Flow Control of A+B→C Fronts by Radial Injection.

Abstract

The dynamics of A+B→C fronts is analyzed theoretically in the presence of passive advection when A is injected radially into B at a constant inlet flow rate Q. We compute the long-time evolution of the front position, r_{f}, of its width, w, and of the local production rate R of the product C at r_{f}. We show that, while advection does not change the well-known scaling exponents of the evolution of corresponding reaction-diffusion fronts, their dynamics is however significantly influenced by the injection. In particular, the total amount of product varies as Q^{-1/2} for a given volume of injected reactant and the front position as Q^{1/2} for a given time, paving the way to a flow control of the amount and spatial distribution of the reaction front product. This control strategy compares well with calcium carbonate precipitation experiments for which the amount of solid product generated in flow conditions at fixed concentrations of reactants and the front position can be tuned by varying the flow rate.