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

Abstract

<p style="text-indent:20px;">Within this paper, we consider a heterogeneous catalysis system consisting of a bulk phase <inline-formula><tex-math id="M1">\begin{document}$ \Omega $\end{document}</tex-math></inline-formula> (chemical reactor) and an active surface <inline-formula><tex-math id="M2">\begin{document}$ \Sigma = \partial \Omega $\end{document}</tex-math></inline-formula> (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 (the reverse process). 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 phase, 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 and positivity of solutions are addressed.