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 Re of the shear
flow, and obtain the critical control parameter Rc​(α,Re) and the critical azimuthal mode number mc​(α,Re). The
Couette flow suppresses the onset of electroconvection, so that Rc​(α,Re)>Rc​(α,0). The calculated suppression is
compared with experiments performed at α=0.56 and 0≤Re≤0.22.Comment: 17 pages, 2 column with 9 included eps figures. See also
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