Analytical Expression of the Substrate Concentration in Different Part of Particles with Immobilized Enzyme and Substrate Inhibition Kinetics

A mathematical model of enzyme flow calorimetry for the monitoring of hysteresis behaviour of immobilized enzyme is developed. The model is based on diffusion equations containing a non linear term related to substrate inhibition kinetics of the enzymatic reaction. This paper presents an approximate analytical method (He’s Homotopy perturbation method) to solve the non-linear differential equations for spherical, cylindrical and planar particles. Closed and simple analytical expressions for substrate concentration have been derived for all possible values of parameters. These results are compared with numerical results and are found to be in good agreement. The obtained results are valid for the whole solution domain.