Mesoscopic model for the fluctuating hydrodynamics of binary and ternary mixtures

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. Introduction. – Hydrodynamic interactions and thermal fluctuations play a crucial role in a wide range of phenomena in soft matter physics and molecular and cellular biology. Because of the complexity of these systems, simulations have played an essential role in much of the research in these areas. In fact, the wide range of length and time scales in these problems places severe requirements on simulation protocol, and has lead to the development of several new coarse-grained, mesoscale simulation techniques such as lattice gas automata [1], the lattice Boltzmann method [2], dissipative particle dynamics [3,4], smoothed particle hydrodynamics [5], and a newer approach variously called multi-particle collision dynamics or stochastic rotation dynamics (SRD) [6]. The basic motivation of all these approaches is to coarse-grain out irrelevant atomistic details while correctly incorporating the essential physics and conservation laws. SRD has several attractive features which have lead to its use in studies ranging from sedimentation in colloidal suspensions [7] to the dynamic behavior of polymers in solution [8,9] and vesicles in flow [10]. In particular, it enables simulations in the microcanonical ensemble while fully incorporating both hydrodynamic interactions and thermal fluctuations; in addition, because SRD is a particle-based method, the coupling to colloidal particles, polymers, or other aggregates is straightforward, and the Brownian motion of these embedded objects is realized in a very natural way—through random collisions with the solvent particles. Finally, the simplicity of the algorithm has made it possible to obtain accurate analytic expressions for the transport coefficients [11–13].