Electrokinetics of particles on a fluid-fluid interface*

Colloidal particles trapped at the interface of a drop assemble in various dynamic patterns, e.g., vortices, when an electric field is applied. In this talk I will overview our experiments exploring the various particle structures, and the theoretical analysis of particle motion along the fluid interface. As a first step, we study the force of the applied electric field on a spherical particle adsorbed at a planar interface. The electric potential is found by using the Mehler-Fock integral transform, which reduces the problem to a system of Fredholm integral equations.  The force on an isolated particle is identified numerically, while the far-field interaction force between two particles is identified asymptotically.  We find that, at leading order, the interaction between perfect dielectric particles is dominated by the induced dipoles and hence it is repulsive. For leaky dielectric particles the induced quadrupole can become significant and the interaction force can be either attractive on repulsive depending on material parameters.