Evolution and Shape of 2D Stokesian Drops Under the Action of Surface Tension and Electric Field: Linear and Nonlinear Theory and Experiment

The creeping-flow theory of two-dimensional ionic-conductor drops under the action of surface tension and the sub-critical (in terms of the electric Bond number) electric field imposed in the substrate plane is developed. The experimental data are acquired for drops impacted or softly deposited on dielectric surfaces of different wettability. The comparison with the theory reveals that it can accurately describe steady-state drop shape on non-wettable substrate. Such a drop is sufficiently raised above the substrate, which diminishes the three-dimensional effects making the two-dimensional description relevant. It is demonstrated how the sub-critical electric field deforms the initially circular drops until an elongated steady-state configuration is reached. The surface tension tends to round off the non-circular drops stretched by the electric Maxwell stresses imposed by the electrodes. A more pronounced substrate wettability leads to more elongated steady-state configurations observed experimentally than those predicted by the two-dimensional theory. In the super-critical electric fields the electrical stretching of drops predicted by the present linearized two-dimensional theory results in splitting into two separate droplets. This scenario is corroborated by the predictions of the fully nonlinear results, and the experimental results on a substrate with slip.