Transport of heat and mass in a two-phase mixture: From a continuous to a discontinuous description

We present a theory that describes the transport properties of the interfacial region with respect to heat and mass transfer. Postulating the local Gibbs relation for a continuous description inside the interfacial region, we derive the description of the Gibbs surface in terms of excess densities and fluxes along the surface. We introduce overall interfacial resistances and conductances as the coefficients in the force-flux relations for the Gibbs surface. We derive relations between the local resistivities for the continuous description inside the interfacial region and the overall resistances of the surface for transport between the two phases for a mixture. It is shown that interfacial resistances depend among other things on the enthalpy profile across the interface. Since this variation is substantial, the coupling between heat and mass flow across the surface is also substantial. In particular, the surface puts up much more resistance to the heat and mass transfer than the homogeneous phases over a distance comparable to the thickness of the surface. This is the case not only for the pure heat conduction and diffusion but also for the cross effects such as thermal diffusion. For the excess fluxes along the surface and the corresponding thermodynamic forces, we derive expressions for excess conductances as integrals over the local conductivities along the surface. We also show that the curvature of the surface affects only the overall resistances for transport across the surface and not the excess conductivities along the surface.