In our work, we present a method for estimation of the diffusion and reaction rates of synthesis at high temperatures using limited information from laboratory experiments, such as synthesis time and dimensions of reactants. Synthesis by sol-gel and solid-state reactions is considered. The inverse modeling problem is solved for one- and two-dimensional models. Explicit formulas for the diffusion coefficient and reaction rate as functions of temperature are obtained. The activation energies are calculated, and the lower bounds of diffusion and reaction rates are estimated, thus obtaining conditions for occurrence of synthesis. [...]
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. [...]
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