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Local and global force balance for diffusiophoretic transport

Published online by Cambridge University Press:  01 April 2020

S. Marbach Open the ORCID record for S. Marbach [Opens in a new window] ,
H. Yoshida  and
L. Bocquet Open the ORCID record for L. Bocquet [Opens in a new window]
S. Marbach
Affiliation:
Ecole Normale Supérieure, PSL Research University, CNRS, 24 rue Lhomond, Paris75005, France Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street,New York, NY10012, USA
H. Yoshida
Affiliation:
Ecole Normale Supérieure, PSL Research University, CNRS, 24 rue Lhomond, Paris75005, France Toyota Central R&D Labs., Inc., Bunkyo-ku, Tokyo 112-0004, Japan
L. Bocquet*
Affiliation:
Ecole Normale Supérieure, PSL Research University, CNRS, 24 rue Lhomond, Paris75005, France
*
†Email address for correspondence: [email protected]
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Abstract

Electro- and diffusio-phoresis of particles correspond respectively to the transport of particles under electric field and solute concentration gradients. Such interfacial transport phenomena take their origin in a diffuse layer close to the particle surface, and the motion of the particle is force free. In the case of electrophoresis, it is further expected that the stress acting on the moving particle vanishes locally as a consequence of local electroneutrality. But the argument does not apply to diffusiophoresis, which takes its origin in solute concentration gradients. In this paper we investigate further the local and global force balance on a particle undergoing diffusiophoresis. We calculate the local tension applied on the particle surface and show that, counter-intuitively, the local force on the particle does not vanish for diffusiophoresis, in spite of the global force being zero, as expected. Incidentally, our description allows us to clarify the osmotic balance in diffusiophoresis, which has been a source of debate in recent years. We explore various cases, including hard and soft interactions, as well as porous particles, and provide analytic predictions for the local force balance in these various systems. The existence of local stresses may induce deformation of soft particles undergoing diffusiophoresis, hence suggesting applications in terms of particle separation based on capillary diffusiophoresis.

JFM classification

Micro-/Nano-fluid dynamics: Microfluidics Low-Reynolds-number flows: Porous media
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 892 , 10 June 2020 , A6
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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