M. Loewenberg, DIFFUSION-CONTROLLED, HETEROGENEOUS REACTION IN A MATERIAL WITH A BIMODAL PORESIZE DISTRIBUTION, The Journal of chemical physics, 100(10), 1994, pp. 7580-7589
A theoretical analysis is developed for diffusion-controlled heterogen
eous reaction in a material with a bimodal poresize distribution. A co
nfigurational averaging procedure is used to describe a sparse, random
network of macropore capillaries contained in a reactive, otherwise h
omogeneous matrix. The analysis is valid for a wide range of reactivit
ies, and is particularly suited for conditions where reactant concentr
ation varies on a length scale comparable to the diameter of, or the s
pacing between the macropores. The results depend on the reactivity on
the matrix, the void volume of the macropore network, and the macropo
re to matrix diffusivity ratio. A local effectiveness parameter, which
depends on the reactivity and macropore void volume, characterizes th
e reaction behavior in the material. An exact numerical solution is ob
tained that depends analytically on the parameters of the problem, and
an accurate analytical representation is derived that depends very si
mply on the local effectiveness, the macropore void volume, and the di
ffusivity ratio; typical results are presented. The solution reduces t
o simplified models of the heterogeneous reaction in the low- and high
-reactivity limits, where reactant concentration varies on a length sc
ale that is large compared to the macropore spacing or small compared
to the macropore diameter.