Molecular mean-field models of capillary dynamics

Abstract

A novel lattice-gas approach has been developed to model the effect of molecular interactions on dynamic interfacial structure and flows of liquid-vapor and liquid-liquid systems in microcapillaries. Within a mean-field approximation, discrete time evolution of species and momentum densities consists of alternating convective and diffusive steps subject to local conservation laws. Stick boundary conditions imposed during the convective step cause momentum transfer to lattice particles in contact with sheared solid walls. However, low densities, and diffusive relaxation of interfaces towards equilibrium give rise to velocity slip at the walls. We demonstrate applications of the single- and two-species isothermal versions of the model to capillary and wetting dynamics. The connections of the new approach to existing models of interfacial dynamics in two-phase flows are discussed, as well as its possible generalizations.