Codimension-two points in annular electroconvection as a function of aspect ratio

Abstract

We rigorously derive from first principles the generic Landau amplitude equation that describes the primary bifurcation in electrically driven convection. Our model accurately represents the experimental system: a weakly conducting, submicron thick liquid crystal film suspended between concentric circular electrodes and driven by an applied voltage between its inner and outer edges. We explicitly calculate the coefficient $g$ of the leading cubic nonlinearity and systematically study its dependence on the system's geometrical and material parameters. The radius ratio $\alpha$ quantifies the film's geometry while a dimensionless group $\mathcal{P}$, similar to the Prandtl number, fixes the ratio of the fluid's electrical and viscous relaxation times. Our calculations show that for fixed $\alpha$, $g$ is a decreasing function of $\mathcal{P}$, as $\mathcal{P}$ becomes smaller, and is nearly constant for $\mathcal{P}\gtrsim 1$. As $\mathcal{P}\to 0$, $g\to \infty$. We find that $g$ is a nontrivial and discontinuous function of $\alpha$. We show that the discontinuities occur at codimension-two points that are accessed by varying $\alpha$.

7 pages, 5 figures and 1 table. See also http://www.physics.utoronto.ca/nonlinear

References in corpus (8)

• Electroconvection in a Suspended Fluid Film: A Linear Stability Analysis
• Annular electroconvection with shear
• Aspect ratio dependence of charge transport in turbulent electroconvection
• Weakly Nonlinear Analysis of Electroconvection in a Suspended Fluid Film
• Electrically driven convection in a thin annular film undergoing circular Couette flow
• Bifurcations in annular electroconvection with an imposed shear
• Sequential Bifurcations in Sheared Annular Electroconvection
• Pattern formation in annular convection

Cited by in corpus (2)

• Localized states in sheared electroconvection
• Electroconvection of Thin Liquid Crystals: Model Reduction and Numerical Simulations