Linear and Nonlinear Surface Waves in Electrohydrodynamics

TL;DR

This paper derives new mathematical models for surface waves in electrohydrodynamics, incorporating effects of gravity, surface tension, and electric fields, revealing conditions for shock wave formation and new dispersive behaviors.

Contribution

It introduces a Kadomtsev-Petviashvili equation with a non-local term for electrohydrodynamic waves and explores special cases like zero electric fields and critical Bond numbers.

Findings

Dispersion disappears at Bond number 1/3, allowing shock wave formation.

A new evolution equation with third and fifth-order dispersion is derived for vanishing electric fields.

Non-local electric field effects significantly influence wave dynamics.

Abstract

The problem of interest in this article are waves on a layer of finite depth governed by the Euler equations in the presence of gravity, surface tension, and vertical electric fields. Perturbation theory is used to identify canonical scalings and to derive a Kadomtsev-Petviashvili equation withan additional non-local term arising in interfacial electrohydrodynamics.When the Bond number is equal to 1/3, dispersion disappears and shock waves could potentially form. In the additional limit of vanishing electric fields, a new evolution equation is obtained which contains third and fifth-order dispersion as well as a non-local electric field term.