The fast-sorption--fast-surface-reaction limit of a heterogeneous catalysis model

TL;DR

This paper investigates a mathematical model of heterogeneous catalysis, focusing on the fast-sorption and fast-surface-reaction limits, and analyzes the existence, positivity, and blow-up criteria of solutions in these regimes.

Contribution

It introduces and analyzes limit models for fast sorption and surface reactions in heterogeneous catalysis, addressing solution existence and blow-up conditions.

Findings

Established local-in-time existence of solutions.

Proved positivity of solutions.

Derived blow-up criteria for global solutions.

Abstract

Every mathematical model describing physical phenomena is an approximation to model reality, hence has its limitations. Depending on characteristic values of the variables in the model, different aspects of the model and, e.g., thermodynamic mechanisms have to be emphasised, or may be neglected in a reduced limit model. Within this paper, a heterogeneous catalysis system will be considered consisting of a bulk phase $\Omega$ (chemical reactor) and an active surface $\Sigma = \partial \Omega$ (catalytic surface), between which chemical substances are exchanged via adsorption (transport of mass from the bulk boundary layer adjacent to the surface, leading to surface-accumulation by a transformation into an adsorbed form) and desorption (vice versa). Quite typically, as is the purpose of catalysis, chemical reactions on the surface occur several orders of magnitude faster than, say, chemical reactions within the bulk, and sorption processes are often quite fast as well. Starting from the non-dimensional version, different limit models, especially for fast surface chemistry and fast sorption at the surface, are considered. For a particular model problem, questions of local-in-time existence of strong and classical solutions, positivity of solutions and blow-up criteria for global existence are addressed.