Phase-field models with tensorial mobilities for accurate solution of
two-phase transport problems
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 simultanuously 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.