Mesoscopic model for the fluctuating hydrodynamics of binary and ternary mixtures

TL;DR

This paper extends a particle-based fluid dynamics model to simulate immiscible binary and ternary mixtures, accurately capturing phase separation, phase diagrams, and line tension, with potential applications in surfactant mixture modeling.

Contribution

It introduces a generalized mesoscopic model for binary and ternary mixtures with explicit phase behavior and validated analytic and simulation results.

Findings

Analytic phase diagram matches simulation data.

Derived explicit equation of state for mixtures.

Measured line tension agrees with Laplace's law.

Abstract

A recently introduced particle-based model for fluid dynamics with continuous velocities is generalized to model immiscible binary mixtures. Excluded volume interactions between the two components are modeled by stochastic multiparticle collisions which depend on the local velocities and densities. Momentum and energy are conserved locally, and entropically driven phase separation occurs for high collision rates. An explicit expression for the equation of state is derived, and the concentration dependence of the bulk free energy is shown to be the same as that of the Widom-Rowlinson model. Analytic results for the phase diagram are in excellent agreement with simulation data. Results for the line tension obtained from the analysis of the capillary wave spectrum of a droplet agree with measurements based on the Laplace's equation. The introduction of "amphiphilic" dimers makes it possible to model the phase behavior and dynamics of ternary surfactant mixtures.