This paper presents mathematical and computational modelling of kinetics of a bioelectroanalytical system based on the interfacial action of hydrolytic enzyme. A system of non-linear differential equations with diffusion is used to describe the kinetics of Termomyces lanuginosa lipase (TLL) catalyzed hydrolysis of L-ascorbic acid palmitate (AAP). The system was solved numerically, and the kinetic prameters of AAP hydrolysis by the enzyme were determined. The experimental and modelling results show linear dependence of the rate of AAP hydrolysis on the TLL concentration. Complex dependence of the initial rate of bioelectrocatalytic current increase on the thickness of total diffusion layer (hydrodynamic diffusion layer plus thickness of dialysis membrane on the electrode surface) is also demonstrated and explained.
A mathematical model for the synthesis of yttrium aluminium garnet (Y 3 Al 5 O 12 , YAG) is presented in the article. The preparation of YAG by two synthesis methods, namely the sol-gel chemistry approach and the solid-state reaction method is considered. The model of YAG synthesis is based on the system of non-stationary diffusion equations containing the nonlinear terms related to the kinetics of the reaction and diffusion rates. The periodisation of the synthesis space is considered. In this study, the computer simulation tool was developed to solve the system of partial differential equations. The developed software is employed to investigate the influence of the concentration of YAG on diffusion rates and the synthesis duration as well as on the duration when the rate of change in reaction product mass is at a maximum.
Oxidized graphite (OG) has been prepared by carrying out the synthesis of graphene in the alkaline media using K3[Fe(CN)6] as the oxidizing agent. This synthesis protocol allowed us to obtain and further to apply the OG as an effective electrode material for the reagentless enzyme electrode in which electron transfer between electrode and enzyme active site proceeds directly, without any additional mediators. Direct electron transfer in this bioelectrocatalytic system has been achieved from the active site of pyrroloquinoline quinone-containing glucose dehydrogenase (PQQ-GDH) to the nanostructurized carbon electrode surface. The numerical modeling of biosensor made possible to determine several structural and kinetic parameters of the sensor constructed. Our model of PQQ-GDH-based biosensor is built under three main assumptions. First, we assume that the electron transfer between enzyme active center and OG proceeds via the electron hopping mechanism, and therefore the rate of this reaction depends on the diffusion coefficient of an electron in OG layer. Second, enzyme is immobilized, and its diffusion coefficient is assumed to be zero. Finally, after the reaction with substrate, enzyme needs to be regenerated by the oxidized functionalities of OG.
We propose a cooler of a laser material which compensates the thermal gradients caused by the pump radiation by the gradients created by the cooler. The mathematical model of the system is based on the numerical solution of the heat transfer equation using a finite - difference technique. The 3-D and 2-D computer simulations were used to investigate the cooling problem and show the reliability of two-dimensional model.
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