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A model for the electric field-driven flow and deformation of a drop or vesicle in strong electrolyte solutions

Published online by Cambridge University Press:  20 June 2022

Manman Ma ,
Michael R. Booty Open the ORCID record for Michael R. Booty [Opens in a new window]  and
Michael Siegel
Manman Ma
Affiliation:
School of Mathematical Sciences, Tongji University, Shanghai 200092, PR China
Michael R. Booty*
Affiliation:
Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ 07102, USA
Michael Siegel
Affiliation:
Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ 07102, USA
*
†Email address for correspondence: michael.r.booty@njit.edu
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Abstract

A model is constructed to describe the flow field and arbitrary deformation of a drop or vesicle that contains and is embedded in an electrolyte solution, where the flow and deformation are caused by an applied electric field. The applied field produces an electrokinetic flow, which is set up on the charge-up time scale $\tau _{*c}=\lambda _{*} a_{*}/D_{*}$, where $\lambda _{*}$ is the Debye screening length, $a_{*}$ is the inclusion length scale and $D_{*}$ is an ion diffusion constant. The model is based on the Poisson–Nernst–Planck and Stokes equations. These are reduced or simplified by forming the limit of strong electrolytes, for which dissolved salts are completely ionised in solution, together with the limit of thin Debye layers. Debye layers of opposite polarity form on either side of the drop interface or vesicle membrane, together forming an electrical double layer. Two formulations of the model are given. One utilises an integral equation for the velocity field on the interface or membrane surface together with a pair of integral equations for the electrostatic potential on the outer faces of the double layer. The other utilises a form of the stress-balance boundary condition that incorporates the double layer structure into relations between the dependent variables on the layers’ outer faces. This constitutes an interfacial boundary condition that drives an otherwise unforced Stokes flow outside the double layer. For both formulations relations derived from the transport of ions in each Debye layer give additional boundary conditions for the potential and ion concentrations outside the double layer.

JFM classification

MHD and Electrohydrodynamics: Electrokinetic flows Drops and Bubbles: Electrohydrodynamic effects Biological Fluid Dynamics: Membranes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 943 , 25 July 2022 , A47
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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