Wed January 17th 2018
14:00 – 15:00
Seminar Electrokinetics of a particle attached to a fluid interface: Electrophoretic mobility and interfacial deformation
Michael Eigenbrod


We consider the electrophoretic mobility of a particle attached to an interface between an electrolyte and a dielectric fluid, assuming a large viscosity and dielectric permittivity ratio. We further assume a constant zeta potential at the particle surface and that the flow field around the particle does not deform the Debye layer. For very thin electric double layers (EDLs), the Smoluchowski limit [1] is recovered. For arbitrary values of the EDL thickness, a spherical particle is considered. In that case, the electrophoretic mobility is a function of the EDL thickness and the contact angle at the particle surface. Hydrophobic particles have a higher mobility than hydrophilic ones. Furthermore, the electrostatic and the hydrodynamic stresses at the particle surface locally balance. As a result, no torque is exerted on the particle. In the absence of gravity, the electrodipping force and hydrodynamic stresses are the only potential causes for the deformation of the fluid interface. We show that at lowest order, the interface deformation is proportional to the capillary number and the electric capillary number. Further, the solution of the Young-Laplace equation indicates that the interface only gets deformed in the range of the order of the Debye layer thickness. As a result, to a good approximation, during the electrophoretic transport of a particle with a very thin Debye layer along a fluid interface, the interface deformation is negligible.
[1] von Smoluchowski, M. 1903 Contribution to the theory of electro-osmosis and related phenomena. Bull. Int. Acad. Sci. Cracovie 3, 184-199
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The 10th Complex Motion in Fluids 2021
Max Planck Gesellschaft
Centre for Scientific Computing