An extended rational thermodynamics model for surface excess fluxes

In this paper, we derive constitutive equations for the surface excess fluxes in multiphase systems, in the context of an extended rational thermodynamics formalism. This formalism allows us to derive Maxwell-Cattaneo type constitutive laws for the surface extra stress tensor, the surface thermal energy flux vector, and the surface mass flux vector, which incorporate a direct coupling to their corresponding bulk fluxes in the adjacent bulk phases. These constitutive laws also incorporate contributions to the time evolution of the surface excess fluxes from spatial inhomogeneities in these flux fields. These phenomenological equations can be used to model the dynamic behavior of complex viscoelastic interfaces in multiphase systems, in the small deformation limit.