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Visco-potential flows in electrohydrodynamics

In this study we consider the problem of the interface motion under the capillary-gravity and an external electric forces. The infinitely deep fluid layer is assumed to be viscous, perfectly conducting and the flow to be incompressible. The weak viscous effects are introduced using the Helmholtz-Leray decomposition and the visco-potential flow approach. The electric charge distributions above and on the free surface are considered. Finally, we derive some linearized analytical solutions for the free surface elevation shape under the localised pressure distribution and the combined action of the forces mentioned hereinabove.