On the approximate analytical solution of a problem of optimization in the field of immobilized enzymes

摘要

The problem of optimizing the thickness of a microporous slab containing an immobilized enzyme is addressed, using an economic criterion as the objective function. The steady#x2010;state material balance to the substrate as transported by diffusion and depleted by a biochemical reaction following classical Micha#xEB;lis#x2010;Menten kinetics within the pellet is obtained. Taking advantage of a number of algebraic manipulations and mathematical artefacts, one is able to solve the resulting second#x2010;order, non#x2010;linear differential equation by an analytical method, provided that an upper error bound for the solution in the order of 5 per cent is acceptable. The validity of the approximation is tested, and useful applications are reported.