Molecular dynamics simulations of the surface tension of oxygen-supersaturatedwaterS. Jain, and L. Qiao

Citation: AIP Advances 7, 045001 (2017); doi: 10.1063/1.4979662View online: https://doi.org/10.1063/1.4979662View Table of Contents: http://aip.scitation.org/toc/adv/7/4Published by the American Institute of Physics

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AIP ADVANCES 7, 045001 (2017)

Molecular dynamics simulations of the surface tensionof oxygen-supersaturated water

S. Jain and L. Qiaoa

School of Aeronautics and Astronautics Engineering, Purdue University, West Lafayette,Indiana 47907, USA

(Received 2 February 2017; accepted 21 March 2017; published online 3 April 2017)

In this work, non-reactive molecular dynamic simulations were conducted to deter-mine the surface tension of water as a function of the concentration of the dissolvedgaseous molecules (O2), which would in turn help to predict the pressure insidethe nanobubbles under supersaturation conditions. Knowing the bubble pressureis a prerequisite for understanding the mechanisms behind the spontaneous com-bustion of the H2/O2 gases inside the nanobubbles. First, the surface tension ofpure water was determined using the planar interface method and the Irving andKirkwood formula. Next, the surface tension of water containing four differentsupersaturation concentrations (S) of O2 gas molecules was computed consideringthe curved interface of a nanobubble. The surface tension of water was found todecrease with an increase in the supersaturation ratio or the concentration of thedissolved O2 gas molecules. © 2017 Author(s). All article content, except where oth-erwise noted, is licensed under a Creative Commons Attribution (CC BY) license(http://creativecommons.org/licenses/by/4.0/). [http://dx.doi.org/10.1063/1.4979662]

Combustion-based small-scale energy devices have applications in many fields, e.g., portablepower devices, sensors, actuators, unmanned aerial microvehicles, microthrusters, and micro-heatingdevices.1–3 At smaller scales, the surface-area-to volume ratio of the combustor increases, and thecharacteristic inertia time decreases. This leads to reduced mixing, increased heat loss from thewall, and strong wall-flame kinetic interactions.4 The successful development of small-scale powergeneration systems continues to face significant challenges. One of the biggest difficulties is that asa result of the increased surface-area-to-volume ratio at smaller scales, combustion is found difficultto be initiated and sustained because heat loss from the wall exceeds heat release from the chemicalreactions.5 Loyal to the scaling law, we would expect combustion to be impossible at nanoscalebecause heat loss would profoundly dominate chemical reactions. However, this is not always thecase. Svetovoy et al.6,7 accidentally discovered that the stoichiometric H2/O2 mixture in nanobubblescould be ignited spontaneously with bubble sizes smaller than 150 nm. These nanobubbles wereproduced from short-time (1-100 µs) water electrolysis by applying high-frequency alternating signvoltage pulses, which resulted in the H2 and the O2 gas production above the same electrode. Motivatedby this, Jain et al.8 developed an independent experiment, similar to that of Svetovoy et al.,6,7 butwith more quantitative determination of the temperature change of the electrode surface, whichwas achieved by using an in-built micro-fabricated Pt resistance thermal sensor. They found that thecombustion only occurred for frequencies greater than 15 kHz and that the amount of heat released wasmaximized for a duty cycle of 0.5, corresponding to the stoichiometric H2/O2 gas production. Thesewere consistent with the findings of Svetovoy et al.,6,7 suggesting that the combustion had indeed takenplace inside the nanobubbles. Recently, in a review paper by Svetovoy et al.,9 the various experimentalwork conducted by their group in relation to the combustion inside the nano/micro-bubbles wassummarized. Moreover, the authors proposed the combustion process to be surface-dominated andto occur at room temperature. Thus, knowing the bubble pressure is a significant first step before thereaction kinetics could be understood.

aCorresponding author: lqiao@purdue.edu. Tel.: (765)494-2040.

2158-3226/2017/7(4)/045001/6 7, 045001-1 © Author(s) 2017

045001-2 S. Jain and L. Qiao AIP Advances 7, 045001 (2017)

As a result of the capillary effect, the pressure inside a nanobubble is much higher as comparedto the pressure inside a micro-sized bubble, which implies that the gases inside the nanobubble can-not be in equilibrium with the atmosphere, since larger pressure means larger chemical potential,and consequently the nanobubble should dissolve (in a saturated environment).10 This contradictsthe longevity and the apparent stability of nanobubbles observed experimentally.11–36 The nanobub-bles can be divided into two categories: surface nanobubbles and bulk nanobubbles. The surfacenanobubbles are gas-filled cavities on a surface in the form of a spherical cap with the uniform radiusof curvature and geometrical center located beneath the surface, whereas the bulk nanobubbles arespherical shaped gas-filled cavities located in the interior of a liquid. The first experimental evidenceof bulk nanobubbles was reported by Johnson et al.,11 where the bubbles were produced by shear inseawater and were observed to be stable for more than 22 hrs. Following this work, a number of otherstudies were conducted to understand the generation and stabilization of these bulk nanobubbles.12–22

As far as the surface nanobubbles are considered, Parker et al.23 first reported their existence to explainthe long-range attraction between the hydrophobic surfaces. After which, many AFM (atomic forcemicroscopy) measurements have confirmed the existence of these spherical-caped gaseous nanobub-bles at solid-liquid interfaces.24–36 Refer to the reviews given by Alheshibri et al.37 and Lohse38 for amore detailed overview on the bulk and the surface nanobubbles. In our previous experimental work5

and in studies performed by Svetovoy et al6,7,9 both kind of nanobubbles (surface and bulk) wereproduced during the water electrolysis processes.

Three hypotheses can explain the contradiction of the experimental evidence of nanobubbleexistence and the paradoxical L-Y (Laplace-Young) equation which suggests that nanobubbles cannotbe stable: (1) The L-Y equation is not valid at nanoscale; (2) The nanobubbles are in equilibrium butin a supersaturated solution; (3) “The traffic jam effect.”39

(1) The L-Y equation, which assumes the application of macroscopic, continuum thermodynamicson the nanoscopic length scales, is derived from balancing the mechanical forces on the bubblesurface. Thus, if the measured stability of nanobubbles is taken as a proof to invalidate theL-Y equation, then the applications of similar continuum theories on the nanoscopic lengthscales such as, the application of macroscopic hydrodynamics to microfluidic flow and theDLVO (Derjaguin, Landau, Verwey, and Overbeek) theory, need to be reconsidered. However,there are a number of experimental and computational work done to support the quantitativeapplication of such continuum theories on the nanoscopic scales with the nanobubbles being theonly exception.10 Thus the L-Y equation, which is nothing but a minimization of the total freeenergy with respect to the bubble radius can be assumed to be valid even for the nanobubbles.

(2) For a nanobubble to be completely stable in a liquid, it needs to be in both mechanical and chem-ical equilibrium simultaneously. The application of the L-Y equation assumes only mechanicalequilibrium, thus for the bubble to be in chemical equilibrium, the chemical potential of the gasesinside and outside the bubble must also be equal i.e. the liquid must be super-saturated with thebubble gases. The supersaturation (S) is defined as the ratio of the concentration of the gas (C)in the liquid to the saturated concentration of the gas, at 1 atm, (C*) i.e. S = C/C*. Moody40

and He41 conducted monte-carlo simulations to calculate the surface tension of supersaturatedLennard-Jones planar liquid-vapor interfaces. They found the surface tension value to decreasewith increasing supersaturation and to vanish at the vapor spinodal. Thus, the surface tension ofwater needs to be modified according to the local supersaturation value in order to get the correctpressure difference across the nanobubble. All of the previous studies40,41 relating to supersat-urations have been performed for pure systems. However, in this work heterogeneous systemswere considered where molecular dynamic simulations were conducted to determine the surfacetension of water as a function of the concentration of the dissolved gaseous molecules undersupersaturation conditions. Here only O2 molecules were considered but the qualitative behaviorof the surface tension value with other types of gases like H2 will be similar. Thus, the mainpurpose was to determine the internal pressure of the nanobubbles within which spontaneouscombustion of the H2/O2 gases takes place.

(3) A nanobubble can also be stable in a closed container where the gases are not allowed to leavethe liquid into the atmosphere. Due to the initial diffusion of the gases out of the nanobubbles,

045001-3 S. Jain and L. Qiao AIP Advances 7, 045001 (2017)

the liquid surrounding the nanobubbles could become supersaturated and thus an equilibriumcould be established that stabilizes the nanobubbles. However, if the container is opened, then thegases leave the liquid, allowing the nanobubbles to completely dissolve. This effect is called “thetraffic jam effect”, as studied by Weijs.39 However, considering our experimental conditions,5

the explanation (2) is more relevant as the liquid droplet was exposed to the atmosphere with theliquid being continuously supersaturated with the gases produced from the water electrolysis.

The simulations were performed using LAMMPS,42 an open source MD simulation codedeveloped by Sandia National Lab. The simulation system consists of three types of interactions:(1) H2O–H2O Interactions: The water molecules were modeled using the extended simple pointcharge (SPC/E) force field,43 which considers both the columbic and the dispersive Lennard-Jones(LJ) interactions. A partial charge of �0.8476|e| and 0.4238|e| was used for the oxygen and the hydro-gen atom respectively, where |e| refers to the electron charge unit. A rigid tetrahedral angle (H–O–H)of 109.47o and a bond length (O-H) of 0.1 nm was assumed. In addition, the SHAKE algorithm44,45

was used to rigidify the water molecules; (2) O2–O2 Interactions: The oxygen molecules were mod-eled as linear with the partial charges on the oxygen atoms being assumed to be zero. The equilibriumbond length (O-O) was set to 0.121 nm. Both the L-J and the columbic interactions were consideredsimilar to the H2O-H2O interactions; (3) H2O–O2 Interactions: The interactions between the waterand the oxygen molecules were obtained again by adding the columbic and the L-J contributions.The values of σH2O-O2 and εH2O-O2 terms were calculated by using the Lorentz-Berthelot mixingrules:46,47

σij =12

(σi + σj) and εij =√εiεj (1)

The L-J parameters for each atom type are given in Table I:48

In order to validate the SPC/E water model and the simulation parameters, the surface tension ofpure water was first determined. A planar interface was used to calculate the surface tension accordingto the Irving and Kirkwood formula.49 The simulation box, as shown in Fig. 1, was divided into threeslabs of sizes (7 x 7 x 7 nm) with the middle slab consisting of N = 12,000 water molecules based onthe water density at P = 1 atm and T = 300 K. Periodic boundary conditions were used in all the threedirections and a time step of 2 fs was used. After the initial set-up of the computational domain, thesystem equilibration to 300 K and 1 atm using the Nose-Hoover thermostat50,51 and barostat52 with arelaxation time of 200 fs and 1000 fs, respectively, was performed for 2 ns. Then the production runwas performed under the NVT (constant number, volume and temperature) ensemble for another 2ns. For all the simulations, a high L-J cut-off value of 2.5 nm was used to ensure that errors introducedinto the surface tension calculations due to the L-J tail-corrections were minimum. A surface tensionvalue of 59.83 ± 2 mN/m was obtained similar to the value of 63.6 mN/m obtained by Vega et al.53

using the SPC/E rigid water model. In a study performed by Vega et al.,53 much better agreementwith the experimental surface tension value of 71.3 mN/m was obtained by the SPC/E, TIP4P/Ew,and TIP4P/2005 models than the SPC, TIP3P, and TIP4P water models.53 Thus, because of the wideuse and simplicity, all of the following surface tensions were conducted using the SPC/E rigid watermodel.

In the nanobubble experimental study, steady faradic currents up to 0.3 mA were obtained for a20 µm x 20 µm sized electrode surface.8 Using the diffusion length and the faradic current equation,the amount of super-saturation in the liquid water surrounding the electrodes could be estimated. Thediffusion length (lO2) is given by the following equation:7

lO2 =√

DO2t (2)

TABLE I. LJ parameters.

Parameter H2O (O atom) H2O (H atom) O2 (O atom)

σ (Ao) 3.166 0 3.094ε (kcal/mol) 0.1553 0 0.09538

045001-4 S. Jain and L. Qiao AIP Advances 7, 045001 (2017)

FIG. 1. A snapshot of the simulation box.

where DO2 is the diffusion coefficient of the oxygen molecule6 (2x10-9 m2/s) and t is half the timeperiod of a complete cycle. The concentration of the dissolved oxygen molecules (CO2) can becalculated using the faradic current equation7 as follows:

CO2 = It

4eAlO2(3)

where I is the faradic steady state current, e is the electron charge value and A is the cross-sectionalarea of the electrode surface. Using the steady state current value of 0.3 mA, 20 µm x 20 µm electrodesurface and t = 33 µs (for a 15 kHz alternating polarity pulse), the CO2 value comes out to be1.5x1020 cm-3. The relative supersaturation (S), which is the ratio of the gas concentration (CO2) tothe saturated concentration, CO2

* = 7.7x1017 cm-3, (at P = 1 atm and T = 300 K)7 comes out to bearound 200. Thus, in the present MD simulations, the water system was supersaturated with O2 gasmolecules with S values ranging from 1-850, which covers most of the saturation levels achieved in theexperiment.

Initially, the O2 and the H2O molecules were randomly added to the simulation box (7 nmx 7 nm x 7nm). The number of initial O2 gas molecules added was based on the supersaturation valuedesired. First the system equilibration to 300 K and 1 atm was performed for 2 ns. The relaxationtime for the Nose-Hoover thermostat and barostat was kept same as that of the pure water simulationi.e. 200 fs and 1000 fs, respectively. A time step of 2 fs was used with the 3d bin sizes being 7 nmx 7 nm x 5 Ao. The L-J-cut off value was 2.5 nm and periodic boundary conditions were used in allthe three directions. After the equilibration, a cavity of size 2.5 nm was created at the center of thesimulation box (by deleting some of the water molecules). The simulation was then run under theNVT conditions (300 K) until the bubble radius attains a steady state value, after which the pressureinside and outside of the bubble was calculated. The surface tension value was calculated by assumingthe validity of the Laplace-Young equation and by using the ∆P across the bubble surface along withthe equilibrated bubble radius value. Fig. 2 shows the bubble growth and stability after the creationof the cavity. In the figure, only the O2 molecules are shown for the visualization purposes.

The supersaturation value of the system changes with time because of the bubble growth. Since,the surface tension values were calculated based on the final bubble radius, only the final supersatu-ration values need to be considered. This is in contrast to the bubble experiment, where the amount ofsupersaturation remained constant because of the constant supply of gases. Four cases correspondingto the final supersaturation values of 1, 200, 400 and 850 were considered. Fig. 3 (a) shows that therelative surface tension of water decreases with an increase in the supersaturation ratio (final) or theconcentration of the dissolved oxygen gas molecules. Svetovoy et al.6 observed that spontaneouscombustion took place only for bubbles with a size smaller than 150 nm. For a bubble size of 150nm, based on the calculated surface tension values from the present MD simulations, we predictthe pressure of around 10 atm can be reached inside the nanobubbles (corresponding to 15 kHz and

045001-5 S. Jain and L. Qiao AIP Advances 7, 045001 (2017)

FIG. 2. Bubble dynamics after the creation of the cavity in the system; A: t=200 ps; B: t=1 ns; C: t = 2 ns. The particular caseshown corresponds to S = 200. The blue molecules represent O2.

FIG. 3. a) Relative surface tension of water, γ(S)/γ(S=1, saturated water), as a function of the supersaturation; b) Internalbubble pressure as a function of the bubble diameter for different supersaturation values.

S = 200). For smaller bubbles, the internal pressure is even higher. Fig. 3 (b) shows how the pressureinside the bubble changes with the bubble diameter, for different supersaturation values. A big dropin the bubble pressure was obtained as the value of S was changed from 1 to 200 but after that thechange in the bubble pressure with S is not significant.

In summary, we performed molecular dynamics simulations to determine the surface tensionof O2-supersaturated water. The surface tension of water was found to decrease with the amount ofsupersaturation, thus, the internal pressure in nanobubbles is much smaller than what would havebeen predicted using the planar-interface surface tension value of water. Nevertheless, the pressureinside nanobubbles is still very high, which may provide a suitable environment for spontaneousignition and combustion to occur.

This work was supported by the National Science Foundation with Dr. Song-Charng Kong asthe technical monitor.

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