Dynamic van der Waals theory

Thermo-osmosis of a near-critical binary fluid mixture: A general formulation and universal flow direction

We consider a binary fluid mixture, which lies in the one-phase region near the demixing critical point, and study its transport through a capillary tube linking two large reservoirs. We assume that short-range interactions cause preferential adsorption of one component onto the tube's wall. The adsorption layer can become much thicker than the molecular size, which enables us to apply hydrodynamics based on a coarse-grained free-energy functional. For transport processes induced by gradients of the pressure, composition, and temperature along a cylindrical tube, we obtain the formulas of the Onsager coefficients to extend our previous results on isothermal transport, assuming the critical composition in the middle of each reservoir in the reference equilibrium state. Among the processes, we focus on thermo-osmosis-mass flow due to a temperature gradient. We explicitly derive a formula for the thermal force density, which is nonvanishing in the adsorption layer and causes thermo-osmosis. This formula for a near-critical binary fluid mixture is an extension of the conventional formula for a one-component fluid, expressed in terms of local excess enthalpy. We predict that the direction of thermo-osmotic flow of a mixture near the upper (lower) consolute point is the same as (opposite to) that of the temperature gradient, irrespective of which component is adsorbed on the wall. Our procedure would also be applied to dynamics of a soft material, whose mesoscopic inhomogeneity can be described by a coarse-grained free-energy functional.

General wetting energy boundary condition in a fully explicit nonideal fluids solver

We present an explicit finite-difference method to simulate the nonideal multiphase fluid flow. The local density and momentum transport are modeled by the Navier-Stokes equations and the pressure is computed by the van der Waals equation of the state. The static droplet and the dynamics of liquid-vapor separation simulations are performed as validations of this numerical scheme. In particular, to maintain the thermodynamic consistency, we propose a general wetting energy boundary condition at the contact line between fluids and the solid boundary. We conduct a series of comparisons between the current boundary condition and the constant contact angle boundary condition as well as the stress-balanced boundary condition. This boundary condition alleviates the instability induced by the constant contact angle boundary condition at θ≈0 and θ≈π. Using this boundary condition, the equilibrium contact angle is correctly recovered and the contact line dynamics are consistent with the simulation by applying a stress-balanced boundary condition. Nevertheless, unlike the stress-balanced boundary condition for which we need to further introduce the interface thickness parameter, the current boundary condition implicitly incorporates the interface thickness information into the wetting energy.

Electron–phonon effects on the photoacoustic response of gold core–silica shell nanoparticles: From the linear regime to nanocavitation

Coating gold nanostructures with a silica shell has been long considered for biomedical applications, including photoacoustic imaging. Recent experimental and modeling investigations reported contradicting results concerning the effect of coating on the photoacoustic response of gold nanostructures. Enhanced photoacoustic response is generally attributed to facilitated heat transfer at the gold/silica/water system. Here, we examine the photoacoustic response of gold core–silica shell nanoparticles immersed in water using a combination of the two temperature model and hydrodynamic phase field simulations. Here, of particular interest is the role of the interfacial coupling between the gold electrons and silica shell phonons. We demonstrate that as compared to uncoated nanoparticles, photoacoustic response is enhanced for very thin silica shells (5 nm) and short laser pulses, but for thicker coatings, the photoacoustic performance are generally deteriorated. We extend the study to the regime of nanocavitation and show that the generation of nanobubbles may also play a role in the enhanced acoustic response of core–shell nanoparticles. Our modeling effort may serve as guides for the optimization of the photoacoustic response of heterogeneous metal–dielectric nanoparticles.

Improved three-dimensional thermal multiphase lattice Boltzmann model for liquid-vapor phase change

Modeling liquid-vapor phase change using the lattice Boltzmann (LB) method has attracted significant attention in recent years. In this paper, we propose an improved three-dimensional thermal multiphase LB model for simulating liquid-vapor phase change. The proposed model has the following features. First, it is still within the framework of the thermal LB method using a temperature distribution function and therefore retains the fundamental advantages of the thermal LB method. Second, in the existing thermal LB models for liquid-vapor phase change, the finite-difference computations of the gradient terms ∇·u and ∇T usually require special treatment at boundary nodes, while in the proposed thermal LB model these two terms are calculated locally. Moreover, in some of the existing thermal LB models, the error term ∂_{t_{0}}(Tu) is eliminated by adding local correction terms to the collision process in the moment space, which causes these thermal LB models to be limited to the D2Q9 lattice in two dimensions and the D3Q15 or D3Q19 lattice in three dimensions. Conversely, the proposed model does not suffer from such an error term and therefore the thermal LB equation can be constructed on the D3Q7 lattice, which simplifies the model and improves the computational efficiency. Numerical simulations are carried out to validate the accuracy and efficiency of the proposed thermal multiphase LB model for simulating liquid-vapor phase change.

Extension of van der Waals theory for supersaturated thin films

The vapor/liquid interface properties play an essential role in both fundamental models and practical applications. Here, we describe a thin planar film surrounded by supersaturated vapor using the extension of van der Waals theory. We derive the analytical equilibrium conditions, which allow us to define the stress tensor and surface tension. Our model provides the surface tension dependence on the film thickness, correctly reflecting the vapor/liquid interface until full disappearance. The numerical estimations show that the surface tension crucially depends on the film thickness-a decrease in the thickness of 50% results in an 85% reduction in the surface tension.

Stochastic order parameter dynamics for phase coexistence in heat conduction

We propose a stochastic order parameter model for describing phase coexistence in steady heat conduction near equilibrium. By analyzing the stochastic dynamics with a nonequilibrium adiabatic boundary condition, where total energy is conserved over time, we derive a variational principle that determines thermodynamic properties in nonequilibrium steady states. The resulting variational principle indicates that the temperature of the interface between the ordered region and the disordered region becomes greater (less) than the equilibrium transition temperature in the linear response regime when the thermal conductivity in the ordered region is less (greater) than that in the disordered region. This means that a superheated ordered (supercooled disordered) state appears near the interface, which was predicted by an extended framework of thermodynamics proposed in Nakagawa and Sasa [Liquid-Gas Transitions in Steady Heat Conduction, Phys. Rev. Lett. 119, 260602 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.260602.].

An Analytical Investigation of Natural Convection of a Van Der Waals Gas over a Vertical Plate

The study focused on a theoretical study of natural convection in a van der Waals gas near a vertical plate. A novel simplified form of the van der Waals equation derived in the study enabled analytical modeling of fluid flow and heat transfer. Analytical solutions were obtained for the velocity and temperature profiles, as well as the Nusselt numbers. It was revealed that nonlinear effects considered by the van der Waals equation of state contribute to acceleration or deceleration of the flow. This caused respective enhancement or deterioration of heat transfer. Results for a van der Waals gas were compared with respective computations using an ideal gas model. Limits of the applicability of the simplified van der Waals equations were pinpointed.

Kinetic Simulations of Compressible Non-Ideal Fluids: From Supercritical Flows to Phase-Change and Exotic Behavior

We investigate a kinetic model for compressible non-ideal fluids. The model imposes the local thermodynamic pressure through a rescaling of the particle’s velocities, which accounts for both long- and short-range effects and hence full thermodynamic consistency. The model is fully Galilean invariant and treats mass, momentum, and energy as local conservation laws. The analysis and derivation of the hydrodynamic limit is followed by the assessment of accuracy and robustness through benchmark simulations ranging from the Joule–Thompson effect to a phase-change and high-speed flows. In particular, we show the direct simulation of the inversion line of a van der Waals gas followed by simulations of phase-change such as the one-dimensional evaporation of a saturated liquid, nucleate, and film boiling and eventually, we investigate the stability of a perturbed strong shock front in two different fluid mediums. In all of the cases, we find excellent agreement with the corresponding theoretical analysis and experimental correlations. We show that our model can operate in the entire phase diagram, including super- as well as sub-critical regimes and inherently captures phase-change phenomena.

Transient coarsening and the motility of optically heated Janus colloids in a binary liquid mixture

A gold-capped Janus particle suspended in a near-critical binary liquid mixture can self-propel under illumination. We have immobilized such a particle in a narrow channel and carried out a combined experimental and theoretical study of the non-equilibrium dynamics of a binary solvent around it - lasting from the very moment of switching illumination on until the steady state is reached. In the theoretical study we use both a purely diffusive and a hydrodynamic model, which we solve numerically. Our results demonstrate a remarkable complexity of the time evolution of the concentration field around the colloid. This evolution is governed by the combined effects of the temperature gradient and the wettability, and crucially depends on whether the colloid is free to move or is trapped. For the trapped colloid, all approaches indicate that the early time dynamics is purely diffusive and characterized by composition layers travelling with constant speed from the surface of the colloid into the bulk of the solvent. Subsequently, hydrodynamic effects set in. Anomalously large nonequilibrium fluctuations, which result from the temperature gradient and the vicinity of the critical point of the binary liquid mixture, give rise to strong concentration fluctuations in the solvent and to permanently changing coarsening patterns not observed for a mobile particle. The early time dynamics around initially still Janus colloids produces a force which is able to set the Janus colloid into motion. The propulsion due to this transient dynamics is in the direction opposite to that observed after the steady state is attained.

Dependence of the surface tension and contact angle on the temperature, as described by the diffuse-interface model

Four results associated with the diffuse-interface model (DIM) for contact lines are reported in this paper. First, a boundary condition is derived, which states that the fluid near a solid wall must have a certain density ρ_{0} depending on the solid's properties. Unlike previous derivations, the one presented here is based on the same physics as the DIM itself and does not require additional assumptions. Second, asymptotic estimates are used to check a conjecture lying at the foundation of the DIM, as well as all other models of contact lines, that liquid-vapor interfaces are nearly isothermal. It turns out that, for water, they are not, although, for a more viscous fluid, they can be. The nonisothermality occurs locally, near the interface, but can still affect the contact-line dynamics. Third, the DIM coupled with a realistic equation of state for water is used to compute the dependence of the surface tension σ on the temperature T, which agrees well with the empirical σ(T). Fourth, the same framework is used to compute the static contact angle of a water-vapor interface. It is shown that, with increasing temperature, the contact angle becomes either 180^{∘} (perfect hydrophobicity) or 0^{∘} (perfect hydrophilicity), depending on whether ρ_{0} matches the density of saturated vapor or liquid, respectively. Such behavior presumably occurs in all fluids, not just water, and for all sufficiently strong variations of parameters, not just that of the temperature, as corroborated by existing observations of drops under variable electric field.

Hybrid particle-field molecular dynamics under constant pressure

Hybrid particle-field methods are computationally efficient approaches for modeling soft matter systems. So far, applications of these methodologies have been limited to constant volume conditions. Here, we reformulate particle-field interactions to represent systems coupled to constant external pressure. First, we show that the commonly used particle-field energy functional can be modified to model and parameterize the isotropic contributions to the pressure tensor without interfering with the microscopic forces on the particles. Second, we employ a square gradient particle-field interaction term to model non-isotropic contributions to the pressure tensor, such as in surface tension phenomena. This formulation is implemented within the hybrid particle-field molecular dynamics approach and is tested on a series of model systems. Simulations of a homogeneous water box demonstrate that it is possible to parameterize the equation of state to reproduce any target density for a given external pressure. Moreover, the same parameterization is transferable to systems of similar coarse-grained mapping resolution. Finally, we evaluate the feasibility of the proposed approach on coarse-grained models of phospholipids, finding that the term between water and the lipid hydrocarbon tails is alone sufficient to reproduce the experimental area per lipid in constant-pressure simulations and to produce a qualitatively correct lateral pressure profile.

Illumination-induced motion of a Janus nanoparticle in binary solvents

Using a fluid particle dynamics method we numerically investigate the motion of a spherical Janus particle suspended in a binary liquid mixture, which emerges under heating of one-half of a colloid surface. The method treats simultaneously the flow of the solvent and the motion of the particle, hence, the velocity of the particle can be computed directly. Our approach accounts for a phenomenon of critical adsorption, therefore, a particle that is adsorptionwise nonneutral is always completely covered by an adsorption layer (droplet). In order to establish the mechanism of self-propulsion, we study systematically various combinations of adsorption preference on both hemispheres of the Janus colloid as function of the heating power for symmetric and nonsymmetric binary solvents and for various particle sizes in three spatial dimensions. Only for a particle for which the heated hemisphere is neutral whereas the other hemisphere prefers one of the two components of the mixture does the reversal of the direction of motion occur. The particle self-propels much faster in nonsymmetric binary solvents. Self-propulsion originates from a gradient of mechanical stress, in a way similar to the Marangoni effect. This stress is not localized at the edge but distributed within the whole droplet. We compare our findings with the experimental observations and other theoretical results.

Entropy production in thermal phase separation: a kinetic-theory approach

Entropy production during the process of thermal phase-separation of multiphase flows is investigated by means of a discrete Boltzmann kinetic model. The entropy production rate is found to increase during the spinodal decomposition stage and to decrease during the domain growth stage, attaining its maximum at the crossover between the two. Such behaviour provides a natural criterion to identify and discriminate between the two regimes. Furthermore, the effects of heat conductivity, viscosity and surface tension on the entropy production rate are investigated by systematically probing the interplay between non-equilibrium energy and momentum fluxes. It is found that the entropy production rate due to energy fluxes is an increasing function of the Prandtl number, while the momentum fluxes exhibit an opposite trend. On the other hand, both contributions show an increasing trend with surface tension. The present analysis inscribes within the general framework of non-equilibrium thermodynamics and consequently it is expected to be relevant to a broad class of soft-flowing systems far from mechanical and thermal equilibrium.

Liquid phase stabilization versus bubble formation at a nanoscale curved interface

We investigate the nature of vapor bubble formation near a nanoscale-curved convex liquid-solid interface using two models: an equilibrium Gibbs model for homogenous nucleation, and a nonequilibrium dynamic van der Waals-diffuse-interface model for phase change in an initially cool liquid. Vapor bubble formation is shown to occur for sufficiently large radius of curvature and is suppressed for smaller radii. Solid-fluid interactions are accounted for and it is shown that liquid-vapor interfacial energy, and hence Laplace pressure, has limited influence over bubble formation. The dominant factor is the energetic cost of creating the solid-vapor interface from the existing solid-liquid interface, as demonstrated via both equilibrium and nonequilibrium arguments.

Liquid-Gas Transitions in Steady Heat Conduction

We study liquid-gas transitions of heat conduction systems in contact with two heat baths under constant pressure in the linear response regime. On the basis of local equilibrium thermodynamics, we propose an equality with a global temperature, which determines the volume near the equilibrium liquid-gas transition. We find that the formation of the liquid-gas interface is accompanied by a discontinuous change in the volume when increasing the mean temperature of the baths. A supercooled gas near the interface is observed as a stable steady state.

Improved thermal lattice Boltzmann model for simulation of liquid-vapor phase change

In this paper, an improved thermal lattice Boltzmann (LB) model is proposed for simulating liquid-vapor phase change, which is aimed at improving an existing thermal LB model for liquid-vapor phase change [S. Gong and P. Cheng, Int. J. Heat Mass Transfer 55, 4923 (2012)10.1016/j.ijheatmasstransfer.2012.04.037]. First, we emphasize that the replacement of ∇·(λ∇T)/∇·(λ∇T)ρc_{V}ρc_{V} with ∇·(χ∇T) is an inappropriate treatment for diffuse interface modeling of liquid-vapor phase change. Furthermore, the error terms ∂_{t_{0}}(Tv)+∇·(Tvv), which exist in the macroscopic temperature equation recovered from the previous model, are eliminated in the present model through a way that is consistent with the philosophy of the LB method. Moreover, the discrete effect of the source term is also eliminated in the present model. Numerical simulations are performed for droplet evaporation and bubble nucleation to validate the capability of the model for simulating liquid-vapor phase change. It is shown that the numerical results of the improved model agree well with those of a finite-difference scheme. Meanwhile, it is found that the replacement of ∇·(λ∇T)/∇·(λ∇T)ρc_{V}ρc_{V} with ∇·(χ∇T) leads to significant numerical errors and the error terms in the recovered macroscopic temperature equation also result in considerable errors.

Response of Soft Continuous Structures and Topological Defects to a Temperature Gradient

Thermophoresis, which is mass transport induced by a temperature gradient, has recently attracted considerable attention as a new way to transport materials. So far the study has been focused on the transport of discrete structures such as colloidal particles, proteins, and polymers in solutions. However, the response of soft continuous structures such as membranes and gels to a temperature gradient has been largely unexplored. Here we study the behavior of a lamellar phase made of stacked surfactant bilayer membranes under a temperature gradient. We find the migration of membranes towards a low-temperature region, causing the increase in the degree of membrane undulation fluctuations towards that direction. This is contrary to our intuition that the fluctuations are weaker at a lower temperature. We show that this can be explained by temperature-gradient-induced migration of membranes under the topological constraint coming from the connectivity of each membrane. We also reveal that the pattern of an edge dislocation array formed in a wedge-shaped cell can be controlled by a temperature gradient. These findings suggest that application of a temperature gradient provides a novel way to control the organization of soft continuous structures such as membranes, gels, and foams, in a manner essentially different from the other types of fields, and to manipulate topological defects.

Phase-field lattice Boltzmann modeling of boiling using a sharp-interface energy solver

The main objective of this paper is to extend an isothermal incompressible two-phase lattice Boltzmann equation method to model liquid-vapor phase change problems using a sharp-interface energy solver. Two discrete particle distribution functions, one for the continuity equation and the other for the pressure evolution and momentum equations, are considered in the current model. The sharp-interface macroscopic internal energy equation is discretized with an isotropic finite difference method to find temperature distribution in the system. The mass flow generated at liquid-vapor phase interface is embedded in the pressure evolution equation. The sharp-interface treatment of internal energy equation helps to find the interfacial mass flow rate accurately where no free parameter is needed in the calculations. The proposed model is verified against available theoretical solutions of the two-phase Stefan problem and the two-phase sucking interface problem, with which our simulation results are in good agreement. The liquid droplet evaporation in a superheated vapor, the vapor bubble growth in a superheated liquid, and the vapor bubble rising in a superheated liquid are analyzed and underlying physical characteristics are discussed in detail. The model is successfully tested for the liquid-vapor phase change with large density ratio up to 1000.

Insights from inside the spinodal: Bridging thermalization time scales with smoothed particle hydrodynamics

We report the influence of the strength of heat bath coupling on the demixing behavior in spinodal decomposing one component liquid-vapor systems. The smoothed particle hydrodynamics (SPH) method with a van der Waals equation of state is used for the simulation. A thermostat for SPH is introduced that is based on the Berendsen thermostat. It controls the strength of heat bath coupling and allows for quenches with exponential temperature decay at a certain thermalization time scale. The present method allows us to bridge several orders of magnitude in the thermalization time scale. The early stage is highly affected by the choice of time scale. A transition from exponential growth to a 1/2 ordinary power law scaling in the characteristic lengths is observed. At high initial temperatures the growth is logarithmic. The comparison with pure thermal simulations reveals latent heat to raise the mean system temperature. Large thermalization time scales and thermal conductivity are figured out to affect a stagnation of heating, which is explained with convective processes. Furthermore, large thermalization time scales are responsible for a stagnation of growth of domains, which is temporally embedded between early and late stage of phase separation. Therefore, it is considered as an intermediate stage. We present an aspect concerning this stage, namely that choosing larger thermalization time scales increases the duration. Moreover, it is observed that diffuse interfaces are formed during this stage, provided that the stage is apparent. We show that the differences in the evolution between pure thermal simulations and simulations with an instantaneously scaled mean temperature can be explained by the thermalization process, since a variation of the time scale allows for the bridging between these cases of limit.

Evaporation Flux Distribution of Drops on a Hydrophilic or Hydrophobic Flat Surface by Molecular Simulations

The evaporation flux distribution of sessile drops is investigated by molecular dynamic simulations. Three evaporating modes are classified, including the diffusion dominant mode, the substrate heating mode, and the environment heating mode. Both hydrophilic and hydrophobic drop-substrate interactions are considered. To count the evaporation flux distribution, which is position dependent, we proposed an azimuthal-angle-based division method under the assumption of spherical crown shape of drops. The modeling results show that the edge evaporation, i.e., near the contact line, is enhanced for hydrophilic drops in all the three modes. The surface diffusion of liquid molecular absorbed on solid substrate for hydrophilic cases plays an important role as well as the space diffusion on the enhanced evaporation rate at the edge. For hydrophobic drops, the edge evaporation flux is higher for the substrate heating mode, but lower than elsewhere of the drop for the diffusion dominant mode; however, a nearly uniform distribution is found for the environment heating mode. The evidence shows that the temperature distribution inside drops plays a key role in the position-dependent evaporation flux.

Density functional theory of gas-liquid phase separation in dilute binary mixtures

We examine statics and dynamics of phase-separated states of dilute binary mixtures using density functional theory. In our systems, the difference of the solvation chemical potential between liquid and gas [Formula: see text] (the Gibbs energy of transfer) is considerably larger than the thermal energy [Formula: see text] for each solute particle and the attractive interaction among the solute particles is weaker than that among the solvent particles. In these conditions, the saturated vapor pressure increases by [Formula: see text], where [Formula: see text] is the solute density added in liquid. For [Formula: see text], phase separation is induced at low solute densities in liquid and the new phase remains in gaseous states, even when the liquid pressure is outside the coexistence curve of the solvent. This explains the widely observed formation of stable nanobubbles in ambient water with a dissolved gas. We calculate the density and stress profiles across planar and spherical interfaces, where the surface tension decreases with increasing interfacial solute adsorption. We realize stable solute-rich bubbles with radius about 30 nm, which minimize the free energy functional. We then study dynamics around such a bubble after a decompression of the surrounding liquid, where the bubble undergoes a damped oscillation. In addition, we present some exact and approximate expressions for the surface tension and the interfacial stress tensor.

Thermal singularity and contact line motion in pool boiling: Effects of substrate wettability

The dynamic van der Waals theory [Phys. Rev. E 75, 036304 (2007)] is employed to model the growth of a single vapor bubble in a superheated liquid on a flat homogeneous substrate. The bubble spreading dynamics in the pool boiling regime has been numerically investigated for one-component van der Waals fluids close to the critical point, with a focus on the effect of the substrate wettability on bubble growth and contact line motion. The substrate wettability is found to control the apparent contact angle and the rate of bubble growth (the rate of total evaporation), through which the contact line speed is determined. An approximate expression is derived for the contact line speed, showing good agreement with the simulation results. This demonstrates that the contact line speed is primarily governed by (1) the circular shape of interface (for slow bubble growth), (2) the constant apparent contact angle, and (3) the constant bubble growth rate. It follows that the contact line speed has a sensitive dependence on the substrate wettability via the apparent contact angle which also determines the bubble growth rate. Compared to hydrophilic surfaces, hydrophobic surfaces give rise to a thinner shape of bubble and a higher rate of total evaporation, which combine to result in a much faster contact line speed. This can be linked to the earlier formation of a vapor film and hence the onset of boiling crisis.

Diffuse interface method for a compressible binary fluid

Multicomponent, multiphase, compressible flows are very important in real life, as well as in scientific research, while their modeling is in an early stage. In this paper, we propose a diffuse interface model for compressible binary mixtures, based on the balance of mass, momentum, energy, and the second law of thermodynamics. We show both analytically and numerically that this model is able to describe the phase equilibrium for a real binary mixture (CO_{2} + ethanol is considered in this paper) very well by adjusting the parameter which measures the attraction force between molecules of the two components in the model. We also show that the calculated surface tension of the CO_{2} + ethanol mixture at different concentrations match measurements in the literature when the mixing capillary coefficient is taken to be the geometric mean of the capillary coefficient of each component. Three different cases of two droplets in a shear flow, with the same or different concentration, are simulated, showing that the higher concentration of CO_{2} the smaller the surface tension and the easier the drop deforms.

Thermohydrodynamics of boiling in binary compressible fluids

We numerically study the thermohydrodynamics of boiling for a CO(2) + ethanol mixture on lyophilic and lyophobic surfaces in both closed and open systems, based on a diffuse interface model for a two-component system. The corresponding wetting boundary conditions for an isothermal system are proposed and verified in this paper. New phenomena due to the addition of another component, mainly the preferential evaporation of the more volatile component, are observed. In the open system and the closed system, the physical process shows very different characteristics. In the open system, except for the movement of the contact line, the qualitative features are rather similar for lyophobic and lyophilic surfaces. In the closed system, the vortices that are observed on a lyophobic surface are not seen on a lyophilic surface. More sophisticated wetting boundary conditions for nonisothermal, two-component systems might need to be further developed, taking into account the variations of density, temperature, and surface tension near the wall, while numerical results show that the boundary conditions proposed here also work well even in boiling, where the temperature is nonuniform.

Hydrodynamic instabilities in shear flows of dry cohesive granular particles

We extend the dynamic van der Waals model introduced by A. Onuki [Phys. Rev. Lett., 2005, 94, 054501] to the description of cohesive granular flows under a plane shear to study their hydrodynamic instabilities. By numerically solving the dynamic van der Waals model, we observed various heterogeneous structures of density fields in steady states, where the viscous heating is balanced with the energy dissipation caused by inelastic collisions. Based on the linear stability analysis, we found that the spatial structures are determined by the mean volume fraction, the applied shear rate, and the inelasticity, where the instability is triggered if the system is thermodynamically unstable, i.e. the pressure, p, and the volume fraction, ϕ, satisfy ∂p/∂ϕ < 0.

Nanobubbles around plasmonic nanoparticles: Thermodynamic analysis

We describe the dynamics of vapor nanobubbles in water, on the basis of simulations of a hydrodynamics phase-field model. This situation is relevant to recent experiments, where a water nanobubble is generated around a nanoparticle immersed in water, and heated by an intense laser pulse. We emphasize the importance of nanoscale effects in the dynamics of the nanobubble. We first analyze the evolution of the temperature inside the bubble. We show that the temperature drops by hundredths of kelvins in a few picoseconds, just after nanobubble formation. This is the result of the huge drop of the thermal boundary conductance between the nanoparticle and the fluid accompanying vaporization. Subsequently, the temperature inside the vapor is almost homogeneous and the temperature gradient is concentrated in the liquid, whose thermodynamic state locally follows the saturation line. We discuss also the evolution of the pressure inside the vapor nanobubble. We show that nanobubble generation is accompanied by a pressure wave propagating in the liquid at a velocity close to the liquid speed of sound. The internal pressure inside the vapor just after its formation largely exceeds Laplace pressure and quickly relaxes as a result of the damping generated by the viscous forces. All these considerations shed light on the thermodynamics of the nanobubbles generated experimentally.

Modeling multiphase flow using fluctuating hydrodynamics

Fluctuating hydrodynamics provides a model for fluids at mesoscopic scales where thermal fluctuations can have a significant impact on the behavior of the system. Here we investigate a model for fluctuating hydrodynamics of a single-component, multiphase flow in the neighborhood of the critical point. The system is modeled using a compressible flow formulation with a van der Waals equation of state, incorporating a Korteweg stress term to treat interfacial tension. We present a numerical algorithm for modeling this system based on an extension of algorithms developed for fluctuating hydrodynamics for ideal fluids. The scheme is validated by comparison of measured structure factors and capillary wave spectra with equilibrium theory. We also present several nonequilibrium examples to illustrate the capability of the algorithm to model multiphase fluid phenomena in a neighborhood of the critical point. These examples include a study of the impact of fluctuations on the spinodal decomposition following a rapid quench, as well as the piston effect in a cavity with supercooled walls. The conclusion in both cases is that thermal fluctuations affect the size and growth of the domains in off-critical quenches.

Thermocapillary-actuated contact-line motion of immiscible binary fluids over substrates with patterned wettability in narrow confinement

We investigate thermocapillary-driven contact-line dynamics of two immiscible fluids in a narrow fluidic confinement comprising substrates with patterned wettability variations. Our study, based on phase field formalism, demonstrates that the velocity of the contact line is a strong function of the combined consequences of the applied thermal gradient and the substrate wetting characteristics. Finally, we evaluate different energy transfer rates and show that the dissipation due to fluid slip over the solid surface plays a dominating role in transferring energy into the contact-line motion. Our analysis, in effect, provides an elegant way of controlling the capillary filling rate in a narrow fluidic confinement by tailoring the applied temperature gradient and the substrate wettability in tandem.

Single-bubble dynamics in pool boiling of one-component fluids

We numerically investigate the pool boiling of one-component fluids with a focus on the effects of surface wettability on the single-bubble dynamics. We employed the dynamic van der Waals theory [Phys. Rev. E 75, 036304 (2007)], a diffuse-interface model for liquid-vapor flows involving liquid-vapor transition in nonuniform temperature fields. We first perform simulations for bubbles on homogeneous surfaces. We find that an increase in either the contact angle or the surface superheating can enhance the bubble spreading over the heating surface and increase the bubble departure diameter as well and therefore facilitate the transition into film boiling. We then examine the dynamics of bubbles on patterned surfaces, which incorporate the advantages of both hydrophobic and hydrophilic surfaces. The central hydrophobic region increases the thermodynamic probability of bubble nucleation while the surrounding hydrophilic region hinders the continuous bubble spreading by pinning the contact line at the hydrophobic-hydrophilic intersection. This leads to a small bubble departure diameter and therefore prevents the transition from nucleate boiling into film boiling. With the bubble nucleation probability increased and the bubble departure facilitated, the efficiency of heat transfer on such patterned surfaces is highly enhanced, as observed experimentally [Int. J. Heat Mass Transfer 57, 733 (2013)]. In addition, the stick-slip motion of contact line on patterned surfaces is demonstrated in one-component fluids, with the effect weakened by surface superheating.

Kinetics of nanobubble generation around overheated nanoparticles

We report on the formation and growth of nanobubbles around laser-heated gold nanoparticles in water. Using a hydrodynamic free-energy model, we show that the temporal evolution of the nanobubble radius is asymmetrical: the expansion is found to be adiabatic, while the collapse is best described by an isothermal evolution. We unveil the critical role of the thermal boundary resistance in the kinetics of formation of the nanobubbles: close to the vapor production threshold, nanobubble generation is very long, yielding optimal conditions for laser-energy conversion. Furthermore, the long appearance times allow nanoparticle melting before the onset of vaporization.

Molecular dynamics simulations for the motion of evaporative droplets driven by thermal gradients along nanochannels

For a one-component fluid on a solid substrate, a thermal singularity may occur at the contact line where the liquid-vapor interface intersects the solid surface. Physically, the liquid-vapor interface is almost isothermal at the liquid-vapor coexistence temperature in one-component fluids while the solid surface is almost isothermal for solids of high thermal conductivity. Therefore, a temperature discontinuity is formed if the two isothermal interfaces are of different temperatures and intersect at the contact line. This leads to the so-called thermal singularity. The localized hydrodynamics involving evaporation/condensation near the contact line leads to a contact angle depending on the underlying substrate temperature. This dependence has been shown to lead to the motion of liquid droplets on solid substrates with thermal gradients (Xu and Qian 2012 Phys. Rev. E 85 061603). In the present work, we carry out molecular dynamics (MD) simulations as numerical experiments to further confirm the predictions made from our previous continuum hydrodynamic modeling and simulations, which are actually semi-quantitatively accurate down to the small length scales in the problem. Using MD simulations, we investigate the motion of evaporative droplets in one-component Lennard-Jones fluids confined in nanochannels with thermal gradients. The droplet is found to migrate in the direction of decreasing temperature of solid walls, with a migration velocity linearly proportional to the temperature gradient. This agrees with the prediction of our continuum model. We then measure the effect of droplet size on the droplet motion. It is found that the droplet mobility is inversely proportional to a dimensionless coefficient associated with the total rate of dissipation due to droplet movement. Our results show that this coefficient is of order unity and increases with the droplet size for the small droplets (~10 nm) simulated in the present work. These findings are in semi-quantitative agreement with the predictions of our continuum model. Finally, we measure the effect of liquid-vapor coexistence temperature on the droplet motion. Through a theoretical analysis on the size of the thermal singularity, it can be shown that the droplet mobility decreases with decreasing coexistence temperature. This is observed in our MD simulations.

Hydrodynamics of Leidenfrost droplets in one-component fluids

Using the dynamic van der Waals theory [Phys. Rev. E 75, 036304 (2007)], we numerically investigate the hydrodynamics of Leidenfrost droplets under gravity in two dimensions. Some recent theoretical predictions and experimental observations are confirmed in our simulations. A Leidenfrost droplet larger than a critical size is shown to be unstable and break up into smaller droplets due to the Rayleigh-Taylor instability of the bottom surface of the droplet. Our simulations demonstrate that an evaporating Leidenfrost droplet changes continuously from a puddle to a circular droplet, with the droplet shape controlled by its size in comparison with a few characteristic length scales. The geometry of the vapor layer under the droplet is found to mainly depend on the droplet size and is nearly independent of the substrate temperature, as reported in a recent experimental study [Phys. Rev. Lett. 109, 074301 (2012)]. Finally, our simulations demonstrate that a Leidenfrost droplet smaller than a characteristic size takes off from the hot substrate because the levitating force due to evaporation can no longer be balanced by the weight of the droplet, as observed in a recent experimental study [Phys. Rev. Lett. 109, 034501 (2012)].

Thermal singularity and droplet motion in one-component fluids on solid substrates with thermal gradients

Using a continuum model capable of describing the one-component liquid-gas hydrodynamics down to the contact line scale, we carry out numerical simulation and physical analysis for the droplet motion driven by thermal singularity. For liquid droplets in one-component fluids on heated or cooled substrates, the liquid-gas interface is nearly isothermal. Consequently, a thermal singularity occurs at the contact line and the Marangoni effect due to temperature gradient is suppressed. Through evaporation or condensation in the vicinity of the contact line, the thermal singularity makes the contact angle increase with the increasing substrate temperature. This effect on the contact angle can be used to move the droplets on substrates with thermal gradients. Our numerical results for this kind of droplet motion are explained by a simple fluid dynamical model at the droplet length scale. Since the mechanism for droplet motion is based on the change of contact angle, a separation of length scales is exhibited through a comparison between the droplet motion induced by a wettability gradient and that by a thermal gradient. It is shown that the flow field at the droplet length scale is independent of the statics or dynamics at the contact line scale.

Droplet motion in one-component fluids on solid substrates with wettability gradients

Droplet motion on solid substrates has been widely studied not only because of its importance in fundamental research but also because of its promising potentials in droplet-based devices developed for various applications in chemistry, biology, and industry. In this paper, we investigate the motion of an evaporating droplet in one-component fluids on a solid substrate with a wettability gradient. As is well known, there are two major difficulties in the continuum description of fluid flows and heat fluxes near the contact line of droplets on solid substrates, namely, the hydrodynamic (stress) singularity and thermal singularity. To model the droplet motion, we use the dynamic van der Waals theory [Phys. Rev. E 75, 036304 (2007)] for the hydrodynamic equations in the bulk region, supplemented with the boundary conditions at the fluid-solid interface. In this continuum hydrodynamic model, various physical processes involved in the droplet motion can be taken into account simultaneously, e.g., phase transitions (evaporation or condensation), capillary flows, fluid velocity slip, and substrate cooling or heating. Due to the use of the phase field method (diffuse interface method), the hydrodynamic and thermal singularities are resolved automatically. Furthermore, in the dynamic van der Waals theory, the evaporation or condensation rate at the liquid-gas interface is an outcome of the calculation rather than a prerequisite as in most of the other models proposed for evaporating droplets. Numerical results show that the droplet migrates in the direction of increasing wettability on the solid substrates. The migration velocity of the droplet is found to be proportional to the wettability gradients as predicted by Brochard [Langmuir 5, 432 (1989)]. The proportionality coefficient is found to be linearly dependent on the ratio of slip length to initial droplet radius. These results indicate that the steady migration of the droplets results from the balance between the (conservative) driving force due to the wettability gradient and the (dissipative) viscous drag force. In addition, we study the motion of droplets on cooled or heated solid substrates with wettability gradients. The fast temperature variations from the solid to the fluid can be accurately described in the present approach. It is observed that accompanying the droplet migration, the contact lines move through phase transition and boundary velocity slip with their relative contributions mostly determined by the slip length. The results presented in this paper may lead to a more complete understanding of the droplet motion driven by wettability gradients with a detailed picture of the fluid flows and phase transitions in the vicinity of the moving contact line.

Thermohydrodynamics of boiling in a van der Waals fluid

We present a modeling approach that enables numerical simulations of a boiling Van der Waals fluid based on the diffuse interface description. A boundary condition is implemented that allows in and out flux of mass at constant external pressure. In addition, a boundary condition for controlled wetting properties of the boiling surface is also proposed. We present isothermal verification cases for each element of our modeling approach. By using these two boundary conditions we are able to numerically access a system that contains the essential physics of the boiling process at microscopic scales. Evolution of bubbles under film boiling and nucleate boiling conditions are observed by varying boiling surface wettability. We observe flow patters around the three-phase contact line where the phase change is greatest. For a hydrophilic boiling surface, a complex flow pattern consistent with vapor recoil theory is observed.

Predrying transition on a hydrophobic surface: statics and dynamics

For one-component fluids, we examine the predrying phase transition between a thin and thick low-density layer in liquid on a wall repelling the fluid. This is the case of a hydrophobic wall for water. A predrying line starts from the coexistence curve and ends at a surface critical point in the phase diagram. We calculate this line numerically using the van der Waals model and analytically using the free-energy expansion up to the quartic order. We also examine the predrying dynamics of a layer created on a hydrophobic spot on a heterogeneous wall. It is from a thin to thick layer during decompression and from a thick to thin layer during compression. Upon the transition, a liquid region above the film is cooled for decompression and heated for compression due to latent heat convection, and a small pressure pulse is emitted from the film into the liquid.

Phase separation in thermal systems: a lattice Boltzmann study and morphological characterization

We investigate thermal and isothermal symmetric liquid-vapor separations via a fast Fourier transform thermal lattice Boltzmann (FFT-TLB) model. Structure factor, domain size, and Minkowski functionals are employed to characterize the density and velocity fields, as well as to understand the configurations and the kinetic processes. Compared with the isothermal phase separation, the freedom in temperature prolongs the spinodal decomposition (SD) stage and induces different rheological and morphological behaviors in the thermal system. After the transient procedure, both the thermal and isothermal separations show power-law scalings in domain growth, while the exponent for thermal system is lower than that for isothermal system. With respect to the density field, the isothermal system presents more likely bicontinuous configurations with narrower interfaces, while the thermal system presents more likely configurations with scattered bubbles. Heat creation, conduction, and lower interfacial stresses are the main reasons for the differences in thermal system. Different from the isothermal case, the release of latent heat causes the changing of local temperature, which results in new local mechanical balance. When the Prandtl number becomes smaller, the system approaches thermodynamical equilibrium much more quickly. The increasing of mean temperature makes the interfacial stress lower in the following way: σ=σ(0)[(T(c)-T)/(T(c)-T(0))](3/2), where T(c) is the critical temperature and σ(0) is the interfacial stress at a reference temperature T(0), which is the main reason for the prolonged SD stage and the lower growth exponent in the thermal case. Besides thermodynamics, we probe how the local viscosities influence the morphology of the phase separating system. We find that, for both the isothermal and thermal cases, the growth exponents and local flow velocities are inversely proportional to the corresponding viscosities. Compared with the isothermal case, the local flow velocity depends not only on viscosity but also on temperature.

Droplet evolution in expanding flow of warm dense matter

We propose a simple, self-consistent kinetic model for the evolution of a mixture of droplets and vapor expanding adiabatically in vacuum after rapid, almost isochoric heating. We study the evolution of the two-phase fluid at intermediate times between the molecular and the hydrodynamic scales, focusing on out-of-equilibrium and surface effects. We use the van der Waals equation of state as a test bed to implement our model and study the phenomenology of the upcoming second neutralized drift compression experiment (NDCX-II) at Lawrence Berkeley National Laboratory (LBNL) that uses ion beams for target heating. We find an approximate expression for the temperature difference between the droplets and the expanding gas and we check it with numerical calculations. The formula provides a useful criterion to distinguish the thermalized and nonthermalized regimes of expansion. In the thermalized case, the liquid fraction grows in a proportion that we estimate analytically, whereas, in case of too rapid expansion, a strict limit for the evaporation of droplets is derived. The range of experimental situations is discussed.

Phase-field model of solid-liquid phase transition with density difference and latent heat in velocity and elastic fields

We present a phase-field model of solid-liquid transitions with inhomogeneous temperature in one-component systems, including hydrodynamics and elasticity. Our model can describe plastic deformations at large elastic strains. We use it to investigate the melting of a solid domain, accounting for the latent heat effect, where there appears a velocity field in liquid and an elastic field in solid. We present simulation results in two dimensions for three cases of melting. First, a solid domain is placed on a heated wall, which melts mostly near the solid-liquid-wall contact region. Second, a solid domain is suspended in a warmer liquid under shear flow, which rotates as a whole because of elasticity and melts gradually. Cooling of the surrounding liquid is accelerated by convection. Third, a solid rod is under high compression in liquid, where slips appear from the solid-liquid interface, leading to a plastic deformation. Subsequently, melting starts in the plastically deformed areas, eventually resulting in the fracture of the rod into pieces. In these phase-transition processes, the interface temperature is kept nearly equal to the coexisting temperature T(cs)(p) away from the heated wall, but this local equilibrium is not attained near the the contact region. We also examine a first-order liquid-liquid phase transition under heating from a boundary in one-component liquids.

Spreading with evaporation and condensation in one-component fluids

We investigate the dynamics of spreading of a small liquid droplet in gas in a one-component simple fluid, where the temperature is inhomogeneous around 0.9T{c} and latent heat is released or generated at the interface upon evaporation or condensation (with T{c} being the critical temperature). In the scheme of the dynamic van der Waals theory, the hydrodynamic equations containing the gradient stress are solved in the axisymmetric geometry. We assume that the substrate has a finite thickness and its temperature obeys the thermal diffusion equation. A precursor film then spreads ahead of the bulk droplet itself in the complete wetting condition. Cooling the substrate enhances condensation of gas onto the advancing film, which mostly takes place near the film edge and can be the dominant mechanism of the film growth in a late stage. The generated latent heat produces a temperature peak or a hot spot in the gas region near the film edge. On the other hand, heating the substrate induces evaporation all over the interface. For weak heating, a steady-state circular thin film can be formed on the substrate. For stronger heating, evaporation dominates over condensation, leading to eventual disappearance of the liquid region.

Bubble and droplet motion in binary mixtures: Evaporation-condensation mechanism and Marangoni effect

Bubble and droplet motion in binary mixtures is studied in weak heat and diffusion fluxes and in gravity by solving the linearized hydrodynamic equations supplemented with appropriate surface boundary conditions. Without gravity, the velocity field is induced by evaporation and condensation at the interface and by the Marangoni effect due to a surface-tension gradient. In pure fluids, the latter nearly vanishes since the interface temperature tends to the coexistence temperature T_{cx}(p) even in heat flow. In binary mixtures, the velocity field can be much enhanced by the Marangoni effect above a crossover concentration c;{ *} inversely proportional to the radius R of the bubble or droplet. Here c;{ *} is usually very small for large R for non-azeotropic mixtures. The temperature and concentration deviations are also calculated.

Universality in early-stage growth of phase-separating domains near the critical point

We present both the experimental and computational methods and results of phase-separating experiments performed with sulfur hexafluoride (SF6) close to its critical density. These experiments were performed in microgravity to suppress buoyancy and convection-driven effects. Phase separation under reduced gravity is analyzed for both 0.3 mK and 3.6 mK temperature quenches in order to derive the early-stage growth law. We found a 1/3 growth law for early stages of phase separation for a volume fraction of minority domains of 50%. Our findings support the hypothesis of a crossover between Brownian motion and hydrodynamic effects in the early stages of phase separation. The temperature inside the bulk of the pure fluid was estimated using a proposed histogram method. Our histogram method allowed temperature estimation below thermistors' sensitivity and detected small temperature variations inside the bulk of the pure fluid.

Thermoacoustic effects in supercritical fluids near the critical point: Resonance, piston effect, and acoustic emission and reflection

We present a general theory of thermoacoustic phenomena in one phase states of one-component fluids. Singular behavior is predicted in supercritical fluids near the critical point. In a one-dimensional geometry we start with linearized hydrodynamic equations taking into account the effects of heat conduction in the boundary walls and the bulk viscosity. We introduce a coefficient Z(omega) characterizing reflection of sound with frequency omega at the boundary in a rigid cell. As applications, we examine acoustic eigenmodes, response to time-dependent perturbations, and sound emission and reflection. Resonance and rapid adiabatic changes are noteworthy. In these processes, the role of the thermal diffusion layers is enhanced near the critical point because of the strong critical divergence of the thermal expansion.

Lattice Boltzmann simulation of thermal nonideal fluids

A thermal lattice Boltzmann model for a van der Waals fluid is proposed. In the continuum, the model reproduces at second order of a Chapman-Enskog expansion, the theory recently introduced by A. Onuki [Phys. Rev. Lett. 94, 054501 (2005)]. Phase separation has been studied in a system quenched by contact with external walls. Pressure waves favor the thermalization of the system at initial times and the temperature, soon with respect to typical times of phase separation, becomes homogeneous in the bulk. Alternate layers of liquid and vapor form on the walls and disappear at late times.