Dynamics ofA+B → Creaction fronts under radial advection in three dimensions

Abstract

The dynamics of A + B → C reaction fronts is studied both analytically and numerically in three-dimensional systems when A is injected radially into B at a constant flow rate. The front dynamics is characterized in terms of the temporal evolution of the reaction front position, r f , of its width, w, of the maximum local production rate, R max , and of the total amount of product generated by the reaction, n C. We show that r f , w, and R max exhibit the same temporal scalings as observed in rectilinear and two-dimensional radial geometries both in the early-time limit controlled by diffusion, and in the longer time reaction-diffusion-advection regime. However, unlike the two-dimensional cases, the three-dimensional problem admits an asymptotic stationary solution for the reactant concentration profiles where n C grows linearly in time. The timescales at which the transition between the regimes arise, as well as the properties of each regime, are determined in terms of the injection flow rate and reactant initial concentration ratio.

Dynamics ofA+B→Creaction fronts under radial advection in a Poiseuille flow

“…Specifically, theoretical analysis of the front dynamics has started to be tackled in the case of 1D radial symmetry with diffusive transport [21,22,28]. Advected fronts developing when A is injected radially at a constant flow rate into B in systems with polar [29][30][31] or spherical [32] symmetry have further been addressed.…”

Influence of rectilinear vs radial advection on the yield of A + B → C reaction fronts: A comparison

“…1,2 In the vast class of chemical fronts, A + B → C fronts have been extensively studied and characterized theoretically because, depending on the interpretation of A and B, they underline many applications. [3][4][5][6] Such fronts typically develop when a zone rich in A is put in contact along a given interface with a zone rich in B. In the absence of any flow, the interplay between the A + B → C kinetics and the diffusive transport of the reactants toward the reaction zone induces a front, the properties of which have been largely studied.…”

“…Before reaching this stationary state, the system evolves through an early-time regime and a transient regime, both characterized by well-defined and different scalings. 6 In this context, we explore here the geometrical control of A + B → C fronts in flow conditions by analyzing the difference in the yield of the reaction in a 3D rectilinear displacement vs a radial injection along an expanding cylinder (see Fig. 1).…”

Oscillatory budding dynamics of a chemical garden within a co-flow of reactants

“…where n C is the number of moles of C. It has been shown 37 that, when A is injected radially into B in 3D, the total amount of C increases with t. Expressing the results by Comolli et al 37 in dimensional units, we have the following scalings:…”

“…38 t ET and t TS are, respectively, the times at which the transitions between the ''early-time'' and the ''transient'' regimes and between the ''transient'' and ''stationary'' regimes occur. 37 The expressions of t ET and t TS are obtained, respectively, by equating eqn (7a) to eqn (7b) and eqn (7b) to eqn (7c):…”