On the time evolution of the liquid meniscus at the end of a capillary placed in an external electric field

Using a linearized set of equations of electrodynamics, the stability of the uniformly charged meniscus of a viscous conducting incompressible liquid at the end of a capillary is investigated and analytical expressions are derived for the electric field outside the meniscus, velocity fields in the liquid flow and meniscus, and generatrix of the meniscus shape. It is found that, if an external electric field near the meniscus exceeds that at which the free liquid surface becomes unstable against the surface charge, a finite number of longest waves become unstable with their instability growth rates nonmonotonically depending on the wavenumber. Analysis of the time evolution of the meniscus shape under various initial conditions shows that cylindrical waves with the highest instability growth rates play a decisive role in this process, while the influence of the initial deformation amplitude is insignificant.     

Effect of a capillary meniscus on the Faraday instability threshold

Threshold for Faraday instability has been experimentally measured for slightly viscous liquids. Changing the size of the container containing the fluid allows us to emphasize the role played by the capillary meniscus on the onset for instability. As the container is getting smaller, an upset of the critical acceleration is observed. Below a given container diameter, eigenmodes are observed along the stability curve. A dissipation term is proposed for considering the viscous dissipation against the walls of the container.     

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)     

On capillary motion of a viscoelastic liquid with a charged free surface

The structure of the capillary-relaxation motion spectrum in a liquid with a charged free surface has been investigated taking into account the viscosity relaxation effect. On the basis of numerical analysis of the dispersion equation for the wave motion in a viscoelastic incompressible liquid, it is shown that for a given wave number the range of characteristic relaxation times in which relaxation-type wave motion exists is limited and expands with increasing wave number. The growth rate of instability of the charged liquid surface markedly depends on the characteristic relaxation time and increases with its growth; in liquids with elastic properties, the energy dissipation rate of capillary motion is enhanced. At a surface charge density that is supercritical for the onset of Tonks-Frenkel instability, both purely gravitational waves and waves of a relaxational nature exist.     

Decay of a turbulent cascade of capillary waves at the surface of liquid hydrogen

Free decay of a turbulent cascade of capillary waves was experimentally studied at the surface of liquid hydrogen after switching off harmonic pumping. It was found that the cascade starts to decay at the high-frequency side of the frequency spectrum and proceeds in the quasi-stationary regime. The characteristic relaxation time of the whole cascade proves to be close to the viscous-damping time of the wave, whose frequency coincides with the surface-excitation frequency.     

On the characteristic time for the realization of instability on a flat charged liquid surface

A nonlinear integral equation that describes the time evolution of the amplitude of a nonlinear unstable wave on the flat uniform charged surface of an ideal incompressible liquid has been derived and solved. The characteristic time for the realization of instability is found to be determined by the initial amplitude of a virtual wave initiating the instability and the supercritical increment in the Tonks-Frenkel parameter. At a zero supercritical increment, the characteristic time for the realization of instability is only determined by the initial amplitude and can be rather long (up to eight hours). This effect is characteristic of a flat charged liquid surface and does not occur in charged drops.     

On the instability of conical protrusions of liquid surface in electric field

Electric field is analyzed at the tip of the conical protrusion of a conductive liquid surface that forms as the field strength approaches certain threshold values. When the field exceeds the threshold, the cone tip generally becomes unstable and emits a slender jet. The field strength at the sharp tip of a conducting liquid cone tends to infinity. Even though the field has a singularity, the cone tip becomes unstable only if the semi-cone angle decreases below the Taylor angle, which is the same for all conducting liquids. It is shown that similar conical protrusions can form if the liquid is a dielectric and its permittivity is sufficiently high. In this case, the equilibrium cone angle depends on the permittivity. When the permittivity is lower than approximately 17.60, cones cannot form, and the ensuing phenomena do not occur.     

The capillary instability of the evaporation surface in soil

The stability of the evaporation surface of subsoil waters is investigated in the presence of capillary pressure, when a light liquid (a mixture of air and vapor) is above a heavy liquid (water). It is found that the instability arises in non-wettable and wettable soil with the capillary-pressure gradient.     

Parametric buildup of the instability of a charged flat liquid surface imposed on Kelvin-Helmholtz instability

The instability of capillary gravitational waves that is developed at the charged flat interface between media is studied for the case when the upper medium moves parallel to the interface with a velocity that has constant and time-dependent components. It is shown that the Mathieu-Hill equation, describing the temporal evolution of the capillary wave amplitudes in such a system, has unstable solutions at those values of physical parameters (electric field strength and wind velocity) meeting the conditions for Saint Elmo fire initiation in the atmosphere.     

Decay of capillary turbulence on the surface of a viscous liquid

Decay of the turbulence of capillary waves on the surface of a real liquid is studied in the presence of the viscous damping of the waves at all frequencies after stepwise removal of external pumping. The investigation is performed using two different models: the weak turbulence approximation and the local turbulence model in which the energy redistribution over frequencies is described by the polynomial expression in the wave-occupation number. It is shown that the decay of turbulence in the viscous liquid proceeds self-similarly and begins at high frequencies. In the decay process, the frequency distribution of the energy of waves is close to the stationary form E _ω ～ ω^?3/2 in a wide frequency range below the boundary frequency of the inertial range during a relatively long time after removal of the external force. The calculation results agree qualitatively with the results of the experiments on capillary turbulence on the charged surface of liquid hydrogen.     

Temperature dependence of surface tension and capillary waves at liquid metal surfaces

The temperature dependence of the surface tension γ(T) is treated theoretically and experimentally. The theoretical model based on the Gibbs thermodynamics of a one-component fluid relates ∂γ/∂T to the surface excess entropy density −ΔS. All specific surface effects, namely ordering, capillary waves, and double layer influence the surface entropy, which in turn governs the sign and the magnitude of ∂γ/∂T. Experimental data collected at a free Hg surface in the temperature range from 0°C to 30°C show that ∂γ/∂T is negative. Zh. éksp. Teor. Fiz. 114, 2034–2042 (December 1998) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

On dynamic excitation of Marangoni instability in a liquid layer with insoluble surfactant on the deformable surface

The European Physical Journal Special Topics - This paper is a continuation of our previous work presented at the IMA-6, see [1]. We continue to analyze the parametric excitation of Marangoni...     

On the interfacial capacitance of an electrolyte at a metallic electrode around zero surface charge

The behaviour of the capacitance of a planar double layer containing a restricted primitive model electrolyte (equi-sized rigid ions moving in a continuum dielectric) at and around zero surface charge is examined for a polarizable electrode with particular emphasis on a metallic surface. Capacitance results are reported for symmetric valency (1:1) salts encompassing a range of concentrations and temperatures covering both electrolyte solution and ionic liquid regimes. Although the modified Poisson–Boltzmann theory is principally employed, at higher concentrations the theoretical calculations have been supplemented by Monte Carlo simulations. Capacitance anomaly, that is, increase of capacitance with temperature at low temperatures, is seen to occur when the electrode is an insulator with a low dielectric constant or when it is unpolarized. No capacitance anomaly is, however, seen for a metallic electrode with an infinite dielectric constant and in this situation the capacitance increases (a) dramatically at low temperatures (strong coupling) at a given concentration, and (b) as concentration increases at a given temperature. These capacitance trends are consistent with earlier works in the presence or absence of surface polarization and, in particular, the results for a conducting electrode at ionic liquid concentrations are consistent with that recently reported by Loth et al. [Phys. Rev. E, 82, 056102 (2010)]. Overall the theoretical predictions are qualitative to semi-quantitative with the simulations.     

Mechanism of charge exchange at a liquid crystal-electrode interface

It is shown that liquid crystal-electrode charge exchange is accomplished via the mechanism of Schottky emission through a thin dielectric layer. The thin dielectric layer (several nanometers) is formed by adsorption of neutral molecules that either are introduced on purpose or occur in even well-purified liquid crystals. The main part of the barrier determining the charge exchange process is due to the ionization of the cation losing an electron and its transformation to the anion. The barrier parameters and the dielectric layer thickness are estimated for the planar and homeotropic alignments of molecules.     

Analog of Kelvin-Helmholtz instability on a free surface of a superfluid liquid

We analyze the analog of the Kelvin-Helmholtz instability on the free surface of a superfluid liquid. This instability is induced by the relative motion of superfluid and normal components of the same liquid along the surface. The instability threshold is found to be independent of the value of viscosity, but turns out to be lower than in the absence of dissipation. The result is similar to that obtained for the interface between two sliding super-fluids (with different mechanisms of dissipation) and confirmed by the first experimental observation of the Kelvin-Helmholtz instability on the interface between ³He-A and ³He-B by Blaauwgeers et al. (cond-mat/0111343).     

On the stability of capillary waves on the surface of a space-charged dielectric liquid jet moving in a material medium

We have derived and analyzed the dispersion equation for capillary waves with an arbitrary symmetry (with arbitrary azimuthal numbers) on the surface of a space-charged cylindrical jet of an ideal incompressible dielectric liquid moving relative to an ideal incompressible dielectric medium. It has been proved that the existence of a tangential jump of the velocity field on the jet surface leads to a periodic Kelvin–Helmholtz- type instability at the interface between the media and plays a destabilizing role. The wavenumber ranges of unstable waves and the instability increments depend on the squared velocity of the relative motion and increase with the velocity. With increasing volume charge density, the critical value of the velocity for the emergence of instability decreases. The reduction of the permittivity of the liquid in the jet or an increase in the permittivity of the medium narrows the regions of instability and leads to an increase in the increments. The wavenumber of the most unstable wave increases in accordance with a power law upon an increase in the volume charge density and velocity of the jet. The variations in the permittivities of the jet and the medium produce opposite effects on the wavenumber of the most unstable wave.     

Some observations on the appearance of instability of a plane charged liquid surface

A dispersion relation is obtained for the capillary oscillations of a hemispherical protrusion (oblate or prolate) on the plane surface of a conducting liquid in a uniform electrostatic field parallel to the symmetry axis of the protrusion. For the fundamental mode of the capillary oscillations realized on the protrusion the critical dependence of the parameter characterizing its stability in an external electrostatic field is obtained as a function of the square of the eccentricity as the protrusion is drawn out from the an oblate to a prolate hemisphere. Such a change in shape lowers the threshold electric field for instability of the protrusion. Zh. Tekh. Fiz. 69, 15–22 (July 1999)     

Polymer adsorption at a liquid surface

Expressions are obtained for the distribution of polymer chains at the surface transition zone of a simple solvent.     

On the topological charge concentrated at a point

For SU(2) gauge fields over the 4-dimensional sphere with a finite number of points x₁, x₂, ..., and x_N removed, there are gauge transformations which modify the topological charge concentrated at x_j by adding n_j, where n₁, n₂, …, and n_N. are integers such that Σ^N_{j = 1}n_j = 0. However, the reduction modulo Z of the topological charge at a point is well defined, being given in terms of the secondary characteristic classes of Chern and Simons, except when the topological charge is indeterminate.