A thermodynamically consistent diffuse interface model for multi-component two-phase flow with partial miscibility

In this paper, we aim to develop a thermodynamically consistent diffuse interface model for two-phase multicomponent fluids with partial miscibility based on the second law of thermodynamics. The resulting governing equations consist of the Allen-Cahn equation for the order parameter representing the phase volume fraction, the Cahn-Hilliard equation for the molar fraction of each component in the mixture, and the full NavisStokes equations coupled with the surface tension force for the velocity and pressure fields. Compared with the previous models, both the phase interface and the molar concentration can be captured simultaneously, and the derived governing equations guarantee thermodynamic consistency. Then, a lattice Boltzmann method is presented to numerically solve the proposed mathematical model. Several numerical simulations are performed to demonstrate the capabilities of the developed model.