Analysis of some heterogeneous catalysis models with fast sorption and fast surface chemistry

TL;DR

This paper analyzes simplified models of heterogeneous catalysis with fast sorption and surface chemistry, establishing well-posedness, positivity, and bounds based on thermodynamic principles.

Contribution

It provides a rigorous mathematical analysis of limit models for heterogeneous catalysis with fast processes, including well-posedness and thermodynamic consistency.

Findings

Proved local-in-time well-posedness of the models.

Established positivity and global existence of solutions.

Derived a priori bounds based on mass conservation and entropy principles.

Abstract

We investigate limit models resulting from a dimensional analysis of quite general heterogeneous catalysis models with fast sorption (i.e.\ exchange of mass between the bulk phase and the catalytic surface of a reactor) and fast surface chemistry for a prototypical chemical reactor. For the resulting reaction-diffusion systems with linear boundary conditions on the normal mass fluxes, but at the same time nonlinear boundary conditions on the concentrations itself, we provide analytic properties such as local-in time well-posedness, positivity and global existence of strong solutions in the class $\mathrm{W}^{(1,2)}_p(J \times \Omega; \mathbb{R}^N)$, and of classical H\"older solutions in the class $\mathrm{C}^{(1+\alpha, 2 + 2\alpha)}(\overline J \times \overline{\Omega})$. Exploiting that the model is based on thermodynamic principles, we further show a priori bounds related to mass conservation and the entropy principle.