Instability of a charged layer of a viscous liquid on the surface of a solid spherical core

The dispersion relation for the spectrum of capillary waves of a spherical layer of a viscous liquid coating a solid spherical core with a layer of finite thickness is introduced and analyzed. It is shown that the existence of two mechanisms for the viscous dissipation of the energy of the capillary-wave motions of the liquid, viz., damping in the bulk of the layer and on the solid core, leads to restriction of the spectrum of the realizable capillary waves of the liquid on both the high-and low-mode sides. At a fixed value of the system charge which is supercritical for the first several capillary modes, the maximum growth rates in the case of a small solid core are possessed by modes from the middle of the band of unstable modes, while in thin liquid layers the highest of the unstable modes have the largest growth rates. This points out differences in the realization of the instability of the charged surface of the spherical layer for small and large relative sizes of the solid core. Zh. Tekh. Fiz. 67, 8–13 (September 1997)     

Capillary oscillations of a thin film of viscous liquid on a solid substrate and its instability against surface charge

In a numerical analysis of the dispersion relation describing capillary motions in a thin film of a viscous, surface-charged liquid with fluctuation forces taken into account, it is found that the critical conditions of instability of the free surface of the liquid for a fixed thickness d of the liquid film in the region where the influence of the fluctuation forces is large (d<100 nm) depend strongly on the wave number and do not depend on the viscosity of the liquid, that the fluctuation forces strongly affect the wave number of the most unstable wavelength and decrease the instability growth rate, and that the capillary motions of the liquid admit an analogy with gravity-capillary motion and can be interpreted as fluctuation-capillary motions. Zh. Tekh. Fiz. 68, 27–31 (October 1998)     

Capillary oscillations of a flat charged surface of liquid with finite conductivity

A dispersion relation is proposed and analyzed for the spectrum of capillary motion at a charged flat liquid surface with allowance made for the finite rate of charge redistribution accompanying equalization of the potential as a result of the wave deformation of the free surface. It is shown that when the conductivity of the liquid is low, a highly charged surface becomes unstable as a result of an increase in the amplitude of the aperiodic chargerelaxation motion of the liquid and not of the wave motion, as is observed for highly conducting media. The finite rate of charge redistribution strongly influences the structure of the capillary motion spectrum of the liquid and the conditions for the establishment of instability of its charged surface when the characteristic charge relaxation time is comparable with the characteristic time for equalization of the wave deformations of the free surface of the liquid. Zh. Tekh. Fiz. 67, 34–41 (August 1997)     

Configuration of a chiral smectic-C film with a circular inclusion

It was shown experimentally (P.V. Dolganov et al., Europhys. Lett. 76, 250 (2006)) and by numerical calculations (C. Bohley, R. Stannarius, Eur. Phys. J. E 23, 25 (2007)) that the c -director profile of a two-dimensional chiral smectic-C (SmC) film around a circular inclusion adopts dipolar rather than quadrupolar configuration observed in achiral SmC films. We give an analytical argument on how spontaneous bend inherent in chiral SmC liquid crystals influences the configuration of a SmC liquid crystal film around a circular inclusion imposing tangential anchoring. We find how the angle α between two surface defects seen from the center of the inclusion depends on the radius of the inclusion R and the strength of the spontaneous bend q . We show, however, that the contribution of the spontaneous bend to the free energy suffers from mathematical ambiguity; it depends on the mathematical treatment of the outer boundary even when it is at infinity. This might indicate that the shape as well as the treatment of the outer boundary of the film can significantly influence the equilibrium configuration of the c -director and the position of the surface defects.     

Instability of the flat surface of a magnetic fluid in a cylindrical cavity in the presence of a vertical magnetic field

The problem of a magnetic liquid which completely fills a vertical cylindrical cavity in an undeformable horizontal layer of a magnet having the same magnetic properties as the liquid is considered. The entire system is immersed in a uniform vertical magnetic field. in a linear formulation of the problem an approximate solution in the form of series is obtained for the evolution of an initial small deviation of the free surface of the liquid from its flat equilibrium shape. An experiment is performed which shows that the initially flat free surface takes on a stable domed shape as the field strength is increased (from zero) and that a further increase in the field in a certain restricted range leads to the formation of an annular corrugation. The structures observed, which are the result of the nonlinear stage in the development of the initial perturbation, are qualitatively similar to the first two modes of the solution obtained. Zh. Tekh. Fiz. 68, 23–30 (January 1998)     

Exact solution of the problem of the equilibrium configuration of the charged surface of a liquid metal

A broad class of exact solutions is obtained for the problem of the equilibrium configuration of the charged surface of a conducting liquid allowing for capillary forces. An analysis of the solutions showed that when the amplitudes of the perturbations reached certain critical values, the region occupied by the liquid ceases to be singly connected, which corresponds to the formation of liquid metal droplets. It is shown that a steady-state liquid metal profile may exist for which appreciable local amplification of the electric field can be achieved. Zh. éksp. Teor. Fiz. 116, 1990–2005 (December 1999)     

Resonant oscillations of an elastic membrane on the bottom of a tank containing a heavy liquid

A study is made of the resonant oscillation modes in a three-dimensional channel filled by a heavy incompressible liquid, with a free surface at the top and an elastic membrane on the bottom. It is shown that for definite relations between the parameters of the channel and the inclusion there is a discrete spectrum, which extends only up to the waveguide cutoff frequency, in addition to the continuous spectrum of oscillation frequencies. The oscillation modes of the liquid have a localized character in the region of the inclusion. Zh. Tekh. Fiz. 69, 37–42 (August 1999)     

Capillary oscillations and Tonks-Frenkel instability of a liquid layer of finite thickness

A dispersion relation is derived and analyzed for the spectrum of capillary motion at a charged flat surface of viscous liquid covering a solid substrate with a layer of finite thickness. It is shown that for waves whose wavelengths are comparable with the layer thickness, viscous damping at the solid bottom begins to play an important role. The spectrum of capillary liquid motion established in this system has high and low wave number limits. The damping rates of the capillary liquid motion with wave lengths comparable with the layer thickness are increased considerably and the Tonks-Frenkel instability growth rates are reduced compared with those for a liquid of infinite depth. Zh. Tekh. Fiz. 67, 27–33 (August 1997)     

Instability of a charged interface of two immiscible viscous liquids with charge relaxation taken into account

On the basis of an analysis of a derived dispersion relation, it is demonstrated that there can be two different types of instability relative to the free charge of a charged, planar interface between two viscous immiscible liquids with finite electrical conductivity in a gravitational field. For large values of the surface charge density, depending on the viscosities and ratio of conductivities of the media, one can observe either an aperiodic (of the Tonks-Frenkel type) or oscillatory instability of the interface. Increasing the viscosity of the lower liquid leads to a substantial drop in the increments of the mentioned instability types and alters the critical conditions for manifestation of the oscillatory instability, whereas varying the viscosity of the upper surface has only a very weak effect on these characteristics. Zh. Tekh. Fiz. 68, 13–19 (September 1998)     

Choice of conditions of an electrical discharge for generating chemically active particles for the decomposition of impurities in water

An electrical discharge between a liquid surface and an electrode positioned above it is considered. A second electrode, which delivers the output from a high-voltage source, is located at the bottom of the vessel containing the liquid. The conditions that must be met by the electrical discharge in order to efficiently initiate reactions in the liquid phase are analyzed. Under these conditions the number of active particles generated by the discharge turns out to depend on the concentration in the liquid of the substance with which the active particles interact. It is shown that for a corona or spark discharge the reactions can occur in a liquid layer 10–20 mm thick and that for specific reactions there exists an optimum value of the electric field at which the energy expenditures on the initiation of the reaction will be minimum. Zh. Tekh. Fiz. 69, 58–63 (January 1999)     

Long-wavelength structure on a charged liquid surface

The problem of the equilibrium form of a charged surface of a dielectric liquid in a strong electric field, such that a flat surface becomes unstable, is studied. A periodic long-wavelength structure with a small amplitude can arise when the gap between the surface and a charged electrode is small compared with the capillary length and the charge completely screens the electric field. The equilibrium form of the surface is calculated assuming that the resulting wave is one-dimensional. The effect of the boundary conditions at the vessel walls on the dependence of the amplitude of the standing wave on the applied voltage is estimated. It is shown that this dependence is very sensitive to the conditions of contact between the vessel walls and the liquid. The possibility is discussed of using the theory developed in this paper to explain the experimental results obtained with a charged liquid-hydrogen surface. Zh. éksp. Teor. Fiz. 115, 43–49 (January 1999)     

Aharonov-Bohm effect for electrons on a liquid-helium surface

A method for obtaining finite electronic systems on a liquid-helium surface is proposed. If a thin film of liquid helium lies above a bottom capacitor plate made in the form of metal rings connected with one another, then electrons will accumulate in potential troughs near these rings. The purity of the helium surface, i.e., the absence of impurities and pinning centers on it, affords an excellent opportunity for investigating the Aharonov-Bohm effect in an ideal ring of a Wigner crystal and a Luttinger liquid Pis’ma Zh. éksp. Teor. Fiz. 67, No. 6, 410–414 (25 March 1998)     

Statistical inversion from reflections of spherical waves by a randomly layered medium

Abstract

We show that the asymptotic theory developed for the analysis of reflected wave pulses from randomly layered media can be used to solve statistical inverse problems. In particular, we recover the large scale behavior of medium properties from a single realization of reflected wave pulses observed at different points on the surface.     

Resonance states of the continuous spectrum of a bounded crystal near the critical points of volume bands

The conditions for the existence of resonance electronic states near the critical points of volume bands are obtained. It is shown that resonances of this type are qualitatively different from surface resonances associated with states induced by an image potential. The manifestation of such “volume” resonances in the scattering of very slow electrons by a TiS₂ surface is studied. Fiz. Tverd. Tela (St. Petersburg) 40, 2003–2007 (November 1998)     

Stability of a bubble in a dielectric liquid in an external electrostatic field

Critical instability conditions are found for a gas bubble in a liquid dielectric in a uniform external electrostatic field E ₀. It is shown that they depend both on the magnitude of E ₀ and on the properties of the liquid, as well as on the gas pressure in the bubble. In a linear approximation with respect to the square of the eccentricity of an equilibrium spheroidal form, the equilibrium eccentricity of the bubble exceeds the equilibrium eccentricity of a drop in the field E ₀. The gas pressure in the bubble lowers the critical electric field E ₀ for development of an instability in the bubble. Zh. Tekh. Fiz. 69, 43–48 (August 1999)     

Characteristics of the capillary motions of surfactant solutions with a charged free surface

Abastract A dispersion relation is derived and analyzed for the spectrum of capillary motions on the charged plane surface of a liquid in which a surfactant is dissolved. It is shown that two additional wave motions are generated in this kind of system by bulk diffusion and surface diffusion of the surfactant and are sensitive to the diffusion coefficients and elastic properties of the surfactant films and to the viscosity of the solution and the presence of a surface charge. In solutions of inactive surfactants the growth rate of Tonks-Frenkel instability increases as the surfactant concentration increases. Zh. Tekh. Fiz. 68, 22–29 (February 1998)     

Prediction of the solid–liquid–liquid equilibria of linear and branched semi-crystalline poly-ethylene in solutions of diphenyl ether by Lattice Cluster Theory

ABSTRACT

Recently, Lattice Cluster Theory has been applied to predict liquid–liquid equilibria and solid–liquid equilibria of low and high molecular weight mixtures taking into account the molecular architecture and the nature of crystallinity of the respective component. Herein, an LCT-based theory is applied to calculate solid–liquid–liquid equilibrium of a polyethylene + diphenyl ether system, depending on branching and degree of crystallinity of the polymeric component. Understanding the role that branching number, branching type and degree of polymer crystallinity play in the behaviour of triple and triple critical points is focused on. Insight is given here into constitution and properties of triple and triple critical points in binary polymer solvent systems depending on the molecular architecture of both components, polymer and solvent respectively, and the semi-crystalline nature of the polymer.     

Capillary oscillations of a charged viscous spheroidal droplet

Dispersion relations are derived for the capillary oscillations of a charged viscous spheroidal droplet by scalarization within perturbation theory using an expansion in two small parameters, viz., the magnitude of the perturbation of the spheroidal surface as a result of thermal fluctuations and the magnitude of the deviation of the equilibrium spheroidal droplet shape from a spherical shape. It is shown analytically that the motion spectrum of the liquid consists of two components that interact in the linear theory: toroidal vortex motion and poloidal potential motions. A numerical analysis reveals that the instability growth rates of the higher modes of a highly charged droplet increase with enhancement of the degree of spheroidal strain and decrease rapidly as the viscosity of the liquid increases. Zh. Tekh. Fiz. 68, 20–27 (April 1998)     

Dynamics of reorientation of a constrained nematic elastomer

A model is proposed for the reorientation dynamics of a confined nematic liquid crystal elastomer, where the effect of crosslinks is to couple the director to deformations of the elastic matrix. The model combines the (equilibrium) `neo-classical' theory of liquid crystal rubber elasticity with the simplest time evolution equations for a system described by two coupled, non-conserved order parameters. Relaxation from an orientation imposed by an electric field is studied as a function of elastic softness, starting angle, surface pretilt, and the relative mobilities of director and strain. Most importantly, the absence of a `semi-soft' elastic threshold changes the long-time behaviour of the effective refractive index of the medium from exponential to inverse power law decay. Predictions are compatible with recent experimental results by Chang, Chien and Meyer [Phys. Rev. E 56, 595 (1997)]. Received 22 June 1998