  We propose and study a one-dimensional model which consists of two
cross-diffusion systems coupled via a moving interface. The motivation stems
from the modelling of complex diffusion processes in the context of the vapor
deposition of thin films. In our model, cross-diffusion of the various chemical
species can be respectively modelled by a size-exclusion system for the solid
phase and the Stefan-Maxwell system for the gaseous phase. The coupling between
the two phases is modelled by linear phase transition laws of Butler-Volmer
type, resulting in an interface evolution. The continuous properties of the
model are investigated, in particular its entropy variational structure and
stationary states. We introduce a two-point flux approximation finite volume
scheme. The moving interface is addressed with a moving-mesh approach, where
the mesh is locally deformed around the interface. The resulting discrete
nonlinear system is shown to admit a solution that preserves the main
properties of the continuous system, namely: mass conservation, nonnegativity,
volume-filling constraints, decay of the free energy and asymptotics. In
particular, the moving-mesh approach is compatible with the entropy structure
of the continuous model. Numerical results illustrate these properties and the
dynamics of the model.
