Charge Transport Scalings in Turbulent Electroconvection
Charge Transport Scalings in Turbulent Electroconvection
Physical Review E 72, 046311 (2005).
Peichun Tsai (1), Zahir A. Daya (2) and Stephen W.
Morris (1)
(1) Department of Physics,
University of Toronto, 60 St. George St., Toronto, Ontario, Canada M5S 1A7.
(2) Defence Research & Development Canada, 9 Grove Street, Dartmouth, Nova Scotia, Canada B2Y 3Z7
We describe a local-power law scaling theory for the mean dimensionless
electric current Nu in turbulent electroconvection. The experimental system consists of a weakly conducting, submicron thick liquid crystal film supported in the annulus between concentric
circular electrodes. It is driven into electroconvection by an applied voltage
between its inner and outer edges. At sufficiently large voltage differences,
the flow is unsteady and electric charge is turbulently transported between
the electrodes. Our theoretical development, which closely parallels the
Grossmann-Lohse model for turbulent thermal convection, predicts the
local-power law Nu ~ F(Gamma) R^gamma P^delta. R and R are dimensionless numbers that are similar to the Rayleigh
and Prandtl numbers of thermal convection, respectively. The dimensionless function
F(Gamma), which is specified by the model, describes the dependence of Nu on the
aspect ratio Gamma. We find that measurements of Nu are consistent with the theoretical model.
