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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-state material balance to the substrate as transported by diffusion and depleted by a biochemical reaction following classical Michaëlis-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-order, non-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.
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Citação
MALCATA, F. Xavier - On the approximate analytical solution of a problem of optimization in the field of immobilized enzymes. International Journal of Mathematical Education in Science and Technology. ISSN 0020-739X. Vol. 22, n.º 2 (1991), p. 177 - 185
Editora
Taylor & Francis