The shape of charged drops over a solid surface and symmetry-breaking instabilities

Fontelos, Marco Antonio and Kindelan Bustelo, Ultano (2008). The shape of charged drops over a solid surface and symmetry-breaking instabilities. "Siam Journal on Applied Mathematics", v. 69 (n. 1); pp. 126-148. ISSN 0036-1399. https://doi.org/10.1137/080713707.

Description

Title: The shape of charged drops over a solid surface and symmetry-breaking instabilities
Author/s:
  • Fontelos, Marco Antonio
  • Kindelan Bustelo, Ultano
Item Type: Article
Título de Revista/Publicación: Siam Journal on Applied Mathematics
Date: August 2008
ISSN: 0036-1399
Volume: 69
Subjects:
Freetext Keywords: electrowetting, symmetry-breaking bifurcations, boundary integral method, varia-tional formulation
Faculty: E.T.S.I. Minas (UPM)
Department: Matemática Aplicada y Métodos Informáticos [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

We study the static shape of charged drops of a conducting fluid placed over a solid substrate, surrounded by a gas, and in absence of gravitational forces. The question can be formulated as a variational problem where a certain energy involving the areas of the solid-liquid interface and of the liquid-gas interface, as well as the electric capacity of the drop, has to be minimized. As a function of two parameters, Young’s angle µY and the potential at the drop’s surface V0, we find the axisymmetric minimizers of the energy and describe their shape. We also discuss the existence of symmetry-breaking bifurcations such that, for given values of µY and V0, configurations for which the axial symmetry is lost are energetically more favorable than axially symmetric configurations. We prove the existence of such bifurcations in the limits of very flat and almost spherical equilibrium shapes. All other cases are studied numerically with a boundary integral method. One conclusion of this study is that axisymmetric drops cannot spread indefinitely by introducing sufficient amount of electric charges, but can reach only a limiting (saturation) size, after which the axial symmetry would be lost and finger-like shapes energetically preferred.

More information

Item ID: 2182
DC Identifier: http://oa.upm.es/2182/
OAI Identifier: oai:oa.upm.es:2182
DOI: 10.1137/080713707
Official URL: http://scitation.aip.org/dbt/dbt.jsp?KEY=SMJMAP&Volume=69&Issue=1
Deposited by: Memoria Investigacion
Deposited on: 08 Feb 2010 11:42
Last Modified: 20 Apr 2016 11:56
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