A simple model to predict mass transfer rates and kinetics of biochemical and biomedical Michaelis–Menten surface reactions

In this paper we propose a simple algebraic equation to compute the steady and laminar mass transfer rate produced by a surface chemical reaction that follows the Michaelis–Menten kinetic equation. This kinetic model characterizes the chemical rates of many catalytic biochemical reactions and many enzymatic reactions and, consequently, the equation can be used in experiments to predict the mass transfer rate or to determine the kinetics of reactions occurring on functionalized surfaces. The proposed correlation has been obtained by fitting results of numerical simulations and it relates the surface averaged Sherwood number, or the non-dimensional mass transfer rate, with the Péclet number based on the shear rate, the Damkhöler number (Da) based on the maximal velocity and the non-dimensional Michaelis constant (KM∗). The validity of the correlation has been analyzed in the range of the non-dimensional parameters that can be found in physically realizable conditions. A procedure to determine experimentally the kinetic constants of the surface reaction is outlined and applied to experimental data.