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

Björn Augner; Dieter Bothe

doi:10.3934/dcdss.2020406

Article Contents

2021, Volume 14, Issue 2: 533-574. Doi: 10.3934/dcdss.2020406

This issue Previous Article On classes of well-posedness for quasilinear diffusion equations in the whole space Next Article Instability of free interfaces in premixed flame propagation

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

Björn Augner and
Dieter Bothe^,

Fachbereich Mathematik, Technische Universität Darmstadt, Alarich-Weiss-Straße 10, 64287 Darmstadt, Germany

^* Corresponding author: Dieter Bothe, bothe@mma.tu-darmstadt.de
^* Corresponding author: Dieter Bothe, bothe@mma.tu-darmstadt.de

Dedicated to Michel Pierre on the occasion of his 70^th anniversary

Received: October 31, 2019

Revised: May 31, 2020

Early access: July 2020

Published: February 2021

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Abstract

Within this paper, we consider a heterogeneous catalysis system 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 (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.

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Mathematics Subject Classification: Primary 35K57; Secondary 35K51, 80A30, 92E20.

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Figure 1. Physical and chemical mechanisms in a bulk-surface reaction diffusion system

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Figure 2. Free sites on the surface are interpreted as an additional species $ A_0^\Sigma $

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