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

TL;DR

This paper develops a theoretical framework for describing heat and mass transfer in the interfacial region of a two-phase mixture, linking continuous and discontinuous descriptions through interfacial resistances and conductances.

Contribution

It introduces a novel approach to relate local interfacial resistivities to overall surface resistances, accounting for enthalpy profiles and surface curvature effects.

Findings

Interfacial resistances depend on enthalpy variation across the interface.

Surface resistance to heat and mass transfer exceeds that of homogeneous phases.

Curvature affects overall resistances but not excess conductivities along the surface.

Abstract

We present a theory which 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 are also substantial. In particular, the surface puts up much more resistance to the heat and mass transfer then 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 like 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.