Wall-induced migration of a drop in a uniform electric field *

A uniform electric field induces an axisymmetric flow about a drop suspended in an unbounded fluid. Accordingly, there is no net force on the drop -- the drop deforms but does not move. A nearby wall, parallel to the applied field, breaks the symmetry and repels the drop, provided R/S < 1, where R/S is the ratio of the bulk charge relaxation times of the drop and suspending fluids. Under the same conditions, a rigid sphere does not migrate which implies that the lift is of electrohydrodynamic (EHD) origin. We experimentally study the EHD drop migration for different fluid and wall properties using leaky dielectrics: silicone oil drop in castor oil. We develop a theoretical model for the drop migration normal to the wall using an image stresslet related the drop polarization. If the applied electric field is perpendicular to the direction of gravity the balance of EHD lift and drop sedimentation leads to an equilibrium separation between the drop and the wall.  Our study highlights the importance of confinement in electrohydrodynamic applications.