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Chemical production on a deforming substrate

Published online by Cambridge University Press:  11 January 2022

E. Guilbert ,
B. Metzger Open the ORCID record for B. Metzger [Opens in a new window]  and
E. Villermaux Open the ORCID record for E. Villermaux [Opens in a new window]
E. Guilbert
Affiliation:
Aix Marseille Université, CNRS, Centrale Marseille, IRPHE UMR 7342, 13384Marseille, France
B. Metzger
Affiliation:
Aix Marseille Université, CNRS, IUSTI UMR 7343, 13453Marseille, France
E. Villermaux*
Affiliation:
Aix Marseille Université, CNRS, Centrale Marseille, IRPHE UMR 7342, 13384Marseille, France Institut Universitaire de France, 75005Paris, France
*
†Email address for correspondence: emmanuel.villermaux@univ-amu.fr
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Abstract

The interplay between chemical reaction and substrate deformation is discussed by adapting Ranz's formulation for scalar mixing to the case of a reactive mixture between segregated reactants, initially separated by an interface whose thickness may not be vanishingly small. Experiments in a simple shear flow demonstrate the existence of three regimes depending on the Damköhler number $Da=t_s/t_c$ where $t_s$ is the mixing time of the interface width and $t_c$ is the chemical time. Instead of treating explicitly the chemical cross-term, we rationalize these different regimes by globalizing it as a production term involving a flux which depends on the rate at which the reaction zone is fed by the reactants, a formulation valid for $Da>1$. For $Da<1$, the reactants interpenetrate before they react, giving rise to a ‘diffusio-chemical’ regime where chemical production occurs within a substrate whose width is controlled by molecular diffusion.

JFM classification

Mixing: Mixing Reacting Flows: Reacting Flows
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 934 , 10 March 2022 , R1
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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