A continuum model of heterogeneous catalysis: Thermodynamic framework for multicomponent bulk and surface phenomena coupled by sorption

Abstract

We derive a thermodynamically consistent model of heterogeneous catalysis for chemically reacting fluid mixtures formulated in the framework of continuum thermodynamics. The model takes into account standard transport phenomena in the bulk domain and involves mass transfer of the species between the bulk and the catalytic (active) part of the boundary where the surface counterparts to the bulk transport processes take place.Concerning the balance laws on the catalytic surface, the model benefits from description of the active part of the boundary as an interface between the bulk domain and its exterior which allows to employ the framework of continuum mechanics with interfacial transport phenomena. The constitutive relations involving vectorial and tensorial quantities such as the Cauchy stress, energy and entropy fluxes and diffusive fluxes relevant to individual constituents are constructed in a systematic manner ensuring compatibility with the second law of thermodynamics. The constitutive procedure follows from the specification of constitutive equations for suitable thermodynamic potentials (free energies) of the mixture in the bulk and on the active part of the boundary and from the identification of the bulk and surface entropy productions. The active part of the boundary is described by means of statistical physics and this description then serves as a building block for the derivation of surface continuum thermodynamic potentials.The derived model is suitable for further mathematical, numerical and computational analysis of relevant initial and boundary value problems. While the model employs a relatively simple description of the active part of the boundary as a monolayer lattice with single-site Langmuir-type adsorption, its detailed derivation presented here provides clear guidelines for the incorporation of other sorption models.