Static and dynamic response of a fluid-fluid interface to electric point and line charge

TL;DR

This paper investigates how dielectric fluid interfaces respond to electric fields from point and line charges, analyzing static elevation and dynamic oscillations through numerical solutions of derived differential equations.

Contribution

It derives and solves differential equations describing static and dynamic fluid interface responses to electric charges, revealing dependencies on field strength, surface tension, and charge velocity.

Findings

Interface elevation depends on electric field strength and surface tension.

Oscillation wavelength relates to gravity and inertia forces.

Oscillation amplitude varies nontrivially with charge velocity.

Abstract

We consider the behaviour of a dielectric fluid-fluid interface in the presence of a strong electric field from a point charge and line charge, respectively, both statically and, in the latter case, dynamically. The fluid surface is elevated above its undisturbed level until balance is reached between the electromagnetic lifting force, gravity and surface tension. We derive ordinary differential equations for the shape of the fluid-fluid interface which are solved numerically with standard means, demonstrating how the elevation depends on field strength and surface tension coefficient. In the dynamic case of a moving line charge, the surface of an inviscid liquid-liquid interface is left to oscillate behind the moving charge after it has been lifted against the force of gravity. We show how the wavelength of the oscillations depends on the relative strength of the forces of gravity and inertia, whereas the amplitude of the oscillations is a nontrivial function of the velocity at which the line charge moves.