Electrically driven convection in a thin annular film undergoing circular Couette flow

Zahir A. Daya; V. B. Deyirmenjian; Stephen W. Morris

doi:10.1063/1.870226

paper

Electrically driven convection in a thin annular film undergoing circular Couette flow

arXiv:patt-sol/9806005 · doi:10.1063/1.870226

Abstract

We investigate the linear stability of a thin, suspended, annular film of conducting fluid with a voltage difference applied between its inner and outer edges. For a sufficiently large voltage, such a film is unstable to radially-driven electroconvection due to charges which develop on its free surfaces. The film can also be subjected to a Couette shear by rotating its inner edge. This combination is experimentally realized using films of smectic A liquid crystals. In the absence of shear, the convective flow consists of a stationary, azimuthally one-dimensional pattern of symmetric, counter-rotating vortex pairs. When Couette flow is applied, an azimuthally traveling pattern results. When viewed in a co-rotating frame, the traveling pattern consists of pairs of asymmetric vortices. We calculate the neutral stability boundary for arbitrary radius ratio $α$ and Reynolds number $R e$ of the shear flow, and obtain the critical control parameter $R_{c} (α, R e)$ and the critical azimuthal mode number $m_{c} (α, R e)$ . The Couette flow suppresses the onset of electroconvection, so that $R_{c} (α, R e) > R_{c} (α, 0)$ . The calculated suppression is compared with experiments performed at $α = 0.56$ and $0 \leq R e \leq 0.22$ .

17 pages, 2 column with 9 included eps figures. See also http://mobydick.physics.utoronto.ca

Electrically driven convection in a thin annular film undergoing circular Couette flow

Abstract

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