Thermodynamically consistent diffuse-interface mixture models of incompressible multicomponent fluids

Abstract

The prototypical diffuse-interface model for incompressible fluid mixtures is the Navier-Stokes Cahn-Hilliard (Allen-Cahn) model. Despite its foundation in continuum mixture theory, it is not fully compatible with this theory due to the diffusive flux approximation. This paper introduces a class of thermodynamically consistent diffuse-interface incompressible fluid mixture models that is fully compatible with the continuum theory of mixtures. The proposed models can be formulated in either constituent or mixture quantities, enabling a direct comparison with the Navier-Stokes Cahn-Hilliard (Allen-Cahn) model with non-matching densities. This comparison reveals the key modelling simplifications employed in the latter.