Electroconvection in Sheared Annular Fluid Films
Electroconvection in Sheared Annular Fluid Films
Thesis for Ph.D. degree, unpublished, Dec. 1999.
Zahir A. Daya
Department of Physics,
University of Toronto, 60 St. George St., Toronto, Ontario, Canada M5S 1A7.
Annular electroconvection in freely suspended thin fluid films undergoing circular Couette flow is a novel nonlinear system which, in this thesis, comes under experimental and theoretical scrutiny. Its novel features, which stem from its geometry and its electrohydrodynamic character, include the superposition of an azimuthal shear flow with a radial electrically driven hydrodynamic instability in a two-dimensional, naturally periodic system. Concentric circular electrodes support a weakly conducting annular fluid film which electroconvects when a sufficiently large voltage V is applied between its inner and outer edges. By rotation of the inner edge, a Couette shear is imposed. The control parameters are a Rayleigh-like number R proportional to V squared and the Reynolds number Re of the azimuthal shear. The geometrical and material properties of the film are characterized by the radius ratio alpha = ri / ro, where ri (ro) is the radius of the inner (outer) electrode, and a Prandtl-like number P. The electroconvective flow whose onset occurs when R = Rc is described by a nonaxisymmetric mode number mc and a traveling rate gamma. The dependence of Rc, mc, gamma on alpha, P, Re has been investigated theoretically by linear stability analysis. Experimental measurements of current-voltage data were used to determine the onset of electroconvection over a broad range of alpha, P and Re. These are compared with the theoretical predictions. The current-voltage data were used to infer the amplitude of convection in the weakly nonlinear regime by fitting to a steady-state amplitude equation with a lowest order cubic nonlinearity with coefficient g. Results for g as a function of alpha, P and Re are reported. Under various conditions, the primary bifurcation can be supercritical (g > 0), tricritical (g = 0) or subcritical (g < 0). Above onset, numerous subcritical secondary bifurcations, that mark transitions from one flow pattern to another, were encountered. A sampling of bifurcation scenarios is presented and their Re dependence is studied.
