20 research outputs found
Charge Transport Scalings in Turbulent Electroconvection
We describe a local-power law scaling theory for the mean dimensionless
electric current in turbulent electroconvection. The experimental system
consists of a weakly conducting, submicron thick liquid crystal film supported
in the annulus between concentric circular electrodes. It is driven into
electroconvection by an applied voltage between its inner and outer edges. At
sufficiently large voltage differences, the flow is unsteady and electric
charge is turbulently transported between the electrodes. Our theoretical
development, which closely parallels the Grossmann-Lohse model for turbulent
thermal convection, predicts the local-power law . and are dimensionless
numbers that are similar to the Rayleigh and Prandtl numbers of thermal
convection, respectively. The dimensionless function , which is
specified by the model, describes the dependence of on the aspect ratio
. We find that measurements of are consistent with the theoretical
model.Comment: 12 pages, 7 figures, Submitted to Phys. Rev. E. See also
http://www.physics.utoronto.ca/nonlinea
Electrically driven convection in a thin annular film undergoing circular Couette flow
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 and Reynolds number of the shear
flow, and obtain the critical control parameter and the critical azimuthal mode number . The
Couette flow suppresses the onset of electroconvection, so that . The calculated suppression is
compared with experiments performed at and .Comment: 17 pages, 2 column with 9 included eps figures. See also
http://mobydick.physics.utoronto.c
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
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
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
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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
Electroconvection in a Suspended Fluid Film: A Linear Stability Analysis
A suspended fluid film with two free surfaces convects when a sufficiently
large voltage is applied across it. We present a linear stability analysis for
this system. The forces driving convection are due to the interaction of the
applied electric field with space charge which develops near the free surfaces.
Our analysis is similar to that for the two-dimensional B\'enard problem, but
with important differences due to coupling between the charge distribution and
the field. We find the neutral stability boundary of a dimensionless control
parameter as a function of the dimensionless wave number .
, which is proportional to the square of the applied voltage, is
analogous to the Rayleigh number. The critical values and
are found from the minimum of the stability boundary, and its
curvature at the minimum gives the correlation length . The
characteristic time scale , which depends on a second dimensionless
parameter , analogous to the Prandtl number, is determined from the
linear growth rate near onset. and are coefficients in the
Ginzburg-Landau amplitude equation which describes the flow pattern near onset
in this system. We compare our results to recent experiments.Comment: 36 pages, 7 included eps figures, submitted to Phys Rev E. For more
info, see http://mobydick.physics.utoronto.ca
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 indepen..
Aspect-Ratio Dependence of Charge Transport in Turbulent Electroconvection
We present measurements of the normalized charge transport or Nusselt number Nu as a function of the aspect ratio Γ for turbulent convection in an electrically driven film. In analogy with turbulent Rayleigh-Bénard convection, we develop the relevant theoretical framework in which we discuss the local power-law scaling of Nu with a dimensionless electrical forcing parameter R. For these experiments where 104≲R≲2×105 we find that Nu∼F(Γ)Rγ with either γ=0.26 (±0.02) or γ=0.20 (±0.03), in excellent agreement with the theoretical predictions of γ=1/4 and 1/5. Our measurements of the aspect-ratio dependence of Nu for 0.3≤Γ≤17 compares favorably with the function F(Γ) from the scaling theory