Dynamics of a sessile droplet under periodic and steady electric fields

The electrohydrodynamics of a sessile droplet under the influence of periodic and steady electric fields in microgravity conditions is theoretically investigated using an inertial lubrication model. Previous studies revealed that a spherical droplet with unequal conductivity and permittivity ratios exhibits distinct dynamics under periodic and equivalent steady forcing in the root-mean-square sense. However, it is unclear what happens for sessile droplets, which we address here for the first time. The equivalence between periodic and steady forcing is shown to be governed by the interfacial charge build-up, which further depends on the competition between the charge relaxation and forcing timescales. A circulation-deformation map is introduced for the sessile droplet that acts as a guideline to achieve electric field-induced wetting or dewetting as the case maybe. We also demonstrate that a droplet may be rendered either more or less wetting solely by tuning the forcing frequency.