Electrokinetics of a particle attached to a fluid interface: Electrophoretic mobility and interfacial deformation

The electrophoretic mobility of a microparticle with a small potential attached to a fluid interface is studied analytically in the limit of two fluids with vanishing viscosity and permittivity ratios under the assumption of a weak applied electric field. The analysis is based on perturbation expansions in the capillary number, the electric capillary number, and in the deviation of the contact angle on the particle surface from 90 degrees. For the case of a very thin electric double layer (EDL), the Smoluchowski limit for the electrophoretic mobility 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. The deformation of the fluid interface is shown to be separable into a dynamic and static part. The motion of the particle (dynamic part) does not contribute to the interfacial deformation in the case of a small capillary number, even for arbitrary EDL thickness. The static interfacial deformation due to electric stresses, known as electrodipping, is examined for spherical particles and shown to be independent of the first-order perturbation in the contact angle. The limits of validity of our theory and possible applications are discussed.