Mathematical modeling of planar and spherical vapor–liquid phase interfaces for multicomponent fluids (original) (raw)
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Journal of Fluid Mechanics, 2021
Classical continuum-based liquid vapour phase-change models typically assume continuity of temperature at phase interfaces along with a relation which describes the rate of evaporation at the interface (Hertz-Knudsen-Schrage, for example). However, for phase transitions processes at small scales, such as the evaporation of nanodroplets, the assumption that the temperature is continuous across the liquid-vapour interface leads to significant inaccuracies (McGaughey & Ward 2002; Rana et al. 2019), as may the adoption of classical constitutive relations that lead to the Navier-Stokes-Fourier equations (NSF). In this article, to capture the notable effects of rarefaction at small scales, we adopt an extended continuum-based approach utilizing the coupled constitutive relations (CCR). In CCR theory, additional terms are invoked in the constitutive relations of NSF equations originating from the arguments of irreversible thermodynamics as well as consistent with kinetic theory of gases. The modelling approach allows us to derive new fundamental solutions for the linearised CCR model and to develop a numerical framework based upon the method of fundamental solutions (MFS) and enables threedimensional multiphase micro-flow simulations to be performed at remarkably low computational cost. The new framework is benchmarked against classical results and then explored as an efficient tool for solving three-dimensional phase-change events involving droplets.
Physical Review E, 2014
We study numerically liquid-vapor phase separation in two-dimensional, nonisothermal, van der Waals (vdW) liquid drops using the method of smoothed particle hydrodynamics (SPH). In contrast to previous SPH simulations of drop formation, our approach is fully adaptive and follows the diffuse-interface model for a single-component fluid, where a reversible, capillary (Korteweg) force is added to the equations of motion to model the rapid but smooth transition of physical quantities through the interface separating the bulk phases. Surface tension arises naturally from the cohesive part of the vdW equation of state and the capillary forces. The drop models all start from a square-shaped liquid and spinodal decomposition is investigated for a range of initial densities and temperatures. The simulations predict the formation of stable, subcritical liquid drops with a vapor atmosphere, with the densities and temperatures of coexisting liquid and vapor in the vdW phase diagram closely matching the binodal curve. We find that the values of surface tension, as determined from the Young-Laplace equation, are in good agreement with the results of independent numerical simulations and experimental data. The models also predict the increase of the vapor pressure with temperature and the fitting to the numerical data reproduces very well the Clausius-Clapeyron relation, thus allowing for the calculation of the vaporization pressure for this vdW fluid.
Nuclear Engineering and Design, 2001
In several numerical methods dedicated to the direct numerical simulation of two-phase flows, the concept of a continuous enlarged interfacial zone is used. In this communication, it is shown that for liquid-vapor systems, it is possible to use this concept in a thermodynamic coherent way. Indeed, if it is considered that the energy of the system depends on the density gradient, this theory being called the Van der Waals or Cahn-Hilliard or more generally the second gradient theory, then it is possible to derive the equations that characterize the fluid motion within a 3-D liquid-vapor interfacial zone. Modifying the thermodynamic behavior of the fluid, it is shown that it is possible to increase the thickness of an interface, so that it can be captured by a 'standard' mesh without changing the surface tension nor loosing the thermodynamic coherence of the model. Several examples of application show that this method can be applied to study various physical problems, including contact line phenomena.
Three-stage phase separation kinetics in a model liquid binary mixture: A computational study
The Journal of Chemical Physics
We study microscopic aspects of initial phase separation through atomistic molecular dynamics simulation of a structure breaking liquid binary mixture. We find that the phase separation kinetics in a fluid binary mixture model system can indeed be unusual. It can be fast, with a crossover from a pronounced exponential to non-exponential and non-linear dynamics. An important outcome of this work is the quantification of time scales involved in phase separation kinetics at an early stage. The initial exponential phase separation is complete within ∼100 ps. The initial phase separation involves aggregation of small droplets that form rapidly after the quench. This is followed by segregation that gives rise to pattern formation with multiple bands of segregated species. During this initial phase, a particle is found to have moved only about ∼5 molecular diameters. The next stage is slower and characterized by break-up and disappearance of small islands of species trapped inside the domains of other species of the binary mixture. The phase separation in this second stage is highly non-exponential and power-law-like. We identify a new feature in the very late stage of phase separation kinetics that seems to have eluded previous attention, the smoothing of the rugged interface between the two species. This is opposite to the roughening transition one finds on the surface of solids in contact with its vapor phase. The present atomistic simulation provides a molecular picture in terms of molecular motions and displacements.
2012
Curved fluid interfaces are investigated on the nanometre length scale by molecular dynamics simulation. Thereby, droplets surrounded by a metastable vapour phase are stabilized in the canonical ensemble. Analogous simulations are conducted for cylindrical menisci separating vapour and liquid phases under confinement in planar nanopores. Regarding the emergence of nanodroplets during nucleation, a non-equilibrium phenomenon, both the non-steady dynamics of condensation processes and stationary quantities related to supersaturated vapours are considered. Results for the truncated and shifted Lennard-Jones fluid and for mixtures of quadrupolar fluids confirm the applicability of the capillarity approximation and the classical nucleation theory.
International Journal of Thermophysics, 2013
In this study, we use the Cahn-Hilliard density Gradient Theory (GT) for predicting the surface tension of various binary mixtures at relatively wide temperature ranges and test the application of the GT for predictions of homogeneous nucleation. The GT was combined with two physically based equations of state (EoS), namely the Perturbed-Chain (PC) Statistical Associating Fluid Theory (SAFT) and its modification for polar substances the Perturbed-Chain Polar (PCP) SAFT. The GT applied to the planar phase interface was classical cubic Peng-Robinson EoS, which is still used for modeling droplet nucleation.
Fluid Phase Equilibria, 2000
NVT-and NpT-Gibbs Ensemble Monte Carlo Simulations were applied to describe the vapor-liquid equilibrium of water (between 323 and 573 K), carbon dioxide (between 230 and 290 K) and their binary mixtures (between 348 and 393 K). The properties of supercritical carbon dioxide were determined between 310 K and 520 K by NpT-Monte Carlo simulations. Literature data for the effective pair potentials (for water: the SPC-, SPC/E-, and TIP4P-potential models; for carbon dioxide: the EPM2 potential model) were used to describe the properties of the pure substances. The vapor pressures of water and carbon dioxide are calculated. For water, the SPC-and TIP4P-models give superior results for the vapor pressure when compared to the SPC/E-model. The vapor liquid equilibrium of the binary mixture carbon dioxide-water was predicted using the SPC-as well as the TIP4P-model for water and the EPM2-model for carbon dioxide. The interactions between carbon dioxide and water were estimated from the pair potentials of the pure components using common mixing rules without any adjustable binary parameter. Agreement of the predicted data for the compositions of the coexisting phases in vapor-liquid equilibrium and experimental results is observed within the statistical uncertainties of the simulation results in the investigated range of state, i.e. at pressures up to about 20 MPa.
Fluid Phase Equilibria, 2005
With the final purpose of describing the important aqueous + hydrocarbon liquid-liquid interfaces, the gradient theory was combined with the Cubic-Plus-Association equation of state (CPA EOS), taking advantage of the correct representation of interfacial tensions provided by the gradient theory and the correct phase equilibrium of water + hydrocarbon systems already obtained from CPA.
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.
Chemical Engineering Science, 2000
We simulate the phase segregation of a deeply quenched binary mixture with an initial concentration gradient. Our theoretical model follows the standard model H, where convection and di!usion are coupled via a body force, expressing the tendency of the demixing system to minimize its free energy. This driving force induces a material #ux much larger than that due to pure molecular di!usion, as in a typical case the Peclet number , expressing here the ratio of thermal to viscous forces, is of the order of 10.