Surface tension Oct 2013. Dispersed liquids in nature.
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Transcript of Surface tension Oct 2013. Dispersed liquids in nature.
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Surface tension
Oct 2013
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Dispersed liquids in nature
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Artificiallly dispersed liquids
http://www-math.mit.edu/~bush/gallery.htmlhttp://lmlm6-62.univ-lille1.fr/lml/perso/pbrunet/page_perso.html
http://www.dolomite-microfluidics.com/products/system-solutions
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There is an extra energy associated with a surface
Molecules on the surface are less bounded than molecules in the bulk.
There is therefore an energy associated with a free surface.
More rigorously: there is a free energy associated with an interface.
This energy is the surface tension g
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Solids have a surface tension too
More about this later
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How many molecules are on the surface of a 10-nm droplet ?
The molar volume of liquid nitrogen is 34.6 cm³/mol, which converts to a molecule « diameter » of 4.8 Ǻ
Consider a drop of diameter D = 100 Ǻ
The total volume is 4/3*p*(D/2)3, and that of the surface layer is 4/3*p*[ (D/2)3 – (D/2-t)3]
A droplet of 10 nm in diameter has therfore 25 % of the molecules on the surface!
t ~ 4.8 Ǻ
D = 100 Ǻ
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The surface tension can be thought of as a force
http://www.funsci.com/fun3_en/exper2/exper2.htm
F
A
The energy per unit area is gIt can often be thought of as a force
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A didactic setup(Cf. Wilhelmy plate)
http://www.funsci.com/fun3_en/exper2/exper2.htm
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Values of g for some usual liquids
Substance Surface tension (mN/m)
Water (10°C) 74.2
Water (25°C) 72.0
Water (50°C) 67.9
Mercury (25°C) 485.5
Acetone (25°C) 23.5
Ethanol (25°C) 23.2
Formamide (25°C) 57.0
Nitrogen (77°K) 8.85
Values from Butt, Graf & Kappl, Physics and Chemistry of Interfaces, Wiley, 2006
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A rough estimation of g from the energy of vaporization
Cyclohexane @ 25°CUevap = 30.5 kJ/mol r=773 kg/m³M=84.16 g/mol
Assuming a cubic structure (6-coordinated), Uevap converts to 5.08 kJ/mol for each bond.Each molecule on the surface has one missing bond.All is left to determine is the area of each molecule on the surface.This can be estimated as a² with NA a³ r = M, i.e. a = 0.565 nm
The final estimate is about 26 mJ/m²(the experimental value is ~ 25 mJ/m²)
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Stefan’s law
From K.S. Birdi, Surface and Colloid Chemistry, Principles and Applications
2010, CRC Press
Jozef Stefan 1835-1893
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There is an entropic contribution to sin addition to the energetic contribution
T
P
Tc
gas
liquid
solid
𝜎=𝜎0 (1−𝑇 /𝑇𝑐 )𝑛 with n ~ 1
The surface tension vanishes at the critical temperature
𝑑𝑈=𝑇𝑑𝑆+𝜎 𝑑𝐴𝑑𝐹=−𝑆𝑑𝑇+𝜎 𝑑𝐴with𝐹=𝑈 −𝑇𝑆
The corresponding Maxwell’s relation reads
( 𝜕𝑆𝜕 𝐴 )𝑇
=−( 𝜕𝜎𝜕𝑇 )𝐴
¿−𝑑𝜎𝑑𝑇
≥0
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Surfactants
Surfactant classification according to the composition of
their head: nonionic, anionic, cationic, amphoteric.
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Effect of surfactants on surface tension
Critical micellar concentration
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Minimal surfaces
Costa’s minimal surface (1982)
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Minimal surfaces in materials sciences
Micron, Volume 38, July 2007, Pages 478–485
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Young-Laplace equation
R
Pext
Pin
g g
The mechanical equilibrium of a half-droplet requires
For a more complex interface, the relation is
with R1 & R2 being the principal radii of curvature
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Laplace
Nous devons donc envisager l’état présent de l’univers comme l’effet de son état antérieur et comme la cause de celui qui va suivre. Une intelligence qui, pour un instant donné, connaîtrait toutes les forces dont la nature est animée, et la situation respective des êtres qui la composent, si d’ailleurs elle était assez vaste pour soumettre ces données à l’Analyse, embrasserait dans la même formule les mouvements des plus grands corps de l’univers et ceux du plus léger atome : rien ne serait incertain pour elle et l’avenir, comme le passé serait présent à ses yeux. (Laplace, Essai philosophique sur les probabilités, 1795)
Géomètre de première catégorie, Laplace n’a pas tardé à se montrer un administrateur plus que médiocre ; de son premier travail nous avons immédiatement compris que nous nous étions trompés. Laplace ne traitait aucune question d’un bon point de vue : il cherchait des subtilités de partout, il avait seulement des idées problématiques et enfin il portait l’esprit de l’infiniment petit jusque dans l’administration. (Napoléon Bonaparte, à propos du passage de Laplace au ministère de l’intérieur)
Pierre-Simon de Laplace(1749-1827)
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Thomas Young
Thomas Young 1773-1829
• Optics: the double-slit interference experiments• Mechanics: Young’s modulus• Wetting phenomena: Young-Laplace & Young-Dupré relations• Vision and color theory: Young-Helmholtz, 3-dimensional color space• Physiology: pulse speed• Linguistics: he introduced the idea of « Indo-European languages »• Egyptology: he decyphered the hieroglyphs (before Champollion)• Music: Young temperament
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What happens now?
A small and a large droplets lie on a fiber wetted by a thin liquid film.
How does the system evolve?
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Laplace equation applies to solid particles as well
Lattice Contraction and Surface Stress of fcc NanocrystalsJ. Phys. Chem. B, 2001, 105 (27), pp 6275–6277
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Ostwald ripening
Wilhelm Ostwald1853-1932
http://iopscience.iop.org/1367-2630/7/1/040/media/movie1_SD.mpg
New Journal of Physics Volume 7 2005D G A L Aarts et al 2005 New J. Phys. 7 40 doi:10.1088/1367-2630/7/1/040
Interfacial dynamics in demixing systems with ultralow interfacial tension
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What is the pressure in a soap bubble ?
« Amusons nous sur la terre comme sur l'onde,Malheureux celui qui se fait un nom
Richesses, Honneurs, Faux éclat de ce monde Tout n’est que boules de savon. »
Taken from the Nobel lecture of P.-G. de Gennes Rev. Modern Phys. 64 (1992) 645
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And in an anti-bubble?
http://www.youtube.com/watch?v=6r_8Pp9WkF0
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Some menisci configurations
1 2
Think about the pressure difference between 1 and 2
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Plateau-Rayleigh instability
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Plateau-Rayleigh instabilities in materials science
Appl. Phys. Lett. 85, 5337 (2004)
Nano Lett., 2007, 7 (1), pp 183–187
Cu nanowires
PMMA in pores
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Joseph Plateau
Joseph Plateau1801-1883
Doctoral thesis at the University of Liège (1829)Professor of experimental physics in Ghent University (1835)
The phenakistiscope(“phenakizein” means “to deceive”)
Plateau’s laws
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John Strutt (1842-1919-3rd baron Rayleigh
Second Cavendish professor of physics at Cambridge (following Maxwell)
• Dynamic soaring (flying of birds)• Rayleigh scattering (why is the sky blue)• Rayleigh waves (acoustics and mechanics)• Rayleigh-Jeans law (blackbody radiation)• Discovery of Argon with Ramsay (Nobel Prize for physics 1904)• Etc.
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Other types of capillary instabilities
Soft Matter, 2008,4, 1403-1413
Rayleigh-Taylor instabilityhttp://www.physicscentral.com/explore/
pictures/cup.cfm
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Sessile drop or bubble
New J. Phys. 5 (2003) 59
Tate’s law
𝑚𝑔=2𝜋 𝑅𝜎
is a rough approximation.
More accurate measurements are obtained by analyzing the shape of droplet using Laplace’s law.Can you do that?
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The spinning droplet
Optics and Lasers in EngineeringVolume 46, Issue 12, December 2008, Pages
893–899
for small values of s(mostly intefacial tensions)
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Capillary forces
What is the force between two spheres?
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A more accurate analysis of forces involved in g measurement
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Surfactants in nature
Pulmonary surfactants
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What can you tell about the pressure in a liquid from the shape of a rising bubble?
http://people.rit.edu/andpph/exhibit-bubbles.html