Patterns at the onset of electroconvection in freely suspended smectic films

Morris, Stephen W.; Bruyn, John R. de; May, A. D.

doi:10.1007/bf01048812

Cited by 15 publications

(34 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Almost all the experiments performed in the rectangular geometry had Λ < ∼ 10 [20][21][22][23][24] and were well-modelled by the theory for an unbounded strip for which Λ = ∞. It is thus resonable to expect g at α = 0.80 to be close to its limiting value for α = 1.…”

Section: Coefficients Of the Cubic Nonlinearity Without Shearmentioning

confidence: 98%

See 1 more Smart Citation

Bifurcations in annular electroconvection with an imposed shear

2001

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Coefficients Of the Cubic Nonlinearity Without Shearmentioning

confidence: 98%

“…As in previous experiments [3,6,[20][21][22][23][24], our study used smectic A octylcyanobiphenyl (8CB). 8CB has a smectic A phase between 21…”

Section: A the Liquid Crystalmentioning

confidence: 99%

Bifurcations in annular electroconvection with an imposed shear

2001

Self Cite

View full text Add to dashboard Cite

show abstract

“…For example, the standard case of buoyancy-driven Rayleigh-Bénard convection (RBC) has been studied in the presence of rotation [7,8,9,10] and shearing due to an open throughflow [11,12], as well as in the geophysically interesting cases of radial gravitation with rotation [5,6]. The phenomenology of two-dimensional (2D) electroconvection in a rectangular geometry was the subject of our previous experimental [13,14,15,16,17] and theoretical [2,3] work. These studies made precise the degree of analogy with RBC; the electrical nature of the forcing introduces some crucial differences in detail, even at the level of linear stability.…”

Section: Introductionmentioning

confidence: 99%

“…To realize this experimentally, we use thin suspended films of a liquid crystal in the smectic A phase. [1,13,14,15,16,17] These submicron films are newtonian and isotropic for flows within the plane of the film, are immune to thickness variation, and have a very low electrical conductivity. The latter is required to keep the onset voltage within an experimentally reasonable range.…”

Section: Introductionmentioning

confidence: 99%

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

1999

Self Cite

View full text Add to dashboard Cite

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

show abstract

“…In the opposite direction, it would be useful to perform laboratory experiments in a rotating hemispherical shell of fluid with a uniform density (hence zero buoyancy) and a radial driving force of electrostatic or other nongravitational form, to test these mathematical predictions. Such experiments have already been performed in a thin annular geometry [25]. For this case, the mathematical model can be modified to change the forcing mechanism from thermoconvection to electroconvection as for the thin annulus, see [28,29].…”

Section: Discussionmentioning

confidence: 99%

Hysteresis in a Rotating Differentially Heated Spherical Shell of Boussinesq Fluid

Lewis

Langford

2008

SIAM J. Appl. Dyn. Syst.

View full text Add to dashboard Cite

A mathematical model of convection of a Boussinesq fluid in a rotating spherical shell is analyzed using numerical computations guided by bifurcation theory. The fluid is differentially heated on its inner spherical surface, with the temperature increasing from both poles to a maximum at the equator. The model is assumed to be both rotationally symmetric about the polar axis and reflectionally symmetric across the equator. This work is an extension to spherical geometry of previous work on the differentially heated rotating annulus. The spherical geometry is motivated by applications to planetary atmospheres. As the temperature gradient increases from zero, large Hadley cells extending from equator to poles form immediately. For larger temperature differences, two or three convection cells appear in each hemisphere. An organizing centre is shown to exist, at which two saddle-node bifurcations come together in a codimension-2 hysteresis bifurcation (or cusp) point, providing a mechanism for hysteretic transitions between different cell patterns as the temperature gradient is varied.

show abstract

Patterns at the onset of electroconvection in freely suspended smectic films

Cited by 15 publications

References 21 publications

Bifurcations in annular electroconvection with an imposed shear

Bifurcations in annular electroconvection with an imposed shear

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

Hysteresis in a Rotating Differentially Heated Spherical Shell of Boussinesq Fluid

Contact Info

Product

Resources

About