Electroconvection in Suspended Fluid Films
Electroconvection in Suspended Fluid Films
Thesis for M.Sc. degree, unpublished, Aug 1996.
Zahir A. Daya
Department of Physics,
University of Toronto, 60 St. George St., Toronto, Ontario, Canada M5S 1A7.
A theoretical electrohydrodynamic model is developed to explain the instability of a freely suspended fluid film to electroconvection; an instability that occurs when a sufficiently large potential is applied across it. The instability, which leads to a steady spatially periodic flow pattern comprised of counter-rotating vortices, is found to result from the interaction of the electric field with the surface charge density that develops on the free surfaces. A linear stability analysis of the relevant equations is presented. We define a dimensionless control parameter R, which is proportional to the square of the applied voltage, and find a neutral stability boundary for this parameter as a function of the dimensionless wavenumber k. The critical values R_c and k_c are found from the minimum of the stability curve. From the curvature of the neutral stability boundary at (k_c, R_c), we calculate the correlation length xi_0 for the amplitude of the pattern. The linear growth rate 1/tau_0, which depends on another dimensionless parameter P, is also calculated. xi_0 and tau_0 are coefficients in the Ginzburg-Landau amplitude equation which describes the weakly nonlinear flow pattern near onset in this system. Results of the analysis are compared with recent experiments on smectic A liquid crystal films.
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