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Advection and diffusion in a chemically induced compressible flow

Published online by Cambridge University Press:  21 May 2018

Florence Raynal Open the ORCID record for Florence Raynal [Opens in a new window] ,
Mickael Bourgoin ,
Cécile Cottin-Bizonne ,
Christophe Ybert  and
Romain Volk
Florence Raynal*
Affiliation:
LMFA, Univ Lyon, École Centrale Lyon, INSA Lyon, Université Lyon 1, CNRS, F-69134 Écully, France
Mickael Bourgoin
Affiliation:
Laboratoire de Physique, ENS de Lyon, Univ Lyon, CNRS, 69364 Lyon CEDEX 07, France
Cécile Cottin-Bizonne
Affiliation:
Institut Lumière Matière, Univ Lyon, Université Lyon 1, CNRS, F-69622 Villeurbanne CEDEX, France
Christophe Ybert
Affiliation:
Institut Lumière Matière, Univ Lyon, Université Lyon 1, CNRS, F-69622 Villeurbanne CEDEX, France
Romain Volk*
Affiliation:
Laboratoire de Physique, ENS de Lyon, Univ Lyon, CNRS, 69364 Lyon CEDEX 07, France
*
†Email addresses for correspondence: florence.raynal@ec-lyon.fr, romain.volk@ens-lyon.fr
†Email addresses for correspondence: florence.raynal@ec-lyon.fr, romain.volk@ens-lyon.fr
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Abstract

We study analytically the joint dispersion of Gaussian patches of salt and colloids in linear flows, and how salt gradients accelerate or delay colloid spreading by diffusiophoretic effects. Because these flows have constant gradients in space, the problem can be solved almost entirely for any set of parameters, leading to predictions of how the mixing time and the Batchelor scale are modified by diffusiophoresis. We observe that the evolution of global concentrations, defined as the inverse of the patches’ areas, are very similar to those obtained experimentally in chaotic advection. They are quantitatively explained by examining the area dilatation factor, in which diffusive and diffusiophoretic effects are shown to be additive and appear as the divergence of a diffusive contribution or of a drift velocity. An analysis based on compressibility is developed in the salt-attracting case, for which colloids are first compressed before dispersion, to predict the maximal colloid concentration as a function of the parameters. This maximum is found not to depend on the flow stretching rate nor on its topology (strain or shear flow), but only on the characteristics of salt and colloids (diffusion coefficients and diffusiophoretic constant) and the initial size of the patches.

JFM classification

Complex Fluids: Colloids Mathematical Foundations: Mathematical Foundations Mixing: Mixing

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 847 , 25 July 2018 , pp. 228 - 243
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Copyright
© 2018 Cambridge University Press 

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