A Thermodynamic Approach to Interfacial Transport Phenomen

Formulating balance equations for extensive quantities at interfaces in terms of excess densities is a subtle problem because these densities change with the precise location of the dividing surface within the interfacial region. We propose to handle such ambiguities for dynamic interfaces by introducing a gauge degree of freedom associated with the location of the dividing surface and by studying all the normal velocities associated with different excess densities. Unambiguous interfacial balance equations can then be obtained directly from the differences between normal velocities. By considering the interfacial entropy balance along with the local equilibrium assumption, and identifying the entropy production rate at the interface, we are naturally led to thermodynamically consistent constitutive equations for the fluxes characterizing transport both within and at the interface. The usefulness and generality of the proposed approach is illustrated in the context of several examples.