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

Augner, Björn; Bothe, Dieter

doi:10.3934/dcdss.2020406

Cited by 5 publications

(8 citation statements)

References 34 publications

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“…Under these assumptions, and the additional assumption that the sorption processes and surface chemistry take place very fast, i.e. on much smaller time scales than the bulk diffusion and the bulk chemistry, it has been demonstrated in [5] that (GFLM) is a reasonable limit model for the limiting case of infinitely fast surface chemistry and sorption processes (actually, independent of whether one of these two fast thermodynamic mechanism is even ultra-fast), and the condensed form of the limit model (including initial values) reads…”

Section: Modelling Assumptionsmentioning

confidence: 99%

“…surface chemistry and sorption processes are modelled as if they would attain an equilibrium configuration instantaneously. Using a dimensionless formulation of such coupled reaction-diffusion-sorption bulk-surface systems, several of such limit models have been proposed in [5], including a general formulation of such a fast sorption and fast surface chemistry model. The mathematical analysis of such systems has been accomplished for the case of a three-component system with chemical reactions of type A 1 + A 2 A 3 on the surface, neglecting any bulk chemistry (the latter being no severe obstacle, and for the construction of (uniquely determined) strong solutions not a highly relevant assumption).…”

Section: Introductionmentioning

confidence: 99%

“…Thereafter, in Sect. 3, the class of heterogeneous catalysis models considered in this manuscript is introduced and the underlying modelling assumptions recalled from the article [5]. Section 4 constitutes the core of this article and is split into subsections on L p -maximal regularity of a linearised version of the fast-sorption-fast-surface-chemistry model, on local-in-time existence of strong W…”

Section: Introductionmentioning

confidence: 99%

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

Augner

Bothe

2021

J. Evol. Equ.

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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, a priori bounds and comment on steps towards global existence of strong solutions in the class $$\mathrm {W}^{(1,2)}_p(J \times \Omega ; {{\,\mathrm{{\mathbb {R}}}\,}}^N)$$ W p ( 1 , 2 ) ( J × Ω ; R N ) , and of classical solutions in the Hölder class $$\mathrm {C}^{(1+\alpha , 2 + 2\alpha )}({\overline{J}} \times {\overline{\Omega }}; {{\,\mathrm{{\mathbb {R}}}\,}}^N)$$ C ( 1 + α , 2 + 2 α ) ( J ¯ × Ω ¯ ; R N ) . Exploiting that the model is based on thermodynamic principles, we further show a priori bounds related to mass conservation and the entropy principle.

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Section: Modelling Assumptionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Augner

Bothe

2021

J. Evol. Equ.

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“…I would like to thank Dieter Bothe for bringing up the interesting fast surface chemistry and fast sorption model considered in [3] and [4] and for encouraging me to extend the appendix of a preprint version of the latter to this full manuscript. Also, I would like to thank Robert Denk for his kind advice.…”

Section: Acknowledgementmentioning

confidence: 99%

$\mathrm{L}_p$-maximal regularity for parabolic and elliptic boundary value problems with boundary conditions of mixed differentiability orders

Augner¹

2021

Preprint

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In the theory of non-linear parabolic and elliptic partial differential equations, the notion of maximal regularity plays an essential role in establishing existence, regularity and boundedness of solutions. There is a long history of works where sufficient conditions for maximal regularity have been established: First scalar equations and systems of finitely many coupled equations have been considered. Around 2000, the vector-valued case with infinite-dimensional range space E became accessible to the development and progress in theory of R-bounded operator families and its close connection to the H ∞ -calculus. The ground-braking results by Denk, Hieber and Prüss for Lp-maximal regularity of vector-valued parabolic and elliptic boundary value problems, however, were restricted to boundary conditions with homogeneous principle parts of the boundary symbol, in contrast to some previous results by Ladyszenskaya, Solonnikov and Uralceva for finite-component systems which also allow for, e.g. both Dirichlet and (mixed) flux boundary conditions at the same position. In this manuscript we aim for closing this gap, and extend the results of Denk, Hieber and Prüss to this slightly more general situation. To this end, we closely review the strategy used in their works and adapt it to the situation considered here.

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“…We also refer to [AB21a,AB21b] for interesting discussions in the context of catalysis, or to [BP17]. For the heat flux, typical are for instance cooling conditions like −r Γ h (x, t, T ) = α (T − T ext (x, t)), where T ext is the given external temeprature and α a positive coefficient.…”

Section: Transport and Mechanics For A Composite Newtonian Fluidmentioning

confidence: 99%

Maximal mixed parabolic-hyperbolic regularity for the full equations of multicomponent fluid dynamics

Druet

2021

Preprint

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We consider a Navier-Stokes-Fick-Onsager-Fourier system of PDEs describing mass, energy and momentum balance in a Newtonian fluid with composite molecular structure. For the resulting parabolic-hyperbolic system, we introduce the notion of optimal regularity of mixed type, and we prove the short-time existence of strong solutions for a typical initial boundary-value-problem. By means of a partial maximum principle, we moreover show that such a solution cannot degenerate in finite time due to blow-up or vanishing of the temperature or the partial mass densities. This second result is however only valid under certain growth conditions on the phenomenological coefficients. In order to obtain some illustration of the theory, we set up a special constitutive model for volume-additive mixtures.

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

Cited by 5 publications

References 34 publications

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

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

$\mathrm{L}_p$-maximal regularity for parabolic and elliptic boundary value problems with boundary conditions of mixed differentiability orders

Maximal mixed parabolic-hyperbolic regularity for the full equations of multicomponent fluid dynamics

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