Analysis of a static undulation on the surface of a thin dielectric liquid layer formed by dielectrophoresis forces

Nigel Mottram, Carl Brown, Glen McHale

Research output: Contribution to journalArticle

12 Citations (Scopus)


A layer of insulating liquid of dielectric constant epsilon(Oil) and average thickness (h) over bar coats a flat surface at y = 0 at which a one-dimensional sinusoidal potential V(x, 0) = V(O) cos(pi x/p) is applied. Dielectrophoresis forces create a static undulation (or "wrinkle") distortion h(x) of period p at the liquid/air interface. Analytical expressions have been derived for the electrostatic energy and the interfacial energy associated with the surface undulation when h(x) = (h) over bar - (1/2)A cos(2 pi x/p) yielding a scaling relationship for A as a function of (h) over bar, p, V(O), epsilon(Oil) and the surface tension. The analysis is valid as A/p -> 0, and in this limit convergence with numerical simulation of the system is shown.
Original languageEnglish
Article number024107
Pages (from-to)1-5
Number of pages5
JournalJournal of Applied Physics
Issue number2
Publication statusPublished - 22 Jul 2011


  • static undulation
  • dielectric liquid
  • dielectrophoresis forces


  • Cite this