Formation of High Pressure Gradients at the Free Surface of a Liquid Dielectric in a Tangential Electric Field

TL;DR

This study uses conformal transformation simulations to show how strong horizontal electric fields cause nonlinear wave interactions on a dielectric liquid surface, leading to high pressure gradients and surface singularities.

Contribution

It demonstrates the formation of high pressure gradients and surface singularities due to wave interactions under strong electric fields, a novel insight into electrohydrodynamic surface behavior.

Findings

Regions with steep wave fronts form at the surface.

Angles of boundary inclination tend to π/2.

Electric pressure exhibits discontinuities at singularities.

Abstract

Nonlinear dynamics of the free surface of an ideal incompressible non-conducting fluid with high dielectric constant subjected by strong horizontal electric field is simulated on the base of the method of conformal transformations. It is demonstrated that interaction of counter-propagating waves leads to formation of regions with steep wave front at the fluid surface; angles of the boundary inclination tend to {\pi}/2, and the curvature of surface extremely increases. A significant concentration of the energy of the system occurs at these points. From the physical point of view, the appearance of these singularities corresponds to formation of regions at the fluid surface where pressure exerted by electric field undergoes a discontinuity and dynamical pressure increases almost an order of magnitude.