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Matematično modeliranje kemijskih procesov postaja vse pomembnejši del kemijsko inženirske prakse. Izvajanje simulacij na podlagi matematičnih modelov je še posebej zanimivo na področju mikrofluidike, saj je opis teh sistemov zaradi laminarnega tokovnega režima razmeroma enostaven in natančen. V tem delu predstavljamo matematični model, ki napoveduje koncentracijski profil substrata in produkta encimsko katalizirane reakcije v mikrokanalu. Ta vsebuje encim, imobiliziran v tankem sloju gela na površini ploskev, ki kanal omejujeta. Skozi mikroreaktor teče laminaren tok topila, masni transport nadzorujeta konvekcija ter difuzija. Kinetika modela sledi predhodno predstavljeni encimski mikrokinetiki, ki temelji na sistemu 14 diferencialnih enačb, katere ob sami pretvorbi substrata v produkt opisujejo tudi interakcije teh molekul s površino encima. Hitrostne konstante kinetičnega modela smo določili s prileganjem napovedi modela encimske mikrokinetike eksperimentalnim podatkom, določenim v šaržnem sistemu. Pridobljene parametre smo nato uporabili za simulacijo encimske kinetike v mikroreaktorju. Mathematical modelling of chemical processes is becoming an increasingly important part of chemical engineering practice. The implementation of simulations based on mathematical models is of particular interest in the field of microfluidics, as the description of these systems is relatively simple and accurate due to the laminar flow regime. In this work, we present a mathematical model that predicts the concentration profile of the substrate and product of an enzyme-catalysed reaction in a microchannel. The latter contains the enzyme immobilised in a thin gel layer on the surface of the two faces that confine the channel. A laminar flow of solvent flows through the microreactor, with mass transport controlled by convection and diffusion. The kinetics of the model follows the previously presented enzyme microkinetics based on a system of 14 differential equations which, in addition to the conversion of substrate into product, also describe the interactions of these molecules with the enzyme surface. The rate constants of the kinetic model were determined by fitting the predictions of the enzyme microkinetics model to the experimental data determined in a batch system. The parameters obtained were then used to simulate enzyme kinetics in a microreactor. |
