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 $.
Categories: patt-sol chao-dyn cond-mat.soft nlin.CD nlin.PS physics.flu-dyn