Nonlinear effects of partitioning and diffusion limitation on the efficiency of three-layer enzyme bioreactors and potentiometric biosensors

The nonlinear effects of the partitioning and diffusion limitation on the efficiency of enzyme-based bioreactors and potentiometric biosensors are investigated analytically and numerically using a three-layer mathematical model involving the Michaelis–Menten type reaction in the transient and steady states. Analytical expressions of the steady state substrate and reaction product concentrations and the bioreactor effectiveness as well as biosensor output potential are presented for the first and zero-order reaction rates. Mathematical modelling of the diffusion limiting membrane and the conditions under which the same values of the steady state characteristics are obtained when simulating the treated system at different values of the diffusion and distribution coefficients are investigated. The effective diffusion coefficients in the total diffusion layer consisting of the diffusion limiting membrane and the outer diffusion (Nernst) layer are applied to reduce the three-layer model to the corresponding two-layer model. The dynamics and behaviour of the substrate consumption rate, product emission rate, effectiveness factor and the output potential are numerically investigated.