Diffuse-interface modeling of liquid-vapor phase separation in a van der Waals fluid (original) (raw)
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The coexistence region in the Van der Waals fluid and the liquid-liquid phase transitions
Frontiers in Chemistry
Cellular membraneless organelles are thought to be droplets formed within the two-phase region corresponding to proteinaceous systems endowed with the liquid-liquid transition. However, their metastability requires an additional constraint—they arise in a certain region of density and temperature between the spinodal and binodal lines. Here, we consider the well-studied van der Waals fluid as a test model to work out criteria to determine the location of the spinodal line for situations in which the equation of state is not known. Our molecular dynamics studies indicate that this task can be accomplished by considering the specific heat, the surface tension and characteristics of the molecular clusters, such as the number of component chains and radius of gyration.
Nucleation, spinodal decomposition, and interface motion in the van der Waals fluid
The Journal of Chemical Physics, 1981
We discuss the predictions of the phenomenological theory of Metiu, Kitahara, and Ross for the most probable evolution of density fluctuations in the van der Waals fluid model. The knowledge of the exact (nonlocal) form for the grand potential functional n permits a precise study of the kinetics of phase change under strongly nonuniform conditions. It is shown that for every subcritical temperature and chemical potential in the spinodal region there exists an infinite family of periodic stationary states in addition to the usual uniform ones. The stability analysis of these states provides a description of spinodal decomposition in its intermediate and later stages. It is also shown that fluctuations separated in space are correlated through the nonlocality of n and that they cooperate in the nucleation process with an additional term absent in the classical and gradient theories. The solitary wave motion which describes condensation-evaporation pr~ is obtained from a perturbation on the thermodynamic conditions for.phase equilibrium.
American Journal of Physics, 2012
As a rule, mean-field theories applied to a fluid that can undergo a transition from saturated vapor at density ρ υ to a liquid at density ρ yield a van der Waals loop. For example, isotherms of the chemical potential µ(T, ρ) as a function of the density ρ at a fixed temperature T less than the critical temperature T c exhibit a maximum and a minimum. Metastable and unstable parts of the van der Waals loop can be eliminated by the Maxwell construction. Van der Waals loops and the corresponding double minimum potentials are mean-field artifacts. Simulations at fixed µ = µ coex for ρ υ < ρ < ρ yield a loop, but for sufficiently large systems this loop does not resemble the van der Waals loop, and reflects interfacial effects on phase coexistence due to finite size effects. In contrast to the the van der Waals loop, all parts of the loop found in simulations are thermodynamically stable. The successive umbrella sampling algorithm is described as a convenient tool for seeing these effects. It is shown that the maximum of the loop is not the stability limit of a metastable vapor, but signifies the droplet evaporation-condensation transition. The descending part of the loop contains information on Tolman-like corrections to the surface tension, rather than describing unstable states.
Gas–liquid transition of van der Waals fluid confined in fluctuating nano-space
The Journal of Chemical Physics, 2022
Gas–liquid transition is generally a complex process, which involves nucleation of droplets and their growth by evaporation–condensation or collision–coalescence processes. Here, we focus on a microscopic system in which there is only one liquid droplet at most. In this case, we can develop an equilibrium theory for the formation of the droplet in the gas phase using the classical nucleation theory. We use the van der Waals fluid model with surface tension and calculate the size fluctuation of the droplet for various confinement conditions, NVT (in which the volume V of the system is fixed), NPT (in which the pressure P of the system is fixed), and NBT (in which the system is confined in a nano-bubble immersed in a host liquid, where both V and P can fluctuate). We show that in the NBT system, the size flexibility along with space confinement induces a wealth of properties that are not found in NVT and NPT. It exhibits richer phase behaviors: a stable droplet appears and coexists wi...
International Journal of Numerical Methods for Heat & Fluid Flow, 2019
Purpose This paper aims to assess the accuracy of Lattice Boltzmann method (LBM) for numerical simulation of the stratification of a Van der Waals (VdW) fluid subjected to a gravity field and non-uniform temperature distribution. A sensitivity analysis of the influence of the pseudopotential parameters and the grid resolution is presented. The effect of gravity force on interface densities, density profiles and liquid volume fraction is studied. Design/methodology/approach The D2Q9 multiple-relaxation-time pseudopotential LBM for two-phase flow is proposed to simulate the phase separation. The analytical solution for density profiles in a one-dimensional problem is derived and used as a benchmark case to validate the numerical results. Findings The numerical results reproduce the analytical density profiles with great accuracy over a wide range of simulation conditions, including variations of the gravity and temperature fields. Particularly, the numerical simulations are able to re...
Thermohydrodynamics of boiling in a van der Waals fluid
Physical Review E, 2012
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.
From the vapor-liquid coexistence region to the supercritical fluid: the van der Waals fluid
arXiv (Cornell University), 2022
In this work the interface system of the van der Waals fluid is investigated by using the density gradient theory incorporated with the mean-field theory. Based on the mean-field dividing interface generated by the Maxwell construction, we propose a highly accurate density profile model for the density gradient theory, which facilitates reliable predictions of various properties for the interface region. It is found that the local intrinsic Helmholtz free energy peaks at the interface and that the maximum difference of the normal and tangential components of the pressure tensor corresponds to the maximum of the intrinsic Gibbs free energy. It is found that the entire phase space is divided into gas-like and liquid-like regions by the single line composed of the mean-field interface and the Widom line. The two-fluid feature of the supercritical fluid is hence inherited from the coexistence region. Phase diagrams extended into the coexistence region in all the temperature-pressure-volume planes are thus completed with the solutions to the vapor-liquid equilibrium problem by the van der Waals equation of state.
Two-dimensional model of phase segregation in liquid binary mixtures
Physical Review E, 1999
The hydrodynamic effects on the late stage kinetics of phase separation in liquid mixtures is studied using the model H. Mass and momentum transport are coupled via a nonequilibrium body force, which is proportional to the Peclet number ␣, i.e., the ratio between convective and diffusive molar fluxes. Numerical simulations based on this theoretical model show that phase separation in low viscosity, liquid binary mixtures is mostly driven by convection, thereby explaining the experimental findings that the process is fast, with the typical size of single-phase domains increasing linearly with time. However, as soon as sharp interfaces form, the linear growth regime reaches an end, and the process appears to be driven by diffusion, although the condition of local equilibrium is not reached. During this stage, the typical size of the nucleating drops increases like t n , where 1 3 ϽnϽ 1 2 , depending on the value of the Peclet number. As the Peclet number increases, the transition between convection-and diffusion-driven regimes occurs at larger times, and therefore for larger sizes of the nucleating drops.
Liquid-Vapor Equilibria of Polar Fluids from a van der Waals-like Theory
1994
A van der Waals-like theory of quadrupolar and dipolar linear fluids is presented. The reference system consists of a hard polar fluid, and attractive forces are considered through the mean field approximation. The effect of polar forces on liquid-vapor equilibria and on critical properties is analyzed for a number of molecular elongations. Trends as predicted by the theory are compared with computer simulations of linear polar fluids, and good agreement is found. Polar forces increase the critical temperature and acentric factor of a fluid. Quadrupole moment increases the critical density of a fluid. However, high dipole moments decrease critical densities. Deviations from the principle of corresponding states are analyzed. Polar forces and molecular elongation provoke a broadening of the coexistence curve and an increase of the slope of the vapor pressure curve when reduced by their critical magnitudes. The presented treatment, being quite simple, describes most of the main features of vapor-liquid equilibria of linear polar fluids.
Multi-scaling properties of phase segregation in quenched binary fluids
Physica A: Statistical Mechanics and its Applications, 1998
The phase separation process in two-dimensional binary uid systems is investigated using molecular dynamics for almost 20 000 particles. Previous works from the same authors have shown that the late-stage coarsening regime at critical volume fractions is described by power laws whose exponents are dependent on particle-particle interactions and on temperature in a non-universal way. At the low-temperature region, however, the emergence of a three-phase regime of percolating domains with atoms of type-A, type-B and voids, invalidates the singlelength scale invariance. We argue in terms of a multiple-length scale analysis. In particular, for the case we studied with symmetric molecular pair potentials we propose two divergent length scales to characterize the dynamic process: one associated to the average size of equalatom domains and the other related to the average size of undistinguishable-atom domains. Two di erent growth exponents can be inferred in such a case but the system does not exhibit scale invariance.