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

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

1998-06-12

arxiv.org/abs/patt-sol/9806005v2

Physics of Fluids, 11, 3613 (1999)

Physics

Condensed Matter

Soft Condensed Matter

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

Scientific paper

10.1063/1.870226

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 $\alpha$ and Reynolds number ${{\cal R} e}$ of the shear flow, and obtain the critical control parameter ${\cal R}_c (\alpha, {{\cal R} e})$ and the critical azimuthal mode number ${m_c (\alpha, {{\cal R} e})}$. The Couette flow suppresses the onset of electroconvection, so that ${\cal R}_c (\alpha, {{\cal R} e}) > {\cal R}_c (\alpha,0)$. The calculated suppression is compared with experiments performed at $\alpha = 0.56 $ and $0 \leq {{\cal R} e} \leq 0.22 $.

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