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