Rate constants of spherical dispersions: From diffusion-limited data to nondiffusion limited results

A simple but accurate equation is derived for calculation of the overall rate constants of nondiffusion-limited incorporation of diffusing species in spherical dispersions, based on the corresponding results of the diffusion-limited cases. The proposed equation checks very well with the accurate nondiffusion limited rate constant data of three regular spherical arrays computed by Lu [J. Chem. Phys. 109, 4985 (1998)]. The relative errors are less than 5% for volume fractions as high as 0.45 for the simple cubic array and 0.6 for both the face-centered and body-centered cubic arrays. Results from the proposed equation deviate the most from the accurate data at intermediate P. Here P is a dimensionless parameter characterizing the relative rate of diffusive transport versus surface incorporation.