5 research outputs found
Localized states in sheared electroconvection
Electroconvection in a thin, sheared fluid film displays a rich sequence of
bifurcations between different flow states as the driving voltage is increased.
We present a numerical study of an annular film in which a radial potential
difference acts on induced surface charges to drive convection. The film is
also sheared by independently rotating the inner edge of the annulus. This
simulation models laboratory experiments on electroconvection in sheared
smectic liquid crystal films. The applied shear competes with the electrical
forces, resulting in oscillatory and strongly subcritical bifurcations between
localized vortex states close to onset. At higher forcing, the flow becomes
chaotic via a Ruelle-Takens-Newhouse scenario. The simulation allows flow
visualization not available in the physical experiments, and sheds light on
previously observed transitions in the current-voltage characteristics of
electroconvecting smectic films.Comment: To be published in EuroPhysics Letters, 6 pages, 6 figures: final
versio
Weakly Nonlinear Analysis of Electroconvection in a Suspended Fluid Film
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.Comment: 26 pages, 2 included eps figures, submitted to Phys Rev E. For more
information, see http://mobydick.physics.utoronto.c
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Spontaneous spirals in vibrated granular chains
We present experimental measurements on the spontaneous formation of compact spiral structures in vertically-vibrated granular chains. Under weak vibration when the chain is quasi two-dimensional and self-avoiding, spiral structures emerge from random initial configurations. We compare the spiral geometry with that of an ideal tight spiral. Globally, the spiral undergoes a slow rotation such that to keep itself wound, while internally, fast vibrational modes are excited along the backbone with transverse oscillations dominating over longitudinal ones
Bifurcations in annular electroconvection with an imposed shear
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
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 , analogous to the Rayleigh
number, which is and the Reynolds number of the
azimuthal shear flow. The geometrical and material properties of the film were
characterized by the radius ratio , and a Prandtl-like number . Using measurements of current-voltage characteristics of a large number of
films, we examined the onset of electroconvection over a broad range of
, and . 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 and .Comment: 17 pages, 12 figures. Submitted to Phys. Rev. E. Minor changes after
refereeing. See also http://mobydick.physics.utoronto.c
Annular electroconvection with shear
We report experiments on convection driven by a radial electrical force in
suspended annular smectic A liquid crystal films. In the absence of an
externally imposed azimuthal shear, a stationary one-dimensional (1D) pattern
consisting of symmetric vortex pairs is formed via a supercritical transition
at the onset of convection. Shearing reduces the symmetries of the base state
and produces a traveling 1D pattern whose basic periodic unit is a pair of
asymmetric vortices. For a sufficiently large shear, the primary bifurcation
changes from supercritical to subcritical. We describe measurements of the
resulting hysteresis as a function of the shear at radius ratio . This simple pattern forming system has an unusual combination of
symmetries and control parameters and should be amenable to quantitative
theoretical analysis.Comment: 12 preprint pages, 3 figures in 2 parts each. For more info, see
http://mobydick.physics.utoronto.c