Vertical shear alters chemical front speed in thin-layer flows

Abstract

The mixing of a reactive scalar by a fluid flow can have a significant impact on reaction dynamics and the growth of reacted regions. However, experimental studies of the fluid mechanics of reactive mixing present significant challenges and puzzling results. The observed speed at which reacted regions expand can be separated into a contribution from the underlying flow and a contribution from reaction–diffusion dynamics, which we call the chemical front speed. In prior work (Nevins & Kelley, Chaos, vol. 28 (4), 2018, 043122), we were surprised to observe that the chemical front speed increased where the underlying flow in a thin layer was faster. In this paper, we show that the increase is physical and is caused by smearing of reaction fronts by vertical shear. We show that the increase occurs not only in thin-layer flows with a free surface, but also in Hele-Shaw systems. We draw these conclusions from a series of simulations in which reaction fronts are located according to depth-averaged concentration, as is common in laboratory experiments. Where the front profile is deformed by shear, the apparent front speed changes as well. We compare the simulations to new experimental results and find close quantitative agreement. We also show that changes to the apparent front speed are reduced approximately 80 % by adding a lubrication layer.

Front propagation in cellular flows: scale dependence versus scale invariance

“…Its global velocity in the cell plane, , then depends linearly on the flow intensity: where denotes the front normal in the cell plane (Edwards 2002; Leconte et al. 2003; Nevins & Kelley 2019). In the narrow-gap limit where diffusion plays a significant role, corresponds to the depth-averaged value of .…”

“…Following the velocity gradient implied by the Poiseuille profile, the front displays some curvature in between the cell plates. Its global velocity in the cell plane, V , then depends linearly on the flow intensity: V = V 0 n+ < U > where n denotes the front normal in the cell plane (Edwards 2002;Leconte et al 2003;Nevins & Kelley 2019). In the narrow-gap limit where diffusion plays a significant role, U corresponds to the depth-averaged value of U.…”