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On the free boundary problem in the wen-langmuir shrinking core model for noncatalytic gas-solid reactions

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Sommario

Si dimostra un risultato locale di esistenza e unicitá della soluzione di un problema con frontiera libera per il modello del nucleo in contrazione in reazioni gas-solido non catalitiche. Le condizioni sulla frontiera libera sono del tipo

$$\begin{gathered} u_x (s(t),t) = g(u(s(t),t)),0< t \leqslant T, \hfill \\ \dot s(t) = f(u(s(t),t)),0< t \leqslant T, \hfill \\ \end{gathered} $$

con funztoni f e g generali soddisfacenti le ipotesi

$$\begin{gathered} g< 0g< 0,g(0) = 0, \hfill \\ f > 0f' > 0,f(0) = 0. \hfill \\ \end{gathered} $$

Le condizioni di Wen e di Langmuir, che sono date rispettivamente daf(x)=-g(x)=x n(n>0) e daf(x) =-g(x)=a x n/(b+cx n) (a,b,c,n>0), rientrano entrambe nel presente schema.

Summary

We prove a local result in time for the existence and uniqueness of the solution of the free boundary problem in the shrinking core model for noncatalytic gas-solid reactions. We impose free boundary conditions of the type

$$\begin{gathered} u_x (s(t),t) = g(u(s(t),t)),0< t \leqslant T, \hfill \\ \dot s(t) = f(u(s(t),t)),0< t \leqslant T, \hfill \\ \end{gathered} $$

with general functions g and f which satisfy the assumptions

$$\begin{gathered} g< 0g'< 0,g(0) = 0, \hfill \\ f > 0f' > 0,f(0) = 0. \hfill \\ \end{gathered} $$

The Wen and Langmuir conditions are given by,f(x)=-g(x)=x n(n>0) andf(x) =-g(x)=a x n/(b+cx n) (a,b,c,n>0), respectively, which both fulfill the above assumptions.

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Authors and Affiliations

  1. Instituto de Matematica ≪B. Levi≫, Facultad de Ciencias Exactas e Ing., Promar (CONICET-UNR), Avda. Pellegrini 250, 2000, Rosario, Argentina

    Domingo A. Tarzia

  2. Facultad de Ciencias Tecnologicas, Iniqui (CONICET-UNSa), Buenos Aires 177, 4400, Salta, Argentina

    Luis T. Villa

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  1. Domingo A. Tarzia
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  2. Luis T. Villa
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Additional information

This paper was finished while the first author was staying in the Istituto Matematico ≪Ulisse Dini≫ (Univ. di Firenze, Viale Morgagni 67A, (50134) Firenze, Italy), as a visiting professor of CNR-CNFM.

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Tarzia, D.A., Villa, L.T. On the free boundary problem in the wen-langmuir shrinking core model for noncatalytic gas-solid reactions. Meccanica 24, 86–92 (1989). https://doi.org/10.1007/BF01560134

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  • DOI: https://doi.org/10.1007/BF01560134

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