Electroconvection in a suspended fluid film: A linear stability analysis

Daya, Zahir A.; Morris, Stephen W.; Bruyn, John R. de

doi:10.1103/physreve.55.2682

Cited by 43 publications

(64 citation statements)

References 12 publications

(51 reference statements)

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“…On other loci, the hysteresis δǫ is a local maximum. As a function of α, linear theory [7] shows that there exist special values of α at which two azimuthal mode numbers m and m+1 are simultaneously linearly unstable. All of the g results we have described pertain to the primary bifurcation; above onset we also observed numerous secondary bifurcations which take the form of hysteretic jumps in m. The location of these secondary bifurcations is a function of Re.…”

Section: Discussionmentioning

confidence: 99%

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Bifurcations in annular electroconvection with an imposed shear

2001

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We report an experimental study of the primary bifurcation in electrically-driven convection in a freely suspended film. A weakly conducting, submicron thick smectic liquid crystal film was supported by concentric circular electrodes. It electroconvected when a sufficiently large voltage V was applied between its inner and outer edges. The film could sustain rapid flows and yet remain strictly two-dimensional. By rotation of the inner electrode, a circular Couette shear could be independently imposed. The control parameters were a dimensionless number R, analogous to the Rayleigh number, which is ∝ V 2 and the Reynolds number Re of the azimuthal shear flow. The geometrical and material properties of the film were characterized by the radius ratio α, and a dimensionless number P, analogous to the Prandtl number. Using measurements of current-voltage characteristics of a large number of films, we examined the onset of electroconvection over a broad range of α, P and Re. We compared this data quantitatively to the results of linear stability theory. This could be done with essentially no adjustable parameters. The current-voltage data above onset were then used to infer the amplitude of electroconvection in the weakly nonlinear regime by fitting them to a steady-state amplitude equation of the Landau form. We show how the primary bifurcation can be tuned between supercritical and subcritical by changing α and Re.

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Section: Discussionmentioning

confidence: 99%

“…[7] Below the onset of convection, the film's electrical state is independent of the imposed shear in the film. It is thus straightforward to superpose shear flows with the radial driving, as these are characterized by independent control parameters.…”

Section: Introductionmentioning

confidence: 99%

Bifurcations in annular electroconvection with an imposed shear

2001

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“…[4][5][6][7] A theoretical model of the onset of electroconvection in suspended films was introduced by Daya, Morris, and de Bruyn. [8] The film was represented as a weakly conducting, twodimensional, isotropic fluid. To find the electric fields and charge densities which drive convection, the electrostatic potential was determined.…”

Section: Introductionmentioning

confidence: 99%

Weakly nonlinear analysis of electroconvection in a suspended fluid film

Deyirmenjian¹,

Daya²,

Morris³

1997

Phys. Rev. E

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It has been experimentally observed that weakly conducting suspended films of smectic liquid crystals undergo electroconvection when subjected to a large enough potential difference. The resulting counter-rotating vortices form a very simple convection pattern and exhibit a variety of interesting nonlinear effects. The linear stability problem for this system has recently been solved. The convection mechanism, which involves charge separation at the free surfaces of the film, is applicable to any sufficiently two-dimensional fluid.In this paper, we derive an amplitude equation which describes the weakly nonlinear regime, by starting from the basic electrohydrodynamic equations. This regime has been the subject of several recent experimental studies. The lowest order amplitude equation we derive is of the Ginzburg-Landau form, and describes a forward bifurcation as is observed experimentally. The coefficients of the amplitude equation are calculated and compared with the values independently deduced from the linear stability calculation.

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“…Indeed it was observed in the experiment that convection rolls were always lost or gained at the system ends and never in the interior. For this system the location of the Eckhaus stability limit was estimated from the location of the neutral curve, which in turn was calculated from the equations of motion [32]. Thus a comparison of the reduced boundary-limited band with the approximate location of the wider Eckhaus band of the infinite system is possible.…”

Section: Introductionmentioning

confidence: 99%

Boundary limitation of wave numbers in Taylor-vortex flow

Linek

Ahlers

1998

Phys. Rev. E

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We report experimental results for a boundary-mediated wavenumber-adjustment mechanism and for a boundary-limited wavenumber-band of Taylor-vortex flow (TVF). The system consists of fluid contained between two concentric cylinders with the inner one rotating at an angular frequency Ω. As observed previously, the Eckhaus instability (a bulk instability) is observed and limits the stable wavenumber band when the system is terminated axially by two rigid, non-rotating plates. The band width is then of order ǫ 1/2 at small ǫ (ǫ ≡ Ω/Ωc − 1) and agrees well with calculations based on the equations of motion over a wide ǫ-range. When the cylinder axis is vertical and the upper liquid surface is free (i.e. an air-liquid interface), vortices can be generated or expelled at the free surface because there the phase of the structure is only weakly pinned. The band of wavenumbers over which Taylor-vortex flow exists is then more narrow than the stable band limited by the Eckhaus instability. At small ǫ the boundary-mediated band-width is linear in ǫ. These results are qualitatively consistent with theoretical predictions, but to our knowledge a quantitative calculation for TVF with a free surface does not exist.

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Electroconvection in a suspended fluid film: A linear stability analysis

Cited by 43 publications

References 12 publications

Bifurcations in annular electroconvection with an imposed shear

Bifurcations in annular electroconvection with an imposed shear

Weakly nonlinear analysis of electroconvection in a suspended fluid film

Boundary limitation of wave numbers in Taylor-vortex flow

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