Weakly Nonlinear Analysis of Electroconvection in a Suspended Fluid
Film
Weakly Nonlinear Analysis of Electroconvection
in a Suspended Fluid
Film
Physical Review E, 56, 1706 (1997).
V. B. Deyirmenjian and Zahir A. Daya
Department of Physics,
University of Toronto, 60 St. George St., Toronto, Ontario, Canada M5S 1A7.
Stephen W. Morris
Department of Physics and Erindale College,
University of Toronto, 60 St. George St., Toronto, Ontario, Canada M5S 1A7.
It has been experimentally observed that weakly conducting suspended films
of smectic liquid crystals undergo electroconvection when subjected to a
large enough potential difference. The resulting counter-rotating vortices
form a very simple convection pattern and exhibit a variety of
interesting nonlinear effects. The linear stability problem for this
system has recently been solved. The convection mechanism, which involves
charge separation at the free surfaces of the film, is applicable to any
sufficiently two-dimensional fluid. In this paper, we derive an amplitude
equation which describes the weakly nonlinear regime, by starting from the
basic electrohydrodynamic equations. This regime has been the subject of
several recent experimental studies. The lowest order amplitude equation
we derive is of the Ginzburg-Landau form, and describes a forward
bifurcation as is observed experimentally. The coefficients of the
amplitude equation are calculated and compared with the values independently
deduced from the linear stability calculation.
PACS numbers: 47.20.K,47.65.+a,61.30.-v
