Gravity capillary waves in fluid layers under normal electric fields

Document Type

Article

Publication Date

11-1-2005

Abstract

We study the formation and dynamics of interfacial waves on a perfect dielectric ideal fluid layer of finite depth, wetting a solid wall, when the region above the fluid is hydrodynamically passive but has constant permittivity, for example, air. The wall is held at a constant electric potential and a second electrode having a different potential is placed parallel to the wall and infinitely far from it. In the unperturbed state the interface is flat and the normal horizontally uniform electric field is piecewise constant in the liquid and air. We derive a system of long wave nonlinear evolution equations valid for interfacial amplitudes as large as the unperturbed layer depth and which retain gravity, surface tension and electric field effects. It is shown that for given physical parameters there exists a critical value of the voltage potential difference between electrodes, below which the system is dispersive and above which a band of unstable waves is possible centered around a finite wavenumber. In the former case nonlinear traveling waves are calculated and their stability is studied, while in the latter case the instability leads to thinning of the layer with the interface touching down in finite time. A similarity solution of the second kind is found to be dominant near the singularity, and the scaling exponents are determined using analysis and computations. © 2005 The American Physical Society.

Identifier

28844509711 (Scopus)

Publication Title

Physical Review E Statistical Nonlinear and Soft Matter Physics

External Full Text Location

https://doi.org/10.1103/PhysRevE.72.051601

e-ISSN

15502376

ISSN

15393755

Issue

5

Volume

72

Grant

0072228

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