Electrohydrodynamic Convection Research Articles

Phase Wave in a Cellular Structure

Phase waves and their stability in a cellular pattern is discussed from a viewpoint of experimentalists. When the cellular pattern exhibits oscillatory instability, rich phenomena can be observed. The prototype experimental system is the electrohydrodynamic convection of a nematic liquid crystal in which a two-dimensional cellular pattern of convection exhibits limit cycle oscillation. We observe localized target pattern of wave fronts emitted from a self-organized center. The localized structure has a life cycle: it arises from a uniform state, grows and collapses by nucleating defects at its center. They are created by a phase instability through the coupling between the oscillatory mode and the underlying cellular pattern. We experimentally determine coupled complex Ginzburg-Landau equations as well as phase equations derived from them, and we confirm that the equations quantitatively describe the instability. We also discussed mechanism and process of collapse of target which are closely related to a turbulent nature of defects in the cellular pattern.

Use of an electric field to alter membrane morphology in a polysulfone-polyvinylpyrrolidone blend

An inherent characteristic of many polymer-based systems used in membrane manufacture is the tendency to form numerous defects such as macrovoids and pinholes. Such defects are manifested as large scale surface pores. In this research note we discuss the potential use of electric fields to influence the mechanisms by which these defects are formed during the precipitation step in the wet-cast phase-inversion process for polymeric membrane formation. Several electrical field phenomena including surface-induced-polarization, electrohydrodynamic convection, and enhanced transport can potentially be used to alter polymeric membrane morphology if the time scale for these electric field effects is short enough. We report preliminary experimental results corresponding to the formation of tubular membranes from a polysulfone-polyvinylpyrrolidone blend in a N,N-dimethylacetamide solution precipitated in water under the influence of an a.c. electric field. This study suggests that the electric field effects can be operative on the short time scale of membrane formation. Based upon the statistically significant differences in the frequency distribution of defect number versus defect area which were obtained, the results indicate that the presence of a 2.2 kV/cm a.c. electric field decreases the average number density of defects while increasing the total defect area. These results suggest that further experiments with more sophisticated equipment would permit the electric field effects to be optimized in order to reduce the number and the size of the surface defects.

Coupled phase instability of a cellular pattern.

We have observed a localised structure and the spontaneous nucleation of topological defects in an experiment on electrohydrodynamic convection. They are created by a phase instability via the coupling between the oscillatory mode and the underlying cellular pattern. By measuring the coefficients of the phase equations derived from coupled complex Ginsburg-Landau equations, we have confirmed that the equations quantitatively describe the instability

Transient bimodality in turbulence-1-turbulence-2 transition in electrohydrodynamic convection in nematic liquid crystals.

In electrohydrodynamic convection, the turbulence-1--turbulence-2 (T1--T2) transition is observed when the applied voltage is very high. The transient property at the T1--T2 transition is studied through the evolution of the probability distribution of the area of T2. At a voltage close to the T1--T2 threshold the distribution transiently shows double peaks, i.e., a transient bimodality.

Symmetry-breaking Hopf bifurcation in anisotropic systems

Symmetry-breaking Hopf bifurcation from a spatially uniform steady state of a spatially extended anisotropic system is considered. This work is motivated by the experimental observation of a Hopf bifurcation to oblique traveling rolls in electrohydrodynamic convection in planarly aligned nematic liquid crystals. Symmetry forces four traveling rolls to lose stability simultaneously. Four coupled complex ordinary differential equations describing the nonlinear interaction of the traveling rolls are analyzed using methods of equivariant bifurcation theory. Six branches of periodic solutions always bifurcate from the trivial state at the Hopf bifurcation. These correspond to traveling and standing wave patterns. In an open region of coefficient space there is a primary bifurcation to a quasiperiodic standing wave solution. The Hopf bifurcation can also lead directly to an aperiodic attractor in the form of an asymptotically stable, structurally stable heteroclinic cycle. The theory is applied to a model for the transition from normal to oblique traveling rolls.

Mean flow effects in the electro-hydrodynamic convection in nematic liquid crystals

On the basis of the weakly nonlinear analysis a set of two coupled amplitude equations is derived, which lead to a better understanding of the electro-hydrodynamic instability in nematic liquid crystals near onset. It is shown that the normal convective patterns are very sensitive against large scale flow (mean flow) modes, which are systematically included. Simulation of the equations shows typically a complex spatio-temporal behavior (“defect turbulence”) very similar to the situation often observed in experiments.

Control of gas permeation via electrohydrodynamic convection in a liquid crystal membrane

We demonstrate a sandwich-like membrane configuration, termed an electroconvective liquid crystal membrane (ECLCM), in which the electric field induced convection of a liquid crystal layer facilitates the transport of gases through the membrane. The permeation rate of CH 4 and N 2 through a N-(4-methoxybenzylidene)-4-butylaniline (MBBA) liquid crystal membrane was increased by a factor of 7 when an alternating electric field of 100 V/mm was applied to the liquid crystal. The permeability of the liquid crystal layer increased by a factor of 50 under the same conditions. The gas permeation rate increase was limited by the porous electrodes confining the liquid crystal. The CH 4/N 2 selectivity of the membrane, about 3, was determined by the solubility of these gases in the liquid crystal and by the electrode permeability.

The electrohydrodynamic instability in homeotropic nematic layers

We calculate the threshold for electrohydrodynamic convection in homeotropically oriented nematic layers with negative dielectric anisotropy that setsin after the bend-Freedericksz transition to a quasi-planar alignment has taken place. Oblique rolls are found in a larger range than in the case of planar anchoring. The most interesting prediction is that in the weakly nonlinear analysis all roll solutions are in fact unstable so that a direct transition to spatio-temporal chaos becomes possible. In the oblique-roll case this may be accompanied by a permanent local rotation of the director bend axis. Application of a planar magnetic field should stabilize the rolls

Complex dynamics of a localized target pattern in electrohydrodynamic convection.

A two-dimensional cellular pattern (lattice) created by electrohydrodynamic convection of a nematic liquid crystal exhibits limit cycle oscillations. We found a localized target pattern of wave fronts emitted from a self-organized oscillating center. The localized structure has a life cycle: it arises from a uniform state, grows, and collapses from nucleating defects at its center. This phenomenon is caused by an interaction between the waves and deformations of the underlying lattice, and is different from that in localized traveling waves.

Localized Oscillation in a Cellular Pattern

We study a coupled system of lattice oscillation and lattice deformation numerically and theoreti­ cally. A localized solution is found as an exact solution and it is stable in a certain parameter region. Recently N asuno, Sano and Sawada found a target pattern in an experiment of nematic liquid crystal. I ) In their experiment of liquid crystal two dimensional celiu­ lar pattern (lattice or grid pattern) is formed by the electro-hydrodynamic convection and the cellular structure exhibits a limit cycle oscillation above a certain critical voltage. Sano et al. investigated further the system and found that the targetlike waves propagate only in a localized region and the grid pattern is deformed in the propagating region of phase waves. Z ) In a previous paper we studied a coupled system of lattice oscillation and lattice deformation and found that a targetlike pattern can be generated by a kind of phase instability of the coupled equation. 3 ) In this paper we show that the same equation has a stable localized solution when the coupling is relatively strong. We first show a result of numerical simulations and then we show that the localized solution can be expressed as an exact solution. The model equation we study was obtained by Coullet and Iooss as an amplitude equation for the Hopf bifurcation in the cellular pattern. 4 ) It is written as

Propagating Structures in a Nematic Liquid Crystal Subjected to Crossed Electric and Magnetic Fields

Abstract The effect of a stabilizing magnetic field applied perpendicular to the electric field on the nematic liquid crystal MBBA undergoing electrohydrodynamic convection is studied on 60 micron thick samples. The resulting convective instability is found to propagate with a voltage dependent velocity that is well described by a power law with an exponent of ½. The pattern velocity at the onset of the instablity also decreases with increasing magnetic field. The wavelength of the instability similarly decreases with increasing electric and magnetic field strength.

Pattern Formation in Electrohydrodynamic Convection

One hundred years after their discovery, we meet liquid crystals everywhere in our daily life. Their most widely known application is the liquid crystal displays (LCDs) in watches, pocket calculators, or gasoline pumps. Applications aside, liquid crystals show many exciting properties, making them highly interesting for fundamental research. For example, electrohydrodynamic convection (EHC) in nematic liquid crystals, which is studied in cells of a configuration similar to liquid crystal displays, serves with its characteristic properties as a model System for investigating central questions of pattern formation and chaos.Today's liquid crystal displays work on the principle described in 1971 by Martin Schadt and Wolfgang Helfrich (Figure 1). In nematic liquid crystals, organic molecules orient on average along a macroscopic direction, described by the director field n(r), that has neither head nor tail (n = −n). Nematics are therefore anisotropic and for energetic reasons, n(r) orients parallel (perpendicular) to an electric field when the dielectric permittivity (ε∥) along n is larger (smaller) than the perpendicular (ε⊦ one. For positive εa = ε∥ − ε⊦, when an electric field is applied perpendicular to the direction of n, a reorientation of n takes place together with a corresponding change in the optical property of the cell. The controlled change by an electric field in the optic axis (orientation) in well-defined areas of the display then allows the representation of numbers, etc.

Experimental studies of defect dynamics and interaction in electrohydrodynamic convection.

A report about experimental studies of the dynamics and interaction of topological defects in the roll structure of electrohydrodynamic convection in nematic liquid crystals is given. It is found that the motion of defects of opposite topological charges towards annihilation has two stages. At large distances they move with a constant velocity that depends mainly linearly on the wave-number mismatch. At a later stage, when the defects come closer, they are accelerated due to attraction. In order to compare these results quantitatively with available theories that are based on the Ginzburg-Landau equation, all coefficients of this equation are measured.

Four-wave resonance in electrohydrodynamic convection.

Four-wave resonance in electrohydrodynamic convection.

A Model for Defect Chaos in Electrohydrodynamic Convection of Nematic Liquid Crystals

A Model for Defect Chaos in Electrohydrodynamic Convection of Nematic Liquid Crystals

Local transition to turbulence in electrohydrodynamic convection.

On the route to turbulence in electrohydrodynamic convection of nematic liquid crystals, the last bifurcation is spatially inhomogeneous via nucleation. Such a transition occurs between two different turbulent states (DSM1 and DSM2). We find good agreement between the nucleation rate of DSM2 nuclei and an expression from conventional nucleation theory. The motion of the DSM1-DSM2 interface behaves similar to propagating fronts in other nonequilibrium systems. Disclinations in the director field are created during the transition, similar to the vortex filaments in the TI-TII transition in superfluid He II.

Spontaneous Nucleation of Turbulence in Electrohydrodynamics and Its Similarity with Crystal Growth

The nucleation and the growth process of turbulent areas in the electrohydrodynamic convection in nematic liquid crystals is investigated. During the transition from one turbulent state (DSM1) to another (DSM2), this fully dissipative system shows, on the qualitative level, a great similarity to classical nucleation phenomena. We found good agreement between the experimentally observed nucleation rates and those from classical nucleation theory. The main difference between the two turbulent states is the density of disclinations in the director field.

Motion and interaction of dislocations in electrohydrodynamic convection of nematic liquid crystals.

Two typical motions of dislocations, climb and glide, and their mutual interactions are studied experimentally in a layered pattern of electrohydrodynamical convective rolls of nematic liquid crystals under well controlled initial conditions. It was found that two kinds of forces acted on the dislocations with opposite Burgers vectors. The first kind is a pattern-selection force under which the dislocation moves at constant velocity. The second kind is an attractive interaction force. When dislocations are approaching each other, the effective length of the latter is of short range, typically of the order of the wavelength of the pattern.

Phase Wave Propagation in the Rectangular Convective Structure of Nematic Liquid Crtstal

Macroscopic circular and spiral phase wave propagation was observed for the first time in the rectangular pattern of electrohydrodynamic convection of nematic liquid crystal. The centers of the phase wave propagation were, in general, neither defects of the rectangular structure nor external heterogeneities. The power spectrum of the transmitted light locally measured exhibited two peaks, one a corresponding phase wave mode and the other an unentrained mode. The frequency of the phase wave mode was lower than that of the other mode.

The shadowgraph method in convection experiments

The shadowgraph method is applied to thermal convection experiments and electro-hydrodynamic convection (EHC) in nematic liquid crystals. In both cases convection leads to a spatially periodic field of the refractive index causing a spatially periodic intensity modulation of parallel light passing the cell. Close to the onset of convection the temperature or director field is given by linear stability analysis. Knowing these functions the determination of their amplitudes becomes possible by means of the shadowgraph method. The method is demostrated using various examples of thermal and EHC convection experiments.