2019/11/29 by Björn Augner, Augner, Björn, Dieter Bothe +1
Mathematics · Physics and Astronomy · #35K51 #35K57 #80A30 #92E20 #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #FOS: Mathematics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1911.13030
openalex publication_date 2019/11/29 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
Every mathematical model describing physical phenomena is an approximation to\nmodel reality, hence has its limitations. Depending on characteristic values of\nthe variables in the model, different aspects of the model and, e.g.,\nthermodynamic mechanisms have to be emphasised, or may be neglected in a\nreduced limit model. Within this paper, a heterogeneous catalysis system will\nbe considered consisting of a bulk phase \Ω (chemical reactor) and an\nactive surface \Σ = \∂ \Ω (catalytic surface), between which\nchemical substances are exchanged via adsorption (transport of mass from the\nbulk boundary layer adjacent to the surface, leading to surface-accumulation by\na transformation into an adsorbed form) and desorption (vice versa). Quite\ntypically, as is the purpose of catalysis, chemical reactions on the surface\noccur several orders of magnitude faster than, say, chemical reactions within\nthe bulk, and sorption processes are often quite fast as well. Starting from\nthe non-dimensional version, different limit models, especially for fast\nsurface chemistry and fast sorption at the surface, are considered. For a\nparticular model problem, questions of local-in-time existence of strong and\nclassical solutions, positivity of solutions and blow-up criteria for global\nexistence are addressed.\n