A Thermodynamically Consistent Approach to Phase-Separating Viscous Fluids

Abstract

Abstract The de-mixing properties of heterogeneous viscous fluids are determined by an interplay of diffusion, surface tension and a superposed velocity field. In this contribution a variational model of the decomposition, based on the Navier–Stokes equations for incompressible laminar flow and the extended Korteweg–Cahn–Hilliard equations, is formulated. An exemplary numerical simulation using C 1 {C}^{1} -continuous finite elements demonstrates the capability of this model to compute phase decomposition and coarsening of the moving fluid.