Drop electrohydrodynamics under strong electric fields: Three singular limits

Department of Mathematics, Technion - Israel Institute of Technology

The leaky-dielectric electrohydrodynamic model was put forward by G. I. Taylor in the mid 1960's as an explanation to puzzling observations of drops deforming into an oblate spheroidal-type shape when subjected to a steady electric field. Taylor's theory neglects both fluid inertia and surface-charge convection. In addition, it assumes that the deformation from sphericity is small. These key assumptions are respectively tantamount to postulating that the Reynolds number, the electric Reynolds number and the capillary number are vanishingly small. Taken together, they eliminate the mutual decoupling between the electrostatic and flow problems, allowing for closed-form solutions where the fluid velocity scales as the square of the applied-field magnitude. Over the years, Taylor's work has been extended to situations where these numbers are asymptotically small (using regular perturbations) or even finite (using numerical simulations). The purpose of the present talk is to highlight the singular limits where the numbers become large, revealing non-conventional flow scaling and topologies.