TRAVELING WAVES FOR DISTRIBUTED GAS-SOLID REACTIONS

We investigate traveling waves for distributed gas-solid reactions wit h a powerlaw reaction rate. In this model the diffusing gas reacts wit h an immobile solid phase, leading to coupled partial and ordinary dif ferential equations. We consider both the case of positive porosity an d the pseudo-steady-problem with zero porosity. The wave profile consi sts of a pair (u, w) where u is the gas concentration and w is the sol id concentration. As boundary conditions we take w(- infinity) = 0, u( + infinity) = 0, w(+ infinity) = 1, as is appropriate for a wave trave ling from left to right while consuming the solid as it moves. Our pri ncipal result, obtained by phase-plane methods, is that to each veloci ty v > 0 there corresponds a unique wave profile, modulo translations. If the power of the solid reaction rate is less than 1, a conversion front exists behind which the solid is fully consumed (w = 0); if the power of the gas reaction rate is less than 1, the gas does not fully penetrate the solid, leading to a penetration front ahead of which u = 0. We provide estimates for the location of these fronts and analyze their local behavior. Our results both agree with and extend those of Bobisud who studies similar equations in a different context and on a semi-infinite interval. (C) 1994 Academic Press, Inc.