Dynamics of A+B→C reaction fronts under radial advection in a Poiseuille flow

A+B→C reaction fronts describe a wide variety of natural and engineered dynamics, according to the specific nature of reactants and product. Recent works have shown that the properties of such reaction fronts depend on the system geometry, by focusing on one-dimensional plug flow radial injection. Here, we extend the theoretical formulation to radial deformation in two-dimensional systems. Specifically, we study the effect of a Poiseuille advective velocity profile on A+B→C fronts when A is injected radially into B at a constant flow rate in a confined axisymmetric system consisting of two parallel impermeable plates separated by a thin gap. We analyze the front dynamics by computing the temporal evolution of the average over the gap of the front position, the maximum production rate, and the front width. We further quantify the effects of the nonuniform flow on the total amount of product, as well as on its radial concentration profile. Through analytical and numerical analyses, we identify three distinct temporal regimes, namely (i) the early-time regime where the front dynamics is independent of the reaction, (ii) the transient regime where the front properties result from the interplay of reaction, diffusion that smooths the concentration gradients and advection, which stretches the spatial distribution of the chemicals, and (iii) the long-time regime where Taylor dispersion occurs and the system becomes equivalent to the one-dimensional plug flow case.