Heat, Mass and Charge Transport, and Chemical Reactions at Surfaces

Abstract

In this work we derive the excess entropy production rate for heat, mass and charge transport into, out of and across a surface, using as basic variables the excess densities proposed by Gibbs. With the help of these variables we define the surface as an autonomous system (i.e. a surface in local equilibrium) and find its excess entropy production rate. This then determines the conjugate fluxes and forces. Equivalent forms of the entropy production rate are given. The forms contain finite differences of intensive variables into and across the surface as driving forces. The general form of the force-flux relations is given. The expressions for the fluxes serve as boundary conditions for integration across heterogeneous systems. Two examples are discussed in more detail. The first example is the practically important coupled transport of heat and mass into and through a liquid-vapor surface. The second example concerns phenomena at electrode surfaces: the coupled transport of heat, mass and charge and a chemical reaction. By assuming that the two sides of the surface can be described as resistances in series, we are able to reduce the number of unknown transport coefficients considerably. For both examples it is shown that the coupling coefficients for heat and mass flow are large at the surface, when the homogeneous phases have a large enthalpy difference. As a consequence it is not sufficient to use, for instance, Fourier’s law for transport of heat across surfaces.