Abstract
The normalized overall rates constant (k/k 0 ) for rectangular arrays of spheroids are computed by solving the relevant boundary value problem with a boundary collocation method. The k/k 0 was found to be a function of f. P, and the array structure as characterized by the particle and array aspect ratios. The dimensionless quantity P characterizes the relative rate of diffusive transport versus surface reaction. At P = 0, it is the diffusion-limited situation and results from the present development agree very well with those from first passage time simulations. As P tends to infinity, the process becomes surface reaction limited and the normalized overall rate constant was shown to exactly equal 1/(1-f), independent of the system structure. The k/k 0 , under most circumstances, is found to increase with increasing f, to decrease with increasing P, to decrease with increasing deviation of r e (array aspect ratio) from unity at a fixed r a (particle aspect ratio) and to increase with increasing deviation of r a from unity at a fixed r e . Exceptions do exist. It is also found that, when the array is more slender or flat than the particle, the normalized overall rate constant may be smaller than unity, signifying a negative particle competition effect. As P increases, the structural effect of k/k 0 weakens. Approximate equations, that enable estimation of k/k 0 of general P from corresponding data at the P value of 0, are also derived and tested. Generally, the accuracy of the approximate model worsens for intermediate P and for arrays that deviate more from the simple cubic array of spheres.