## 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.