Electroconvection in a Suspended Fluid Film: A Linear
Stability Analysis
Electroconvection in a Suspended Fluid Film: A Linear
Stability Analysis
Physical Review E, 55, 2682 (1997).
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.
John R. de Bruyn
Department of Physics, Memorial University of Newfoundland,
St. John's, Newfoundland, Canada A1B 3X7
A suspended fluid film with two free surfaces convects when a
sufficiently large voltage is applied across it. We present a linear
stability analysis for this system. The forces driving convection are
due to the interaction of the applied electric field with space charge
which develops near the free surfaces. Our analysis is similar to that
for the two-dimensional Bénard problem, but with important
differences due to coupling between the charge distribution and the
field. We find the neutral stability boundary of a
dimensionless control parameter R as a function of the dimensionless
wave number k. R, which is proportional to
the square of the applied voltage, is analogous to the Rayleigh number.
The critical values R_c and
k_c are found from the minimum of the stability boundary, and
its curvature at the minimum gives the correlation length xi_0.
The characteristic time scale tau_0, which depends on a second
dimensionless parameter P, analogous to the Prandtl number, is
determined from the linear growth rate near onset. xi_0 and
tau_0 are coefficients
in the Ginzburg-Landau amplitude equation which describes the flow
pattern near onset in this system. We compare our results to recent
experiments
PACS numbers: 47.20.K,47.65.+a,61.30.-v
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