Electroconvection in sheared annular fluid films

Annular electroconvection in freely suspended thin fluid films undergoing circular Couette flow is a novel nonlinear system which, in this thesis, conies 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. Dyrotation of the inner edge, a Couette shear is imposed. The control parameters are a Rayleigh-like number R x V(2) and the Reynolds number Re of the azimuthal shear. The geometrical and material properties of the film are characterized by the radius ratio a = r1/r0, where r1(ro) is the radius of the inner (outer) electrode and a Prandtl-like number P. The electroconvective flow whose onset occurs when R = R c is described by a nonaxisym metric mode number mc and a traveling rate 7e. The dependence of Rc Mc, 7e c on a,V, R e 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 a, P and Re.These are compared with the theoretical predictions. The current-voltage d a ta 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 a, P and Re are reported. Under various conditions, the primary bifurcation can be supercritical (g>0), tricritical (g=0) or subcritical(g