dorsal/arxiv
View SchemaElectrically driven convection in a thin annular film undergoing circular Couette flow
| Authors | Zahir A. Daya, V. B. Deyirmenjian, Stephen W. Morris |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9806005 |
| URL | https://arxiv.org/abs/patt-sol/9806005 |
| DOI | 10.1063/1.870226 |
| Journal | Physics of Fluids, 11, 3613 (1999) |
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 $\alpha$ 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 $.
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"abstract": "We investigate the linear stability of a thin, suspended, annular film of\nconducting fluid with a voltage difference applied between its inner and outer\nedges. For a sufficiently large voltage, such a film is unstable to\nradially-driven electroconvection due to charges which develop on its free\nsurfaces. The film can also be subjected to a Couette shear by rotating its\ninner edge. This combination is experimentally realized using films of smectic\nA liquid crystals. In the absence of shear, the convective flow consists of a\nstationary, azimuthally one-dimensional pattern of symmetric, counter-rotating\nvortex pairs. When Couette flow is applied, an azimuthally traveling pattern\nresults. When viewed in a co-rotating frame, the traveling pattern consists of\npairs of asymmetric vortices. We calculate the neutral stability boundary for\narbitrary radius ratio $\\alpha$ and Reynolds number ${{\\cal R} e}$ of the shear\nflow, and obtain the critical control parameter ${\\cal R}_c (\\alpha, {{\\cal R}\ne})$ and the critical azimuthal mode number ${m_c (\\alpha, {{\\cal R} e})}$. The\nCouette flow suppresses the onset of electroconvection, so that ${\\cal R}_c\n(\\alpha, {{\\cal R} e}) \u003e {\\cal R}_c (\\alpha,0)$. The calculated suppression is\ncompared with experiments performed at $\\alpha = 0.56 $ and $0 \\leq {{\\cal R}\ne} \\leq 0.22 $.",
"arxiv_id": "patt-sol/9806005",
"authors": [
"Zahir A. Daya",
"V. B. Deyirmenjian",
"Stephen W. Morris"
],
"categories": [
"patt-sol",
"chao-dyn",
"cond-mat.soft",
"nlin.CD",
"nlin.PS",
"physics.flu-dyn"
],
"doi": "10.1063/1.870226",
"journal_ref": "Physics of Fluids, 11, 3613 (1999)",
"title": "Electrically driven convection in a thin annular film undergoing circular Couette flow",
"url": "https://arxiv.org/abs/patt-sol/9806005"
},
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