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

Abstract

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. Fluids, 11, 3613 (1999). See also http://mobydick.physics.utoronto.ca. Physics of

Bifurcations in annular electroconvection with an imposed shear

“…It can be shown that any arbitrary rotation of the inner and outer edges can be transformed to a rotation of only the inner edge by moving to the appropriate rotating coordinates. [3,30] Such a coordinate transformation has no effect on the dynamics as long as the flow is strictly two-dimensional. The theoretical model is completely specified by the radius ratio α and three additional dimensionless parameters:…”

“…[3] examined the linear stability of the two-dimensional annular fluid film when it is subjected to a voltage V at the inner electrode of the annulus while the outer electrode is held at ground potential. In addition, the theory allowed for the rotation of the inner edge of the annulus at angular frequency ω, while the outer edge is held fixed.…”

“…The theory is constructed with a number of simplifying assumptions. [3,7] The fluid film is treated as an annular sheet of inner radius r i , outer radius r o and thickness s. A schematic is shown in Fig. 1.…”

“…We test the adequacy of the theoretical model by direct comparisons between the experimental results and theoretical predictions at the linear level. [3] We then proceed to describe how the coefficient of the lowest order nonlinear term depends on the experimental parameters. Interestingly, we find that the coefficient can be made to change sign and thus that the primary bifurcation can be tuned between subcritical and supercritical.…”

“…It was previously described in Refs. [3] and [6]. The film was suspended between concentric circular electrodes and was driven by a voltage difference between the electrodes.…”