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

*Physics of Fluids*, **11**, 3613 (1999).

### Zahir A. Daya,
V. B. Deyirmenjian and
Stephen W. Morris

Department of Physics,
University of Toronto, 60 St. George St., Toronto, Ontario, Canada M5S 1A7.

### 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 *a* and Reynolds
number *Re* of the shear flow, and obtain the critical
control parameter *R*_{c}(a, Re) and the
critical azimuthal mode number *m*_{c}(a, Re). The
Couette flow suppresses the onset of electroconvection, so that
*R*_{c}(a, Re) > *R*_{c}(a, 0). The
calculated suppression is compared with experiments performed at
*a* = 0.56 and 0 < *Re* < 0.22 .

PACS numbers: 47.20.K,47.65.+a,61.30.-v