Mathematical Analysis of Unsteady-State Dynamics of a Liquid-Membrane-Encapsulated Urease System

Abstract

In the present investigation, a mathematical model describing the transient behavior of a water in oil type liquid-membrane-immobilized enzyme system has been presented. A deterministic model (as opposed to a stochastic one) has been presented in an attempt to elucidate the effect of mass-transfer limitation due to immobilization on the kinetics of hydrolysis of urea using an unstructured Michaelis-Menten equation and a mechanistic approach toward diffusion phenomena. An immobilized urease system has been selected to test the model within the initial substrate (urea) concentration range 0.001-4 M. With the help of concentration distribution curves of the product-carrier complex as a function of dimensionless length along each globule of emulsion with time as a parameter, an attempt has been made to show how mass-transfer resistance affects the reaction engineering behavior of the system. It has been observed that the product distribution and reaction velocity as a function of substrate concentration as predicted from the proposed model explains reality quite satisfactorily.

Development of a multiphysics model to characterize the responsive behavior of urea-sensitive hydrogel as biosensor

“…From the open literature, it is found that most of the published mathematical models were unable to capture the coupled biochemo-electromechanical behavior of the hydrogel. For example, the published mathematical models were inadequate in predicting the volumetric behavior of the hydrogels in response to the urea, where the simulated diffusion and reaction of the reactive solutes were associated with the urea hydrolysis and not the concomitant mechanical behavior of the hydrogels (Blaedel and Kissel, 1975;Chen and Chiu, 2000), including Moynihan et al (1989) and Chowdhury and Bhattacharya (1997), where they modelled the kinetic parameters of the urea-sensitive hydrogel via the mass balance and Michaelis-Menten equations.…”