Effectiveness factor calculations for immobilized enzyme catalysts

Abstract

The steady state, nonlinear diffusion equations which describe reactions in constrained enzyme solutions are of great interest in many biological and engineering applications. As in other types of nonlinear differential equations, exact analytical solutions do not exist except in some simplified cases. In this paper, a general procedure is presented for solving numerically for the substrate concentration profile and effectiveness factor utilizing the transformation method suggested by Na and Na. Design correlations for enzyme solutions constrained within spherical membranes are included. The use of a unique definition of the Thiele Modulus in these charts permits the clear illustration of the effects of substrate concentration and external mass transfer resistances on the overall effectiveness factor for the catalyst particle.