Advection and diffusion in a chemically induced compressible flow

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 o...

Full description

Saved in:
Bibliographic Details
Published in:Journal of fluid mechanics 2018-07, Vol.847, p.228-243
Main Authors: Raynal, Florence, Bourgoin, Mickael, Cottin-Bizonne, Cécile, Ybert, Christophe, Volk, Romain
Format: Article
Language:English
Subjects:
Additives
Advection
Coefficients
Colloids
Compressibility
Compressible flow
Condensed Matter
Diffusion coefficient
Diffusion coefficients
Dispersion
Divergence
Fluid mechanics
Gradients
JFM Papers
Mathematical analysis
Mechanics
Numerical analysis
Organic chemistry
Parameters
Patches (structures)
Physics
Salts
Shear flow
Soft Condensed Matter
Stretching rate
Topology
Velocity
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2018.335