226 research outputs found
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
Where are the Hedgehogs in Nematics?
In experiments which take a liquid crystal rapidly from the isotropic to the
nematic phase, a dense tangle of defects is formed. In nematics, there are in
principle both line and point defects (``hedgehogs''), but no point defects are
observed until the defect network has coarsened appreciably. In this letter the
expected density of point defects is shown to be extremely low, approximately
per initially correlated domain, as result of the topology
(specifically, the homology) of the order parameter space.Comment: 6 pages, latex, 1 figure (self-unpacking PostScript)
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
Surface alignment and anchoring transitions in nematic lyotropic chromonic liquid crystal
The surface alignment of lyotropic chromonic liquid crystals (LCLCs) can be
not only planar (tangential) but also homeotropic, with self-assembled
aggregates perpendicular to the substrate, as demonstrated by mapping optical
retardation and by three-dimensional imaging of the director field. With time,
the homeotropic nematic undergoes a transition into a tangential state. The
anchoring transition is discontinuous and can be described by a double-well
anchoring potential with two minima corresponding to tangential and homeotropic
orientation.Comment: Accepted for publication in Phys. Rev. Lett. (Accepted Wednesday Jun
02, 2010
Colloidal particles at a nematic-isotropic interface: effects of confinement
When captured by a flat nematic-isotropic interface, colloidal particles can
be dragged by it. As a result spatially periodic structures may appear, with
the period depending on a particle mass, size, and interface
velocity~\cite{west.jl:2002}. If liquid crystal is sandwiched between two
substrates, the interface takes a wedge-like shape, accommodating the
interface-substrate contact angle and minimizing the director distortions on
its nematic side. Correspondingly, particles move along complex trajectories:
they are first captured by the interface and then `glide' towards its vertex
point. Our experiments quantify this scenario, and numerical minimization of
the Landau-de Gennes free energy allow for a qualitative description of the
interfacial structure and the drag force.Comment: 7 pages, 9 figure
The Cone Phase of Liquid Crystals: Triangular Lattice of Double-Tilt Cylinders
We predict the existence of a new defect-lattice phase near the nematic -
smectic-C (NC) transition. This tilt- analogue of the blue phase is a lattice
of double-tilt cylinders. We discuss the structure and stability of the cone
phase. We suggest that many `nematics' exhibiting short range layering and tilt
order may in fact be in the molten cone phase, which is a line liquid.Comment: 4 Pages, 3 Figure
Orientational transitions in a nematic confined by competing surfaces
The effect of confinement on the orientational structure of a nematic liquid
crystal model has been investigated by using a version of density-functional
theory (DFT). We have focused on the case of a nematic confined by opposing
flat surfaces, in slab geometry (slit pore), which favor planar molecular
alignment (parallel to the surface) and homeotropic alignment (perpendicular to
the surface), respectively. The spatial dependence of the tilt angle of the
director with respect to the surface normal has been studied, as well as the
tensorial order parameter describing the molecular order around the director.
For a pore of given width, we find that, for weak surface fields, the alignment
of the nematic director is perpendicular to the surface in a region next to the
surface favoring homeotropic alignment, and parallel along the rest of the
pore, with a interface separating these regions (S phase). For strong surface
fields, the director is distorted uniformly, the tilt angle exhibiting a linear
dependence with the distance normal to the surface (L phase). Our calculations
reveal the existence of a first-order transition between the two director
configurations, which is driven by changes in the surface field strength, and
also by changes in the pore width. In the latter case the transition occurs,
for a given surface field, between the S phase for narrow pores and the L phase
for wider pores. A link between the L-S transition and the anchoring transition
observed for the semi-infinite case is proposed. We also provide calculations
with a phenomenological approach that yields the same main result that DFT in
the scale length where this is valid.Comment: submitted to PR
Geometrically-controlled twist transitions in nematic cells
We study geometrically-controlled twist transitions of a nematic confined
between a sinusoidal grating and a flat substrate. In these cells the
transition to the twisted state is driven by surface effects. We have
identified the mechanisms responsible for the transition analytically and used
exact numerical calculations to study the range of surface parameters where the
twist instability occurs. Close to these values the cell operates under minimal
external fields or temperature variations
Casimir Torques between Anisotropic Boundaries in Nematic Liquid Crystals
Fluctuation-induced interactions between anisotropic objects immersed in a
nematic liquid crystal are shown to depend on the relative orientation of these
objects. The resulting long-range ``Casimir'' torques are explicitely
calculated for a simple geometry where elastic effects are absent. Our study
generalizes previous discussions restricted to the case of isotropic walls, and
leads to new proposals for experimental tests of Casimir forces and torques in
nematics.Comment: 4 pages, 1 figur
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