Diffusion and reaction in rectangular arrays of spheroids

Abstract

The overall rate constant of surface reaction of diffusing species in rectangular arrays of spheroidal particles is investigated. The surface reaction occurring on the particle surface may be of finite rate. Calculation results for a wide range of array structures are obtained, by varying the particle and array aspect ratios. The normalized overall rate constant, k/k0, is found to be a function of the particle volume fraction (f ), a dimensionless parameter P characterizing the relative rate of diffusive transport vs surface reaction, and the array structure characterized by the particle (ra) and array (re) aspect ratios. When the process is diffusion-limited (P=0), results from the present development agree very well with those from first passage time simulations. When it is surface reaction limited (P→∞), k/k0 is shown to exactly equal 1/(1−f ), independent of the system structure. Generally, k/k0 decreases with increasing P, but increases with increasing f. At a fixed ra,k/k0 decreases with increasing deviation of re from unity, while, for a fixed re,k/k0 increases with increasing deviation of ra from unity. Under some particular circumstances, k/k0 may be less than unity, meaning that particle competition may play a negative role for k/k0. This occurs when the deviation of re from unity is greater than that of ra, i.e., the array is more slender or flat than the particle. An approximate relation for estimation of nondiffusion limited k/k0 based on the corresponding diffusion-limited datum is derived. This approximation works well for systems of small and large P and for array structures not deviating too much from the simple cubic array of spheres.