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 Rc(a, Re) and the
critical azimuthal mode number mc(a, Re). The
Couette flow suppresses the onset of electroconvection, so that
Rc(a, Re) > Rc(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
