A mathematical analysis of transport and kinetics in electrocatalytic thin film biosensors with non-Michaelis-Menten kinetics

Vembu Ananthaswamy; V Vijayalakshmi; J. Anantha Jothi; Seenith Sivasundaram

Vembu Ananthaswamy The Madura College, Madurai, Tamil Nadu, India.
V Vijayalakshmi Research Centre and PG Department of Mathematics, The Madura College (Affiliated to Madurai Kamaraj University), Madurai, Tamil Nadu, India.
J. Anantha Jothi Research Centre and PG Department of Mathematics, The Madura College (Affiliated to Madurai Kamaraj University), Madurai, Tamil Nadu, India.
Seenith Sivasundaram Department of Mathematics, College of Science, Engineering and Mathematics, Daytona Beach, Florida 321114, USA

Abstract

A mathematical modelling of catalytic kinetics and transport of substrate concentrations in surface deposited films and currents are derived. Here, the enzymatic kinetics cannot be well explained by the Michaelis-Menten equation. The model is created on nonlinear reaction-diffusion equations with nonlinear terms related to enzymatic reactions of non Michaelis-Menten kinetics. This paper provides semi-analytical expressions of substrate concentrations and amperometric current for steady-state conditions. These nonlinear reaction-diffusion equations are solved by using the Ananthaswamy-Sivasankari method (ASM). The effect on current density of various parameters is explained. The numerical simulation of substrate concentration are achieved and compared with our analytical solutions. It is mentioned that a good agreement is noted.