Axisymmetric solutions for the equations of motion of a dielectric liquid with a free charged surface

Evolution of a boundary of the ideal dielectric liquid with a free charged surface is described in the limiting case of large surface curvature. Particular axisymmetric solutions of the equations of motion are obtained, which describe a paraboloidal boundary drawn inward the liquid at a constant velocity.     

Autooscillation instability of the free surface of a viscoelastic medium

Oscillation instability of a layer of viscoelastic liquid is revealed on the basis of the numerical analysis of the dispersion equation. The instability is observed in the case of time-independent uniform external force action on the free surface of the liquid and may lead to the formation of a regular wavelike relief of a finite amplitude.     

Large-scale magnetohydrodynamic instability of a conducting liquid surface

The stability of a current-carrying rectangular liquid metal conductor with respect to small longitudinal surface perturbations was theoretically studied. It is shown that the instability increment tends to zero in both short-and longwave limits and, hence, passes through a maximum at a finite wavenumber. The characteristic times of instability development are estimated.     

Dissolution of a hot body in contact with a free liquid surface

The effect of capillary forces on the dissolution of a hot body in contact with a free liquid surface is examined.     

Hydrodynamics of classical and quantum liquid with free surface

Nonlinear effects of the interaction of the second sound with surface waves in superfluid He are studied. It is shown that the standing surface waves, excited by the second sound on the surface of superfluid He, are stationary.     

On the free convection boundary layer on a vertical plate with prescribed surface heat flux

The free convection boundary layer on a vertical plate with a prescribed surface heat flux proportional to (1 +x ²)^µ (µ a constant) is discussed. For µ > –12 the boundary-layer solution develops from a similarity solution valid forx small to the one valid forx large. However, with µ –12 the similarity equations forx large are not solvable and the behaviour for largex in this case is discussed. It is found that there are two cases to consider, namely µ < –12 and µ = –12. In both cases the leading-order problem is homogeneous involving an arbitrary constant which is determined from an integral property of the full boundary-layer problem. However, in the former case the asymptotic behaviour is algebraic, with the perturbation to the leading-order solution, arising from the heat flux boundary condition, being ofO[x ^1+2µ]. The latter case also involves logarithmic terms, with the perturbation to be leading-order solution now being ofO[(logx)^–1].     

Nonlinear dispersion relation for electrocapillary waves on the surface of a dielectric liquid

It is shown that the problem of determining the profile of an electrocapillary wave on the surface of the ideal dielectric liquid in a tangential electric field admits exact solution in the limiting case of a large permittivity of the liquid. An exact expression for the nonlinear dispersion relation between the frequency, wavenumber, and amplitude of the wave is obtained and analyzed.     

Effect of the dielectric layer with photo-controllable surface relief on liquid crystal devices

We present experimental results for the dielectric layer effect on the electro-optical properties of liquid crystal (LC) devices together with numerical simulations. The photo-controllable polymer is used as a dielectric material on which the alignment agent of the LC is prepared. The surface relief structure can be induced on the dielectric polymer layer by photo-irradiation for fabricating LC microlens arrays or wide-viewing LC displays. It is found that the operation voltage of the LC device decreases with increasing the dielectric constant or with decreasing the layer thickness of the polymer. The experimental data agree well with theoretical results predicted from a simple dielectric model in the continuum theory.     

Nondispersive propagation of waves with finite amplitudes on the surface of a dielectric liquid in a tangential electric field

The evolution of waves with finite amplitudes on the free surface of the ideal dielectric liquid in a strong tangential electric field is considered. It is shown that, in the case of a large permittivity of the liquid, nonlinear waves of arbitrary configuration can propagate in this system without distortions.     

Reflection of piezothermoelastic waves from the charge and stress free boundary of a transversely isotropic half space

The present paper concentrates on the study of propagation and reflection characteristics of waves from the stress free, thermally insulated/isothermal boundary of a piezothermoelastic half space. The non-classical (generalized) theories of linear piezo-thermoelasticity have been employed to investigate the problem. In the two-dimensional model of the transversely isotropic piezothermoelastic medium, there are three types of plane waves quasi-longitudinal (QL), quasi-transverse (QT) and thermal wave (T-mode), whose velocities depend on the angle of incidence and frequency. These waves are dispersive in character and are also affected by piezoelectric as well as pyroelectric properties of the materials. The low and high frequency approximations for the speeds of propagation and the attenuation coefficients of these waves have been obtained. The quasi-longitudinal (QL), quasi-transverse (QT) and thermal wave (T-mode) incident cases at the stress free, thermally insulated or isothermal open circuit boundary of a transversely isotropic piezothermoelastic half space are considered to discuss the reflection characteristics of various waves. The amplitude ratios of reflected waves to that of incident one in each case have been obtained. The special cases of normal and grazing incidence are also derived and discussed. Finally, the numerical computations of reflection coefficients are carried out for cadmium Selenide (CdSe) material by using Gauss elimination procedure. In addition the phase velocities and attenuation coefficients are also computed along various directions of wave propagation. The obtained results in each case are presented graphically.     

Criteria of rigid instability on a flat surface of dielectric fluid in external electric field

Subcritical behavior of a free surface of the ideal dielectric liquid in an external electric field has been theoretically studied. A system of amplitude equations is obtained, which describe nonlinear interaction of three standing waves forming a hexagonal structure. Within the framework of a model described by these equations, a sufficient integral criteria are formulated for the rigid instability excitation on the flat surface of the liquid medium.     

Interaction of relaxational waves with waves of a redistributing surfactant on a free surface of a liquid

Thermal capillary wave motion on a charged free surface of a liquid covered with a surfactant film gives rise to waves of redistributing charge (equalizing the electrical potential) and waves of the surfactant (equalizing the concentration of the surfactant). Numerical analysis of the dispersion equation shows that in some range of physical parameters the waves of charge interact with the waves of surfactant, forming two new branches of charge-concentration waves. Pis’ma Zh. Tekh. Fiz. 23, 25–31 (September 26, 1997)     

Festoon instability of a drop of volatile insoluble liquid on the surface of other liquid under evaporation cooling conditions

A festoon structure having the form of round hills has been observed at the periphery of a drop of o-oxylene or isooctane lying on the surface of a layer of hot water. On reaching a diameter of about 1 mm, festoons are ejected toward the drop center at a velocity of 1–2 mm/s. The growth of festoons is caused by thermocapillary flows, while their ejection is related to the capillary forces, which tend to decrease the free surface. This kind of stability substantially differs from the other known thermocapillary instabilities, since the ejection of festoons prevents the drop from spreading and thus prolongs its life.     

Density and capacitance profiles and edge effects in a two-dimensional charge layer on a dielectric surface

The density and capacitance profiles and edge effects in a two-dimensional (2D) layer of electrons held on a liquid helium surface between two horizontal plates of a parallel-plate capacitor are studied by solving Laplace's equation on a computer. An effective length for experimental cells is defined to take into account nonuniform charge density and capacitance near the edges of the cells. The profiles and edge effects are studied as a function of charge density on the helium surface, helium depth inside the cell, repelling voltages on guard electrodes around the capacitor plates, and the frequency of excitation. The results should be useful in designing cells for experiments and better analyzing the results of measurements.     

Nonlinear oscillations of the free surface of a charged drop of a highly viscous liquid

An analytical expression for the shape of a charged drop of a highly viscous, incompressible conducting liquid performing nonlinear axisymmetric oscillations upon a small multimode initial deformation have been obtained by direct expansion within the second order of smallness. Using the obtained expression, it is possible to study the temporal evolution of the shape of initially deformed viscous drops bearing charges that are both sub-and supercritical from the standpoint of the Rayleigh criterion of stability.     

Withdrawal of fluid through a line sink beneath a free surface above a sloping boundary

A series truncation method is used to compute the flow into a line sink from a region of fluid with a free surface and a sloping wall beneath the sink. The method admits a well-known exact solution for a particular value of the slope. Solutions with a cusp above the sink, and with a stagnation point above the sink are computed for all values of the slope, and compared with results at both ends of the range, i.e. with results for both a vertical wall and a horizontal bottom, with good agreement.     

Stability of the boundary layer of liquid under a nonuniform temperature distribution of the surface

We study the effect of a longitudinal gradient of the surface temperature on the stability of the boundary layer of an incompressible liquid. A comparison shows a good agreement of the results with experimental data.     

Influence of gas compressibility on the critical conditions for instability in the electrostatic field of a bubble in a dielectric liquid

It is shown that unlike the case of a liquid droplet, the critical strength of a uniform electrostatic field required for instability of a gas bubble in a liquid dielectric decreases as the compressibility of the gas in the bubble increases. Pis’ma Zh. Tekh. Fiz. 24, 49–54 (November 12, 1998)     

A nonlinear dispersion relationship for electrocapillary waves on the charged surface of a dielectric liquid

It is shown that the problem of describing a profile of a progressive electrocapillary wave on the boundary of a dielectric liquid, with a free surface charge completely screening the electric field above the liquid, admits an analytical solution. An exact expression for the nonlinear dispersion relationship between the frequency, wavenumber, and amplitude of such a wave is derived and analyzed.     

Nonlinear dynamics of the free surface of a conducting liquid in an electric field

The nonlinear dynamics of the free surface of an ideal conducting liquid in an external electric field is investigated. It is found that in the absence of gravity and surface tension the equations of the two-dimensional motion of the medium can be solved in the approximation of small angles of inclination of the surface. It is shown that singularities of the square-root type, for which the curvature is infinite but the surface itself remains smooth, can form on the surface of a conducting liquid over a finite time. Pis’ma Zh. Tekh. Fiz. 24, 25–29 (June 26, 1998)