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Vertical shear alters chemical front speed in thin-layer flows

Published online by Cambridge University Press:  04 July 2019

Thomas D. Nevins Open the ORCID record for Thomas D. Nevins [Opens in a new window]  and
Douglas H. Kelley Open the ORCID record for Douglas H. Kelley [Opens in a new window]
Thomas D. Nevins
Affiliation:
Department of Physics, University of Rochester, Rochester, NY 14623, USA
Douglas H. Kelley*
Affiliation:
Department of Mechanical Engineering, University of Rochester, Rochester, NY 14623, USA
*
†Email address for correspondence: d.h.kelley@rochester.edu
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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.

JFM classification

Low-Reynolds-number flows: Hele-Shaw flows Reacting Flows: Laminar reacting flows Reacting Flows: Turbulent reacting flows

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 874 , 10 September 2019 , pp. 235 - 262
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© 2019 Cambridge University Press 

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Nevins and Kelley supplementary movie 1

Simulated vertical front profiles evolving under supporting and opposing flows in single- and two-layer configurations. Reacted regions are white; unreacted regions are grey. Front speed is 72 microns/s, matching the Belousov-Zhabotinsky reaction. The two-layer configuration reduces front distortion significantly.

Download Nevins and Kelley supplementary movie 1(Video)
Video 11.7 MB

Nevins and Kelley supplementary movie 2

Simulated apparent concentration evolving under supporting flows in single- and two-layer configurations. Front speed is 72 microns/s, matching the Belousov-Zhabotinsky reaction. The two-layer configuration reduces smearing, such that the concentration gradient at the front stays much steeper.

Download Nevins and Kelley supplementary movie 2(Video)
Video 5.3 MB

Nevins and Kelley supplementary movie 3

Apparent concentration evolving under supporting flows in single- and two-layer experiments with the Belousov-Zhabotinsky reaction. The two-layer configuration reduces smearing, such that the concentration gradient at the front stays much steeper.

Download Nevins and Kelley supplementary movie 3(Video)
Video 7.9 MB