Abstract

A thermal-dynamical consistent model for mass transfer across permeable moving interfaces is proposed by using energy variation method. We consider a restricted diffusion problem where the flux across the interface depends on its conductance and the difference of the concentration on each side. The diffusive interface phase-field has several advantages: 1) explicit tracking of the interface is no longer necessary, 2) the interfacial condition can be incorporated with a variable diffusion coefficient. A detailed asymptotic analysis confirms the diffusive interface model converges to the sharp interface model. An energy stable numerical scheme is developed to solve this system efficiently. Numerical simulations illustrate the effectiveness of our phase-field approach.

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