Shortcut method for lumping diffusion-reaction kinetics in lamellar systems

A simple method for evaluating the time evolution of reactant concentrations for diffusion-reaction kinetics in lamellar systems is developed. This method provides an efficient lumping strategy for reducing a system of partial differential equations to a low-dimensional system of ordinary differential equations. In the method proposed, the concentration fields are expressed as a linear combination of the solutions calculated in the two limiting cases of infinitely fast and infinitely slow reactions. The solution for the limiting case of infinitely fast reactions is obtained analytically by evaluating the profile of an auxiliary function (corresponding to the difference function in simple bimolecular reactions), accounting for the global stoichiometry, which satisfies a pure diffusion equation. The method is applied to bimolecular reactions and to more complex schemes, such as parallel and competitive-consecutive reactions in lamellar systems, and provides a satisfactory level of agreement with the solution obtained by means of standard numerical methods.