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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.
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Electrohydrodynamics of deflated vesicles: budding, rheology and pairwise interactions
We develop a new boundary integral method for solving the coupled electro- and hydrodynamics of vesicle suspensions in Stokes flow. This relies on a well-conditioned boundary integral equation formulation for the leaky-dielectric model describing the electric response of the vesicles and an efficient numerical solver capable of handling highly deflated vesicles. Our method is applied to explore vesicle electrohydrodynamics in three cases. First, we study the classical prolate–oblate–prolate transition dynamics observed upon application of a uniform DC electric field. We discover that, in contrast to the squaring previously found with nearly spherical vesicles, highly deflated vesicles tend to form buds. Second, we illustrate the capabilities of the method by quantifying the electrorheology of a dilute vesicle suspension. Finally, we investigate the pairwise interactions of vesicles and find three different responses when the key parameters are varied: (i) chain formation, where they self-assemble to form a chain that is aligned along the field direction; (ii) circulatory motion, where they rotate about each other; (iii) oscillatory motion, where they form a chain but oscillate about each other. The last two are unique to vesicles and are not observed in the case of other soft particle suspensions such as drops.
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- PAR ID:
- 10342562
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 867
- ISSN:
- 0022-1120
- Page Range / eLocation ID:
- 334 to 347
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2019.143
