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We consider the incompressible flow of two immiscible fluids in the presenceof a solid phase that undergoes changes in time due to precipitation anddissolution effects. Based on a seminal sharp interface model a phase fieldapproach is suggested that couples the Navier-Stokes equations and the solid'sion concentration transport equation with the Cahn-Hilliard evolution for thephase fields. The model is shown to preserve the fundamental conservationconstraints and to obey the second law of thermodynamics for a novel freeenergy formulation. An extended analysis for vanishing interfacial widthreveals that in this limit the sharp interface model is recovered, includingall relevant transmission conditions. Notably, the new phase field model isable to realize Navier-slip conditions for solid-fluid interfaces in the limit.

A Ternary Cahn-Hilliard Navier-Stokes Model for Two Phase Flow with Precipitation and Dissolution