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The general problem of two-phase transport in phase-field models is analyzed:the flux of a conserved quantity is driven by the gradient of a potentialthrough a medium that consists of domains of two distinct phases which areseparated by diffuse interfaces. It is shown that the finite thickness of theinterfaces induces two effects that are not present in the analogoussharp-interface problem: a surface excess current and a potential jump at theinterfaces. It is shown that both effects can be eliminated simultaneously onlyif the coefficient of proportionality between flux and potential gradient(mobility) is allowed to become a tensor in the interfaces. This opens thepossibility for precise and efficient simulations of transport problems withfinite interface thickness.

Tensorial mobilities for accurate solution of transport problems in models with diffuse interfaces