THERMODYNAMICALLY CONSISTENT, FRAME INDIFFERENT DIFFUSE INTERFACE MODELS FOR INCOMPRESSIBLE TWO-PHASE FLOWS WITH DIFFERENT DENSITIES

TLDR

The authors introduce a thermodynamically consistent, frame‑indifferent diffuse interface model for incompressible two‑phase flows with different densities, also extended to include soluble species. The model is derived from rational continuum mechanics and generalized to soluble species, and matched asymptotic expansions yield sharp interface limits whose form depends on the mobility scaling, producing either classical or diffusion‑enabled models. The model satisfies local and global dissipation inequalities, is frame‑indifferent, introduces a surface‑diffusion term in the interface momentum balance, and all sharp interface limits obey natural energy inequalities.

Abstract

A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is frame indifferent. Moreover, it is generalized to situations with a soluble species. Using the method of matched asymptotic expansions we derive various sharp interface models in the limit when the interfacial thickness tends to zero. Depending on the scaling of the mobility in the diffusion equation, we either derive classical sharp interface models or models where bulk or surface diffusion is possible in the limit. In the latter case a new term resulting from surface diffusion appears in the momentum balance at the interface. Finally, we show that all sharp interface models fulfill natural energy inequalities.