Unsteady electrohydrodynamic drop deformation
Javier Lanauze (Carnegie Mellon University), Lynn Walker (Carnegie Mellon University), Aditya Khair (Carnegie Mellon University)
Electrohydrodynamics and electrokinetics of fluid systems
Mon 4:20 - 5:40
Barus-Holley 161
The steady electrohydrodynamic flow around, and deformation of, a drop immersed in a weakly conductive ("leaky dielectric") fluid under a uniform DC electric field is a well-studied phenomenon, starting from G. I. Taylor’s seminal analysis. However, the nature of the approach to that steady state has received continued attention: numerical simulations using the Navier-Stokes equations suggest that the deformation proceeds in a non-monotonic fashion with time, whereas analytical models that assume quasi-steady Stokes flow and instantaneous charge relaxation indicate the opposite. Here, we develop an analytical model for drop deformation that takes into account transient fluid inertia and a finite electrical relaxation time over which the interface charges. Capillary forces are assumed to be sufficiently large that the drop only slightly deviates from its equilibrium spherical shape at all times. The temporal droplet deformation is governed by two dimensionless groups: (i) the ratio of capillary to momentum diffusion time scales: an Ohnesorge number Oh; and (ii) the ratio of charge relaxation to momentum diffusion time scales, which we denote by Sa. If charge and momentum relaxation occur quickly compared to interface deformation, Sa << 1 and Oh >> 1 for the droplet and medium, a monotonic deformation is acquired. In contrast, Sa > 1 and Oh < 1 for either phase can lead to a non-monotonic deformation. In the latter case, the droplet and medium behave as perfect dielectrics at early times, which always favors an initial prolate (parallel to the applied field) deformation. As a consequence, for a final oblate (normal to the applied field) deformation, there is a shape transition from prolate to oblate at intermediate times. Notably, after the transition, there may be an “overshoot” in the deformation, i.e., the deformation exceeds its steady-state value, which is proceeded by an algebraic tail describing the arrival towards the final, steady deformation.