A spatially smoothed jump condition is developed for the process of diffusi
on and reaction at a catalytic surface where a first-order, irreversible re
action takes place at isolated regions on the fluid-solid interface. The po
int jump condition for this process is given by
-n(gamma kappa).D gamma delc(A gamma) = kc(A gamma) at the gamma-kappa inte
rface,
in which the rate coefficient k undergoes abrupt changes with position on t
he fluid-solid interface. The averaging procedure leads to a spatially smoo
thed jump condition that takes the form
-n(gamma kappa).D(gamma)del [c(A gamma)](gamma) = k(eff)[c(A gamma)](gamma)
at the gamma-kappa interface,
in which the effective reaction rate coefficient is determined by the solut
ion of a closure problem. It is this effective reaction rate coefficient, t
imes the interfacial area per unit volume, that is measured in a typical ex
perimental study of diffusion and reaction in a porous catalyst. The soluti
on 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. (C) 2000
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