Abstract
In this paper, mathematical models of immobilized enzyme system that follow the Michaelis-Menten mechanism for both reversible and irreversible reactions are discussed. This model is based on the diffusion equations containing the non-linear term related to Michaelis-Menten kinetics. An approximate analytical technique employing the modified Adomian decomposition method is used to solve the non-linear reaction diffusion equation in immobilized enzyme system. The concentration profile of the substrate is derived in terms of all parameters. A simple expression of the substrate concentration is obtained as a function of the Thiele modulus and the Michaelis constant. The numerical solutions are compared with our analytical solutions for slab, cylinder and spherical pellet shapes. Satisfactory agreement for all values of the Thiele modulus and the Michaelis constant is noted. Graphical results and tabulated data are presented and discussed quantitatively to illustrate the solution.
Highlights
Many problems in theoretical and experimental biology involve reaction diffusion equations with nonlinear chemical kinetics
Benaiges et al [5] studied the isomerzation of glucose into fructose using a commercial immobilized glucose-isomerase
We have presented the analytical expressions for substrate concentrations for all the three cases of kinetic models and for all possible values of the parameters using modified Adomian decomposition method [16,17,18,19,20,21]
Summary
Many problems in theoretical and experimental biology involve reaction diffusion equations with nonlinear chemical kinetics Such problems arise in the formulation of substrate and product material balances for enzymes immobilized within particles [1] in the description of substrate transport into microbial cells [2], in membrane transport, in the transfer of oxygen to respiring tissue and in the analysis of some artificial kidney systems [3]. For such cases, the problem is often well poised as a two-point nonlinear boundary-value problem because of the saturation, Michaelis-Menten, or Monod expressions which are used to describe the consumption of the substrate. The general expressions for the mean integrated effectiveness factor for all values of parameters are presented
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