TY - JOUR

T1 - On the approximate analytical solution of a problem of optimization in the field of immobilized enzymes

AU - Xavier Malcata, F.

PY - 1991

Y1 - 1991

N2 - 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–enten 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.

AB - 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–enten 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.

UR - http://www.scopus.com/inward/record.url?scp=0002752095&partnerID=8YFLogxK

U2 - 10.1080/0020739910220202

DO - 10.1080/0020739910220202

M3 - Article

AN - SCOPUS:0002752095

VL - 22

SP - 177

EP - 185

JO - International Journal of Mathematical Education in Science and Technology

JF - International Journal of Mathematical Education in Science and Technology

SN - 0020-739X

IS - 2

ER -