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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: [email protected]
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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

REFERENCES

Arshadi, M. & Rajaram, H. 2015 A transition in the spatially integrated reaction rate of bimolecular reaction-diffusion systems. Water Resour. Res. 51, 7798–7810.CrossRefGoogle Scholar
Bandopadhyay, A., Le Borgne, T., Méheust, Y. & Dentz, M. 2017 Enhanced reaction kinetics and reactive mixing scale dynamics in mixing fronts under shear flow for arbitrary Damköhler numbers. Adv. Water Resour. 100, 78–95.CrossRefGoogle Scholar
Batchelor, G.K. 1959 Small-scale variation of convected quantities like temperature in a turbulent fluid. Part 1. General discussion and the case of small conductivity. J. Fluid Mech. 5, 113–133.CrossRefGoogle Scholar
Duplat, J. & Villermaux, E. 2008 Mixing by random stirring in confined mixtures. J. Fluid Mech. 617, 51–86.CrossRefGoogle Scholar
Gibson, C.H. & Libby, P.A. 1972 On turbulent flows with fast chemical reactions. Part II. The distribution of reactants and products near a reacting surface. Combust. Sci. Technol. 6 (1–2), 29–35.CrossRefGoogle Scholar
Guilbert, E., Almarcha, C. & Villermaux, E. 2021 Chemical reaction for mixing studies. Phys. Rev. Fluids 6, 114501.CrossRefGoogle Scholar
Guilbert, E. & Villermaux, E. 2021 Chemical reactions rectify mixtures composition. Phys. Rev. Fluids 6, L112501.CrossRefGoogle Scholar
Larralde, H., Araujo, M., Havlin, S. & Stanley, H.E. 1992 Reaction front for ${\rm A}+{\rm B}\to {\rm C}$ diffusion-reaction systems with initially separated reactants. Phys. Rev. A 46 (2), 855.CrossRefGoogle Scholar
Meunier, P. & Villermaux, E. 2003 How vortices mix. J. Fluid Mech. 476, 213–222.CrossRefGoogle Scholar
Ou, J.J. & Ranz, W.E. 1983 Mixing and chemical reactions: a contrast between fast and slow reactions. Chem. Engng Sci. 38 (7), 1005–1013.CrossRefGoogle Scholar
Perez, L.J, Hidalgo, J.J & Dentz, M. 2019 Upscaling of mixing-limited bimolecular chemical reactions in Poiseuille flow. Water Resour. Res. 55 (1), 249–269.CrossRefGoogle Scholar
Ranz, W.E. 1979 Applications of a stretch model to mixing, diffusion, and reaction in laminar and turbulent flows. AIChE J. 25 (1), 41–47.CrossRefGoogle Scholar
de Rivas, A. & Villermaux, E. 2016 Dense spray evaporation as a mixing process. Phys. Rev. Fluids 1 (1), 014201.CrossRefGoogle Scholar
Seonkyoo, Y., Dentz, M. & Kang, P.K. 2021 Optimal fluid stretching for mixing-limited reactions in rough channel flows. J. Fluid Mech. 916, A45.Google Scholar
Souzy, M., Lhuissier, H., Villermaux, E. & Metzger, B. 2017 Stretching and mixing in sheared particulate suspensions. J. Fluid Mech. 812, 611–635.CrossRefGoogle Scholar
Souzy, M., Zaier, I., Lhuissier, H., Le Borgne, T. & Metzger, B. 2018 Mixing lamellae in a shear flow. J. Fluid Mech. 838, R3.CrossRefGoogle Scholar
Turuban, R., Lhuissier, H. & Metzger, B. 2021 Mixing in a sheared particulate suspension. J. Fluid Mech. 916, R4.CrossRefGoogle Scholar
Ucon, oil 2021 UCON 75-H-90, 000, a very viscous oil miscible with water, available from DOW company, Michigan, USA.Google Scholar
Villermaux, E. 2019 Mixing versus stirring. Annu. Rev. Fluid Mech. 51, 245–273.CrossRefGoogle Scholar