Reactive mixing, in which fluid flow affects the dynamics of a chemical or biological process by continually altering local concentrations, is common in industrial systems. Often a key design goal is to generate reaction products as quickly as possible while expending minimal energy to drive the flow. In systems like microfluidic devices, where turbulence is inaccessible, efficient reactive mixing requires choosing flows carefully. Here we compare product generation rates of an autocatalytic reaction in a collection of steady, laminar shear flows, all with the same kinetic energy, to each other and to the case of reaction without flow. The resulting advection-reaction-diffusion dynamics are estimated by tracking reaction fronts using the computationally inexpensive eikonal approximation, then simulated directly; the two approaches agree closely. Prior studies noted that reaction fronts in Poiseuille flow converged over time to steady shapes that advance at constant speed (solitary chemical waves), and we find the same phenomenon in all the flows considered. Observing that solitary waves advance at speeds dependent on flow velocity extrema, we construct an analytic model that accurately predicts their shape and speed from the flow velocity profile and chemical front speed. The model implies that concentrating kinetic energy in a narrow region maximizes product generation, and we validate that prediction with further simulations. We show that in the case of solitary waves with speed zero, the model reproduces prior theoretical, experimental, and numerical studies of frozen fronts. By simulating full advection-reaction-diffusion dynamics, we find that the eikonal approximation predicts the size of the reacted region within a few percent and predicts the converged product generation rate within a few tenths of a percent.

• Received 7 November 2019
• Accepted 11 June 2020

DOI:https://doi.org/10.1103/PhysRevFluids.5.063201