15Γ 0.20Γ 0.50Γ 0.75

Newtonian fluid

FIG. 1: Critical Rayleigh number Rac2 for the bifurcation to transversal rolls as a function of ψ, for λ1 = 0.5

and different values of Γ. The solid green line represents the Rayleigh number Raopt corresponding to maximum

separation; the dashed region represents the conductive state, previous to the onset of the monocellular flow.

[1] Elhajjar, B., Charrier-Mojtabi, M.-C., Mojtabi, A., Phys. Rev. E., 77, pp. 026310, 2008.[2] Krishnan, M., Ugaz, V. M., Burns, M. A., Science, x, 298, (5594), pp. 793, 2002.

8186

Stability and secondary flow regimes in a horizontal binary fluid

layer subjected to the horizontal temperature gradient

Dmitriy Lyubimov1), Tatyana Lyubimova2) and Dmitriy Nikitin2)

1) Perm State University, 614990, Perm, Russia, [email protected]


The paper deals with the investigation of stability and secondary regimes of steady convective flow of binary fluids in a horizontal layer subjected to the horizontal temperature gradient. The layer boundaries are rigid and adiabatic. Mass flux through the boundaries is absent and concentration inhomogeneities are created due to the thermodiffusion.

In spite of the simple flow structure, for finite values of Rayleigh number the problem on steady plane-parallel convective flow is non-linear which leads to the possibility of the solution non-uniqueness. The boundaries of non-uniqueness domain correspond to the tangential bifurcation; they are found analytically. In the case of positive Soret effect (ε >0) thermodiffusion leads to the accumulation of light component in warmer part of the layer and the velocity of flow increases in comparison with the case of single-component fluid. At ε < 0 thermodiffusion leads to the accumulation of light component in colder part. In this case the flow is decelerated and at ε = −1 the velocity and density gradient take zero values. At ε < −1 the flow direction is opposite due to the change of the density gradient sign.

Long wave instability of steady flow is studied analytically and instability to finite wave-length perturbations numerically by spectral method. The calculations are performed for three sets of Prandtl and Schmidt numbers: (1) 0.01, 10 (liquid metal); (2) 0.7, 1.3 (gaseous mixture); (3) 6.7, 676.7 (liquid mixture, for instance, the solution of salt in water). Plane perturbations in the form of rolls with axes perpendicular to the temperature gradient (transverse rolls) and spiral perturbations in the form of rolls with axes parallel to the temperature gradient (longitudinal rolls) are considered.

It is found that for the mixture 1, at ε > 0 and in the range 0.88 0ε− < < plane monotonous perturbations with finite wave-length related to the development of immovable vortices on the boundary of towards flows are most dangerous. Thermodiffusion does not make significant influence on the stability boundary to these perturbations. In narrow range 0.89 0.88ε− < < − long-wave spiral perturbations are most dangerous and at 0.89ε < − long-wave plane perturbations. In the case of gaseous mixture, at ε >0 and in the range 0.84 0ε− < < spiral monotonous perturbations with finite wave-length are responsible for instability; stability to these perturbations grows with the increase of ε. In the range 0.85 0.84ε− < < − long-wave spiral perturbations are most dangerous and at 0.85ε < −again spiral monotonous perturbations with finite wave-length. In the case of mixture 3 no instability to the perturbations with finite wave-length is found in the considered parameter range; only long-wave instability existing at ε < 0 is found.

We also performed numerical investigation of two-dimensional secondary flows by finite difference method. The calculations show that in the parameter range where the steady solution is unique, at Rayleigh numbers lower than critical value Rac the dependence of flow intensity on the Rayleigh number is close to linear and at Ra=Rac two new solutions branch according to the square root law. At Ra<Rac the flow is nearly plane-parallel and at Ra<Rac it is multicellular, besides the spatial period of the secondary flow corresponds to the wave-length of most dangerous perturbations according to results of linear stability analysis.

87

Measurements of diffusion, thermodiffusion, and Soret coefficients in

water-isopropanol mixtures by different techniques

A. Mialdun,1 V. Yasnou,1 V. Shevtsova,1 A. Koniger,2 W.

Kohler,2 D. Alonso de Mezquia,3 and M. M. Bou-Ali3

1 MRC, CP165/62, Universite Libre de Bruxelles, Av. F.D. Roosevelt,

50, B-1050, Brussels, Belgium [email protected] Institut, Universitat Bayreuth, D-95440 Bayreuth,

Germany [email protected]. and Manufacturing Dept, MGEP Mondragon Goi Eskola Politeknikoa,

Loramendi 4 Apdo. 23, 20500 Mondragon, Spain [email protected]

We report on the measurement of diffusion (D), thermodiffusion (DT ) and Soret (ST ) coefficients

in water-isopropanol mixtures by four different instrumental techniques: thermogravitational column

(TGC) in combination with sliding symmetric tubes (SST), optical beam deflection (OBD), optical digital

interferometry (ODI), and microgravity measurements (SODI/IVIDIL) on the International Space Station

(ISS). All the coefficients have been measured over the full concentration range. Results from different

instruments are in excellent agreement over a broad overlapping composition (water mass fraction) range

0.2 < c < 0.7, providing new reliable benchmark data [1]. Comparison with literature data gives, where

available, a generally good agreement. Contrary to theoretical predictions and previous experimental

expectations we have not observed a second sign change of ST at low water concentrations.

FIG. 1: Soret coefficients ST for water/IPA measured by different experimental techniques.

[1] Mialdun A., Yasnou V., Shevtsova V., Koeniger A., Koehler W., Alonso de Mezquia D., Bou-Ali M.M, A

comprehensive study of diffusion, thermodiffusion, and Soret coefficients of water-isopropanol mixtures, sub-

mitted to J. Chem. Phys., 2012

88

Determination of Soret Coefficient of Binary Mixtures Measured by

different Experimental Techniques

David Alonso de Mezquia,1 M. Mounir Bou-Ali,1 Michael Klein,2 and Simone Wiegand2



20500 Mondragon, Spain [email protected] fur FestkKorperforschung Forschungszentrum Julich

52425 Julich Germany [email protected]

The molecular, thermal and Soret coefficients are of great importance in different processes in several

fields such as medicine, industry or energy generation.

In this work, the results obtained for thermal, molecular and Soret coefficients in hydrocarbon binary

mixtures are presented. The mixtures have been studied using different techniques. On one hand, the

Thermal Diffusion Forced Rayleigh Scattering (TDFRS) [1] technique (Figure 1) has been used for the

determination of the molecular diffusion (D), thermodiffusion (DT ) and the Soret coefficients (ST ) of

the mixtures. On the other hand, the thermogravitational (TG) technique [2] (Figure 1) and the Sliding

Simmetric Tubes (TSD) technique [3] (Figure 1) have been used for the determination of the thermal

diffusion coefficient (DT ) and the molecular diffusion coefficient of these mixtures respectively. In this

case the Soret coefficient of the mixtures has been determined using the relation ST = DT/D.

Figura 1: Experimental set-ups used in this study: TDFRS, thermogravitational column and SST.

The mixtures corresponding to toluene, n-hexane and n-dodecane compounds have been studied. The

obtained results for the molecular diffusion, the thermal diffusion and Soret coefficient show a good

agreement between the different techniques.

[1] S. Wiegand and W. Kohler, Thermal Nonequilib. Phenom, 129, pp. 36-43, 2002.

[2] P. Blanco, M.M. Mounir Bou-Ali, J.K. Platten, P. Urteaga, J. Madariaga and C. Santamaria, Journal of Chem-

ical Physics, 129, pp. 174504-174510, 2008.

[3] Alonso de Mezquia, D., Bou-Ali, M.M., Larranaga, M., Madariaga, J.A., and Santamarıa, C., Journal of

Physical Chemistry B, (accepted).

89

Thermal Diffusion Behavior ofAqueous Solution of Non-ionic

Surfactant C12E5Studied in Micellar Phase

Kousaku Maeda, Rio Kita, Naoki Shinyashiki,and Shin Yagihara

Department of Physics, Tokai University, Hiratsuka, Kanagawa 259-1292, Japan

[email protected]

We have studied the thermal diffusion behavior of non-ionic surfactant, C12E5 (penta

ethylene-glycol mono n-dodecyl ether), in water. We have employed a beam deflection method to

obtain the concentration gradient which is induced by temperature gradient. Soret coefficient ST,

thermal diffusion coefficient DT, and diffusion coefficient D are obtained in the concentration range of

5 - 45 wt% and in the temperature range of 15 - 35 oC.

Figure 1 shows the results of ST, D, and DT as a function of concentration of C12E5. The value

ofST decreases with increasing concentration. The decreasing behavior of ST can be fitted by an

inversely proportional-type function.The magnitudes of D and DT show linear behavior as a function

of concentration.

Figure 2 shows the developed concentration difference cagainst the applied temperature

difference Tfor various sample concentrations.The results show that the relationship between c and

Tholds the c = STcwatercC12E5 T. This implies thatST is independent on T in the investigated

temperature range.

We will show interesting signals of beam deflection method which is obtained at the phase

boundary of the micellar phase and hexagonal phase. This means the upper and the lower temperature

of the C12E5 solution corresponds to the miceller phase and the hexagonal phase, respectively. Here,

we found that the phase transition affects the formation of concentration gradient due to a heat of

transition.

DT / 10 12

m 2s 1

K 1

D / 1010 m

2 s1

ST,D

,DT

c / wt%

ST / 10 2

K 1

5.0 wt%10.0 wt%15.0 wt%20.0 wt%30.0 wt%40.0 wt%45.0 wt%

T / oC

c / c

wat

er c

C12

E5

Figure 1.Concentration dependence of Soret coefficientST, diffusion coefficient D,and thermal diffusion coefficient DT at 25 oC. Open symbol is obtained by DLS.

Figure 2. Temperature difference T

dependence of concentrationdifference cfor various concentrations of C12E5at 15 - 35 oC

[1]Ning, H., Kita, R., Kriegs, H., Luettmer-Strathmann, J., and Wiegand, S., J. Phys. Chem. B, 110, pp.

10746-10756, 2006.

[2] Ning, H., Datta, S., Sottmann, T., and Wiegand, S., J. Phys. Chem. B, 112, pp. 10927-10934, 2008.

[3] Polyakov, P. and Wiegand, S., Phys. Chem. Chem. Phys., 11, pp. 864-871, 2009.

90

Measurement of Soret Coefficients in Binary Solutions by

Phase-Shifting Interferometry

Juan F. Torres1,2), Atsuki Komiya3), Daniel Henry2), Shigenao Maruyama3)

1) Graduate School of Engineering, Tohoku University, 980-8577 (2-1-1) Sendai, Japan, [email protected]

2) Laboratoire de Mécanique des Fluides et d’Acoustique, UMR CNRS 5509, ÉcoleCentrale de Lyon, 36 avenueGuy-de-Collongue 69134EcullyCedex, France, [email protected], [email protected]

3) Institute of Fluid Science, Tohoku University, 980-8577 (2-1-1) Sendai, Japan, [email protected], [email protected]

Thermodiffusion in transparent solutions inside a Soret cell was visualized by phase-shifting interferometry. This high-resolution interferometer, initially used by Komiya et al. [1] to measure binary and ternary diffusion coefficients, was modified to measure the Soret coefficient in binary systems. The small height of the Soret cell, adjustable to 1.5–6 mm, allows a faster measurement of the Soret coefficient compared to similar methods developed in the literature [2].

In this study, ethanol-water solutions at different mean concentrations were subject to an upward linear-temperature gradient inside a Soret cell. The Soret cell, shown in Fig. 1(a), consists of a rectangular parallelepiped of variable heightand fixed surface area 10×20 mm2; the lateral walls of the cell are made of quartz; the upper and lower walls are made of copper. The temperature at the liquid boundary is measured by thermocouples and simultaneously controlled by two Peltier modules through a PID system. After filling the cavity with the ethanol-water solution, the experiment is initiated by creating a temperature difference between the upper and lower copper blocks. Then, mass transport occurs due to thermodiffusion. Since the Lewis number for the presentsystem is in the order of 102, the temperature field within the cell reaches a linear steady state much faster than the concentration field. Both transient temperature and concentration profiles are measured from the phase-shifted data until a zero mass flux is reached. The final concentration difference between the copper boundaries is obtained from the variation of the phase difference between phase-shifted data (b) and (c) shown in Fig. 1(b). The Soret coefficient isthen determined from the concentration and temperature differences between the copper walls measured by the phase-shifting interferometer and the thermocouples, respectively. The Soret coefficient for each mean concentration was measured within 30 min. The measured coefficients agree with the averaged literature values within 2.5%.

Even though Mialdun et al. [2] have already pioneered the measurement of thermodiffusion by digital interferometry, a long-time measurement and dense fringe patternwere required. In contrast, the current interferometric method is suitable for both short time and small temperature difference measurements, which will be an asset for the measurement of thermodiffusion in specific binary solutions, such as protein solutions [3] where conformational changes occur quickly.

�

2 m

m�

(a)� (b)� (c)�

�

(a) Experimental set-up (b) Phase-shifted data and its temporal variation Fig. 1 Experiment

[1] Komiya, A., Torres, J.F. and Maruyama, S., Defect and Diffusion Forum, 297-301, pp. 624-630, 2010. [2] Mialdun, A. and Shevtsova, V.M., International Journal of Heat and Mass Transfer, 51, pp. 3164-3178, 2008. [3] Vigolo, D.,Brambilla G. and Piazza R.,Physical Review E,75, 040401, 2007.

91

Traveling wave convection and heat transfer in a nanofluid

Ivan N. Cherepanov and Boris L. SmorodinPerm State University, Physics of Phase Transitions Department, 15, Bukirev str., 614990, Perm, Russia, [email protected]

Thermal diffusion (the Ludwig-Soret effect) influences the relationship between the concentration and temperature fields in molecular and colloidal mixtures in spite of the large difference in the sizes of the dispersed particles. The difference between the characteristic times of thermal and diffusive processes in colloidal mixtures is the cause of the interesting properties of convection in the systems with nanoparticles [1-3]. This paper presents the results of a theoretical study of convection in a cell filled with a suspension of solid nanoparticles in an incompressible viscous fluid stratified by i) the gravity; or ii) the thermal diffusion. The influence of sedimentation length and separation ratio on the oscillatory convection is studied.

Nonlinear convective flow patterns in a colloidal mixture are investigated in the case of cell with rigid, impermeable horizontal boundaries heated from below. To examine the complex nonlinear dynamics of the system, numerical simulations are carried out using a finite difference method. Two different conditions on vertical walls are considered: i) periodic and ii) rigid, impermeable, isothermal vertical boundaries (closed cell). Simulations have been performed for the parameter set adapted to laboratory experiments with the colloid mixture [1,3]. The following values were used: the Lewis number 4Le 10−

� , the Prandtl number Pr 5.5;10= , and the separation ratio 7.5; 0= −ψ . To describe the spatiotemporal changes in the different oscillatory scenarios the Fourier spectra of temporal oscillations have been studied.

In the case of gravity stratification mirror-glide (MG) symmetry of solutions is broken. In the case of thermal diffusion as in experimental work [3] it is considered the convective

processes origin on the background of initially homogeneous density profile after applying the thermal gradient. The different aspect ratio of the convective cell is investigated: Γ=4,6,8. On the first stage stationary convection appears. Further evolution depends on the vertical boundary conditions. In the periodical case convection is damped. In the closed cell travelling wave is stable.

Bifurcations, heat transfer and spatiotemporal properties of dissipative structures caused by the interaction of induced concentration gradient, nonlinear advection and mixing of the fluid with nanoparticles are considered. It is shown that the traveling wave regime is stable within a specified range of heating intensity (the Rayleigh number interval). When the Rayleigh number decrease to some critical value, the dynamic balance between mixing and sedimentation is broken, the convective motion settles down with discrete change of the Nusselt number, and the system passes into the mechanical equilibrium state.

[1] ��, �, �� ,��and Giglio, M., PRE, 66, 055301, 2002. [2] Shliomis, M. I., Smorodin, B. L, PRE, 71, 036312, 2005. [3] ��, ��, �� ,��PRL, ��

92

Computer generated Earth diffusion processes in liquid binary Al-Cu alloys

O. Sanchez1 , X. Ruiz2 , O. Batiste1, I. Mercader1

(1) Departament de Física Aplicada, Universitat Politècnica de Barcelona, UPC. Barcelona. Spain. (2) Institut d’Estudis Espacials de Catalunya, IEEC, Barcelona, Spain (also Departament Química Física i Inorgànica, Universitat Rovira i Virgili, URV. Tarragona, Spain)

The determination of diffusion coefficients in Al-based liquid binary alloys at high temperature and their relation to thermodynamics play a capital role in nucleation theories and in the correct predictions of the computational models of solidification. Up to now interdiffusion coefficients are usually treated as constants in computational growth models but real systems with large segregation coefficients, need the consideration of the concentration dependence of the difffusion coefficients because the strong gradients generated at the growing interfaces. The knowledge of these dependences can help to improve the accuracy of the numerical predictions. In addition, concentration gradients are correlated with chemical gradients, so it is very important to deep also in the determination and understanding of such thermodynamic relationships in order to be properly applied in the predictive models.

Classical determinations of the interdiffusion coefficient involved for a long time the use of capillary methods (long-capillaries and shear cells). In these cases the quantitative determination of the interdiffusion coefficients is made post-mortem, that is to say, by the use of chemical analyses of the final solidified samples. Nevertheless, recent X-ray radioscopic techniques allow in-situ measurements of concentration profiles by taking absorption pictures of capillary experiments during the transient of measure. In this sense, X-Ray techniques avoid the old typical blindness, opening a window to the high temperature experiment [1].

The aim of the present work is to extend previous solutal 2D finite volume calculations concerning the quantitative determination of diffusion coefficients in shear cells [2] in three aspects. The first one covers the natural 3D extension of the problem using an efficient cylindrical spectral code widely tested in the literature [3]. The second aspect is to check exhaustively all different details of the 3D model based on extensive comparisons between gray level radiograms and computational patterns projected in the plane of measure. The configuration used for checking is the so-called interdiffusion one. No centered or lateral thick layer configurations are discussed here. Initial conditions involved the localization of lighter liquid, AlCu15at%, in one side (top) and heavier liquid, AlCu10at%, in the other (bottom). Earth gravity acts parallel to the concentration gradient and points down (stable position). Finally, using the validated code, a third aspect is to make some predictions about the flow and comments about the error of using concentration profiles in different possible Earth experimental conditions.

[1] B. Zhang, A. Griesche, A. Meyer, Diffusion in Al-Cu melts studied by time-resolved X-ray

radiography. Physical Review Letters 104 (2010) 035902 – 035902-4.

[2] X. Ruiz, J. Pallarés, F.X. Grau, On the accuracy of the interdiffusion measurements at low and

moderate solutal Rayleigh numbers. Some computational considerations. International Journal of Heat and Mass Transfer 53 (2010) 3708-3720.

[3] I. Mercader, O. Batiste, A. Alonso, An efficient spectral code for incompressible flows in cylindrical

geometries, Computers and Fluids, 39 (2010) 215–224.

93

LIST OF PARTICIPANTS

94

Name of the Participant E-mail

1 Ali Khouzam [email protected]

2 Alonso de Mezquia David [email protected]

3 Augustin Matthias [email protected]

4 Batiste Oriol [email protected]

5 Bataller Henri [email protected]

6 Blums Elmars [email protected]

7 Bringuier Eric [email protected]

8 Bresme Fernando [email protected]

9 Bou-Ali M. Mounir [email protected]

10 Cordido Flaminio [email protected]

11 Cheddadi Abdelkhalek [email protected]

12 Cichos Frank [email protected]

13 Costanzo Andrea [email protected]

14 Delenda Nassim [email protected]

15 Croccolo Fabrizio [email protected]

16 Dennery F. M. [email protected]

17 Firoozabadi Abbas [email protected]

18 Fedorov Oleg [email protected]

19 Gaponenko Yuri [email protected]

20 Galliéro Guillaume [email protected]

21 Giraudet Cedric [email protected]

22 Gebhardt Matthias [email protected]

23 Glavatskiy Kirill [email protected]

24 Goldobin Denis S. [email protected]

25 Hannaoui Rachid [email protected]

26 Hennenberg Marcel [email protected]

27 Henry Daniel [email protected]

28 Hodor Ilie [email protected]

29 Kita Rio [email protected]

30 Kohler Werner [email protected]

31 Koniger Andreas [email protected]

32 Larrañaga Miren [email protected]

33 Legros Jean Claude [email protected]

34 Luecke Manfred [email protected]

35 Luybimova Tatyana [email protected]

36 Maeda Kousaku [email protected]

37 Martin Alain [email protected]

38 Mazzoni Stefano [email protected]

39 Melnikov Denis [email protected]

40 Mercader Isabel [email protected]

41 Mezulis Ansis [email protected] 42 Mialdun Aliaksandr [email protected]

43 Mojtabi Abdelkader [email protected]

44 Montel François [email protected]

95

45 Moritz Kreysing [email protected]

46 Morozov Konstantin I. [email protected]

47 Naumann Philipp [email protected]

48 Nepomnyashchy Alexander [email protected]

49 Ortiz de Zarate Jose M. [email protected]

50 Ouarzazi Mohamed-Najib [email protected]

51 Quentin Galand [email protected]

52 Reinhart Guillaume [email protected]

53 Ribeiro Ana C.F. [email protected]

54 Ripoll Marisol [email protected]

55 Romer Frank [email protected]

56 Rousseau Bernard [email protected]

57 Ruiz Xavier [email protected]

58 Ryzhkov Ilya I. [email protected]

59 Saez Nuria [email protected]

60 Salloum Abou Jaoude G. [email protected]

61 Sanchez Odalys [email protected]

62 Santos Cecilia I.A.V. [email protected]

63 Sechenyh Vitaliy [email protected]

64 Shevtsova Valentina [email protected]

65 Shinohara, Haruka [email protected]

66 Slavtchev Slavtcho [email protected]

67 Smorodin Boris L. [email protected]

68 Sottmann Thomas [email protected]

69 Sprenger Lisa [email protected]

70 Torres Juan F. [email protected]

71 Triller Thomas [email protected]

72 Wang Zilin [email protected]

73 Wiegand Simone [email protected]

74 Wurger Alois [email protected]

75 Van Vaerenbergh Stefan [email protected]

76 Vesovic Velisa [email protected]

77 Yang Mingcheng [email protected]

78 Yoshinaga Natsuhiko [email protected]

79 YACINE Loujaine [email protected]

80 Yasnou Viktar [email protected]

81 Zablotsky Dmitry [email protected] �

96

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