Long-wave dynamics of an inextensible planar membrane in an electric field

Y. N. Young, Shravan Veerapaneni, Michael J. Miksis

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

In this paper the dynamics of an inextensible capacitive elastic membrane under an electric field is investigated in the long-wave (lubrication) leaky dielectric framework, where a sixth-order nonlinear differential equation with an integral constraint is derived. Steady equilibrium profiles for a non-conducting membrane in a direct current (DC) field are found to depend only on the membrane excess area and the volume under the membrane. Linear stability analysis on a tensionless flat membrane in a DC field gives the growth rate in terms of membrane conductance and electric properties in the bulk. Numerical simulations of a capacitive conducting membrane under an alternating current (AC) field elucidate how variation of the membrane tension correlates with the nonlinear membrane dynamics. Different membrane dynamics, such as undulation and flip-flop, are found at different electric field strength and membrane area. In particular a travelling wave on the membrane is found as a response to a periodic AC field in the perpendicular direction.

Original languageEnglish (US)
Pages (from-to)406-431
Number of pages26
JournalJournal of Fluid Mechanics
Volume751
DOIs
StatePublished - Jul 2014

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Keywords

  • biological fluid dynamics
  • membranes
  • thin films

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