Electrohydrodynamics of droplet pairs #

Michael McDougall, Debasish Das, Stephen K Wilson

12:30 Monday in 4Q04.

Part of the Droplets and impact session.

Abstract #

When a weakly conducting (leaky dielectric) droplet is suspended in another fluid and exposed to a uniform DC electric field, it becomes polarised and electric stresses tangential to the droplet interface drive fluid motion inside and outside the droplet. The EHD flow deforms the droplet and the resulting disturbances to the ambient electric and velocity fields are azimuthally symmetric around the axis aligned with the applied electric field. If a second droplet is present, its polarisation perturbs the electric field around the first droplet, disrupting the symmetry and driving translational motion of the two droplets. A three-dimensional small deformation theory for a pair of widely separated, leaky dielectric droplets suspended in a weakly conducting fluid medium is presented, valid in the limit of high droplet viscosity and surface tension, such that the drop remains almost spherical. The theory is constructed in accordance with the Melcher-Taylor leaky dielectric model under the assumptions of negligible charge convection and relaxation. Interfacial Maxwell stresses are found from a harmonic electric potential accounting for the applied field and the polarisation of both droplets, and the resulting fluid velocity, which satisfies the Stokes equations, is used to calculate the droplet shape and velocity.