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

Abstract

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