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

Abstract

In the presence of advection at a constant flow rate in a rectilinear geometry, the properties of planar A + B → C reaction fronts feature the same temporal scalings as in the pure reaction-diffusion case. In a radial injection geometry where A is injected into B radially at a constant flow rate Q, temporal scalings are conserved, but the related coefficients depend on the injection flow rate Q and on the ratio γ of initial concentrations of the reactants. We show here that this dependence of the front properties on the radial velocity allows us to tune the amount of product obtained in the course of time by varying the flow rate. We compare theoretically the efficiency of the rectilinear and radial geometries by computing the amount of product C generated in the course of time or per volume of reactant injected. We show that a curve γc(Q) can be defined in the parameter space (γ, Q) below which, for similar experimental conditions, the total amount of C is larger in the radial case. In addition, another curve γ * (Q) < γc(Q) can be defined such that for γ < γ * , the total amount of C produced is larger in the radial geometry, even if the production of C per unit area of the contact interface between the two reactants is larger in the rectilinear case. This comes from the fact that the length of the contact zone increases with the radius in the radial case, which allows us to produce in fine more product C for a same injected volume of reactant or in reactors of a same volume than in the rectilinear case. These results pave the way to the geometrical optimization of the properties of chemical fronts.

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

“…2D radial 3D spherical r f Early-time const → t 3/2 [22][23][24] ( Qt ) 1/2 [28] ( Qt ) 1/3 (22) Long-time α(γ ) t 1/2 [17] ( Qt ) 1/2 [27,41] ( Qt…”

“…The notations introduced in Ref. [41] are used for the coefficients of the long-time scalings in the rectilinear and radial 2D cases. In rectilinear geometry, if advection at constant velocity is considered, those results are still valid in a frame moving at that speed.…”

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.…”

Reaction induced interfacial instability of miscible fluids in a channel

“…Here since the channel aspect ratio is 1 : 40, the growing contact area for the reaction increases with time, as the reactive interface is axially spread over the whole domain as time evolves. Hence the total product grows proportional to (see the log–log plot in the inset of figure 8 a for the stable case () which is an even faster rate as compared with the reactive VF results Brau & De Wit 2020). Moreover in the unstable situation (), the product formation follows a -type growth after time .…”

“…Hence the instability helps in the formation of more product than the stable case. It is shown in the context of VF (Brau & De Wit 2020) that grows as in advection–diffusion–reaction (ADR) system for a rectilinear geometry and linearly for the radial advection, where speed depends on the injection flow rate and the circle radius. Here since the channel aspect ratio is 1 : 40, the growing contact area for the reaction increases with time, as the reactive interface is axially spread over the whole domain as time evolves.…”