Bifurcations in annular electroconvection with an imposed shear

Abstract

We report an experimental study of the primary bifurcation in electrically-driven convection in a freely suspended film. A weakly conducting, submicron thick smectic liquid crystal film was supported by concentric circular electrodes. It electroconvected when a sufficiently large voltage $V$ was applied between its inner and outer edges. The film could sustain rapid flows and yet remain strictly two-dimensional. By rotation of the inner electrode, a circular Couette shear could be independently imposed. The control parameters were a dimensionless number $\mathcal{R}$, analogous to the Rayleigh number, which is $\propto V^2$ and the Reynolds number $\mathcal{R}e$ of the azimuthal shear flow. The geometrical and material properties of the film were characterized by the radius ratio $\alpha$, and a Prandtl-like number $\mathcal{P}$. Using measurements of current-voltage characteristics of a large number of films, we examined the onset of electroconvection over a broad range of $\alpha$, $\mathcal{P}$ and $\mathcal{R}e$. We compared this data quantitatively to the results of linear stability theory. This could be done with essentially no adjustable parameters. The current-voltage data above onset were then used to infer the amplitude of electroconvection in the weakly nonlinear regime by fitting them to a steady-state amplitude equation of the Landau form. We show how the primary bifurcation can be tuned between supercritical and subcritical by changing $\alpha$ and $\mathcal{R}e$.

17 pages, 12 figures. Submitted to Phys. Rev. E. Minor changes after refereeing. See also http://mobydick.physics.utoronto.ca

References in corpus (3)

• Annular electroconvection with shear
• Weakly Nonlinear Analysis of Electroconvection in a Suspended Fluid Film
• Electrically driven convection in a thin annular film undergoing circular Couette flow

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• Localized states in sheared electroconvection
• Sequential Bifurcations in Sheared Annular Electroconvection
• Codimension-two points in annular electroconvection as a function of aspect ratio
• Limitation of Finite Difference Scheme in Electroconvection with Unipolar Charge Injection: A base-state Analysis