Effectiveness factors for substrate and product inhibition

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Abstract
The transformation technique of Na and Na (Math. Biosci., 6, 25, 1970) is extended to convert boundary‐value problems involving the steady‐state diffusion equation for spherical immobilized enzyme particles exhibiting substrate and product inhibition to initial‐value problems. This allows a study of the influence of external mass transfer resistances on the effectiveness factors. It also considerably reduces the number of calculations required to investigate the effect of changes in the kinetic parameters on the overall rate of reaction. The existence of multiple steady states for substrate inhibition kinetics in spherical catalyst particles is illustrated and a criterion for uniqueness of steady states is developed. Effectiveness factors for competitive and noncompetitive product inhibition increase with increasing value of the Sherwood number for the substrate and increasing value of the ratio of substrate to product effective diffusivities within the particle.