Jump conditions at non-uniform boundaries: the catalytic surface

Abstract

A spatially smoothed jump condition is developed for the process of diffusion and reaction at a catalytic surface where a first-order, irreversible reaction takes place at isolated regions on the fluid–solid interface. The point jump condition for this process is given by − n γκ· D γ∇c Aγ=kc Aγ at the γ–κ interface, in which the rate coefficient k undergoes abrupt changes with position on the fluid–solid interface. The averaging procedure leads to a spatially smoothed jump condition that takes the form − n γκ· D γ∇〈c Aγ〉 γ=k eff 〈c Aγ〉 γ at the γ–κ interface, in which the effective reaction rate coefficient is determined by the solution of a closure problem. It is this effective reaction rate coefficient, times the interfacial area per unit volume, that is measured in a typical experimental study of diffusion and reaction in a porous catalyst. The solution of the closure problem allows one to relate the intrinsic properties of the catalytic surface to k eff, and the results are presented in terms of a surface effectiveness factor as a function of a Thiele modulus.