IMA Postdoc Seminar (December 18, 2007)

Speaker: Erkan Tüzel (IMA)

Title: Mesoscopic model for the fluctuating hydrodynamics of binary and ternary mixtures

Abstract: Recent improvements in fluorescence microscopy and digital image processing enable direct observations of thermal fluctuations in phase separating binary mixtures. For example, the analysis of capillary wave statics and dynamics in suspended mixed lipid monolayer membranes is being used to gain insight into the nature of the intermolecular interactions. Due to the level of complexity in these systems, mesoscale simulations which incorporate thermal fluctuations can significantly improve our understanding of these systems. Here we describe a recently introduced particle-based model for the fluid dynamics of 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. 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 dispersion relation for the capillary waves is derived and compared with the numerical measurements of the time correlations of the radial fluctuations in the damped and over-damped limits. The introduction of ``amphiphilic'' dimers makes it possible to model the phase behavior of ternary surfactant mixtures.