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Drop deformation during diffusiophoresis

Published online by Cambridge University Press:  28 September 2022

Brian E. McKenzie Open the ORCID record for Brian E. McKenzie [Opens in a new window] ,
Henry C.W. Chu Open the ORCID record for Henry C.W. Chu [Opens in a new window] ,
Stephen Garoff ,
Robert D. Tilton  and
Aditya S. Khair Open the ORCID record for Aditya S. Khair [Opens in a new window]
Brian E. McKenzie
Affiliation:
Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA Center for Complex Fluids Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
Henry C.W. Chu
Affiliation:
Department of Chemical Engineering, University of Florida, Gainesville, FL 32611, USA
Stephen Garoff
Affiliation:
Center for Complex Fluids Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213, USA
Robert D. Tilton
Affiliation:
Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA Center for Complex Fluids Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA Department of Biomedical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
Aditya S. Khair*
Affiliation:
Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA Center for Complex Fluids Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
*
†Email address for correspondence: akhair@andrew.cmu.edu
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Abstract

Diffusiophoresis refers to the motion of a colloidal particle in a solute concentration gradient, animated by particle–solute interactions. We present a theoretical analysis of the diffusiophoretic motion of a viscous drop in a gradient of neutral solute at zero Reynolds number. In a spatially uniform gradient, the translational velocity of a spherical drop was found by Anderson et al. (J. Fluid Mech., vol. 117, 1982, pp. 107–121). Here, we show additionally that the drop experiences no tendency to deform, regardless of the magnitude of the interfacial tension at the interface of the drop and suspending fluid. Next, we consider a non-uniform gradient, where the ambient solute concentration takes the form of a quadrupole around the drop centroid. This gradient does not induce drop translation, due to symmetry, but does induce a deformation in the drop shape, which is spheroidal to first order in the capillary number $Ca=\beta k_B T R^2 K/\gamma$, where $\beta$ is the magnitude of the quadrupolar variation in solute concentration, $k_B T$ is the thermal energy, $R$ is the drop radius, $K$ is the Gibbs adsorption length, and $\gamma$ is the interfacial tension. Whether the drop becomes prolate or oblate depends on whether the solute–drop interaction is attractive or repulsive. Therefore, our work shows that in principle, a drop could undergo deformation during diffusiophoresis in a non-uniform solute gradient.

JFM classification

Complex Fluids: Colloids Drops and Bubbles: Drops
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 949 , 25 October 2022 , A17
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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