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

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

2004-11-10

arxiv.org/abs/nlin/0411029v1

Nonlinear Sciences

Pattern Formation and Solitons

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

Scientific paper

10.1103/PhysRevE.72.036211

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 ${\cal P}$, 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 ${\cal P}$, as ${\cal P}$ becomes smaller, and is nearly constant for ${\cal P} \gtrsim 1$. As ${\cal P} \to 0$, $g \to \infty$. 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 $\alpha$.

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