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

TL;DR

This paper introduces tensorial mobilities in phase-field models to accurately simulate two-phase transport, accounting for diffuse interface effects like surface excess current and potential jump, enabling more precise and efficient computations.

Contribution

It proposes using tensorial mobility coefficients within diffuse interfaces to eliminate interface effects, improving the accuracy of transport simulations in phase-field models.

Findings

Tensorial mobilities remove interface effects.

Enhanced accuracy in diffuse interface transport simulations.

Potential for more efficient computational methods.

Abstract

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 potential through a medium that consists of domains of two distinct phases which are separated by diffuse interfaces. It is shown that the finite thickness of the interfaces induces two effects that are not present in the analogous sharp-interface problem: a surface excess current and a potential jump at the interfaces. It is shown that both effects can be eliminated simultaneously only if the coefficient of proportionality between flux and potential gradient (mobility) is allowed to become a tensor in the interfaces. This opens the possibility for precise and efficient simulations of transport problems with finite interface thickness.