Global stability of symmetric and asymmetric concentration profiles in catalyst particles

Abstract

Consider the simultaneous occurrence of a catalytic reaction together with heat and mass transfer in a uniform symmetric environment. Until recently it has been customary to assume that in such a situation all equilibrium temperature and concentration profiles would share the symmetry of the environment. This assumption was first challenged in 1967 by PIS'MEN • KHARKATS [9], who proved that in certain cases there also exist asymmetric equilibrium profiles. Moreover, by the usual heuristic arguments, they showed that it is possible for an asymmetric equilibrium profile to be stable with respect to small perturbations. Subsequent work [1], [3], [5] has extended these results to a variety of situations. In this paper we study a model of a porous catalytic particle proposed by M. MAREK [7]. For this model, we determine the dependence of the configuration of asymmetric equilibrium profiles on the Nusselt number, and derive the global stability properties of all of the equilibrium profiles. We consider an infinite slab of a homogeneous inert porous material both of whose faces are the sites of a catalytic reaction. The slab is situated in a bath in which the reactant is present with a constant concentration V. It is assumed that the reaction rate is independent of the temperature. If we choose the x-axis perpendicular to the slab and position the origin of coordinates so that the two faces are at x = 0 and x=l, then the concentration c(x, t) satisfies the differential equation ct=Dcx~ for O O