Reactions in systems with mixing

Publisher Website
Google Scholar
Abstract
We study the evolution of the concentrations of reactants which perform the irreversible reaction A + B --> 0. The reactants are initially separated and are contained in a system undergoing mechanical mixing. We introduce a continuous mixing model which is related to Baker's transformation: the continuous aspect makes it possible to implement mixing in a reaction-diffusion scheme. Furthermore, under very weak requirements, we succeed in presenting analytical expressions for the decay: we show that the initial reaction stages are controlled by mixing so that the concentration of reactants follows the mixing (exponential) time pattern. Furthermore we show that for the usual values of the pertinent parameters (size of the system, diffusion constants, microscopic reaction rates) the standard diffusion-controlled mechanism is recovered only when the reactants are completely mixed.