On the possibility of corona initiation at the surface of a liquid layer nonlinearly oscillating on the surface of a charged hailstone placed in a uniform electrostatic field

An expression for the electric field strength near a watered hailstone is derived in an approximation quadratic in the amplitude of capillary oscillations of a charged conducting liquid layer covering the hailstone. As the number of the mode governing the initial deformation of the equilibrium spherical free surface of the liquid layer increases and its thickness decreases, the electric field strength in the neighborhood of the capillary wave crests rises. Even in the case of small charges and low electric fields, the electric field near the hailstone is high enough to initiate a corona.     

On the initiation of a corona discharge near the surface of a nonlinearly oscillating liquid layer on the surface of a charged hailstone

An expression is derived for the electric field strength near a wet hailstone in an approximation quadratic in the oscillation amplitude of a charged liquid layer on its surface. It is found that the electric field strength in a small neighborhood of the capillary wave crests grows with the number of a mode governing the initial deformation of the equilibrium (spherical) shape of the liquid layer. Even if the charge is small (when the Rayleigh parameter of the hailstone equals one-hundredth of the value critical for stability against the self-charge), the electric field near the hailstone is high enough for initiating a corona discharge in its vicinity.     

Structure-mechanical approach to surface tension of solids

Some problems of applying the Lippmann equation to adsorption studies on solid electrodes are shortly reviewed. A novel nonthermodynamic approach to consider the role of elastic and plastic deformation of electrode surfaces during adsorption is proposed. The extremely thin electrode surface layers affected electrically and mechanically by adsorbate are supposed to be free of dislocations because of volume discrepancy. The nearest structure-mechanical analogs of such layers are the whisker crystals whose side surface could have one- and two-dimensional defects, but have no active dislocations. Like whiskers, surface metal layers should possess a high ultimate strength close to the theoretical one and a purely elastic deformation. Affected only by adsorbate, the surface electrode layer should be considered as absolutely elastic body, whose plastic deformation is impossible, i.e. the Lippmann equation and other equations containing terms of plastic deformation cannot be used in thermodynamics of the solid metal surface.     

Nonlinear resonance interaction between the oscillation modes of a spherical liquid layer on the surface of a melting hailstone

Evolutionary equations are derived and solved that describe the time dependence of the oscillation mode amplitudes on the surface of a charged conducting liquid layer resting on a solid core. It is assumed that the layer experiences a multimode initial deformation. The equations are solved asymptotically in the second order of smallness in the small dimensionless amplitude of capillary oscillations on the surface of the layer. Mechanisms behind internal nonlinear resonance interaction between the modes of the liquid layer oscillations and behind energy transfer between the modes both in degenerate and in secondary combination resonances are investigated. It is found that in the degenerate resonance interaction between oscillation modes, the energy may be transferred not only from lower to higher modes but also vice versa if the higher mode is excited at the zero time. This conclusion is valid not only for a liquid layer on the surface of a solid core but also for a drop.     

On granular surface flow equations

Conservation equations are written for surface flows (either fluid or granular). The particularity of granular surface flows is then pointed out, namely that the depth of the flowing layer is not a priori fixed, leading to open equations. It is shown how some hypothesis on the flowing layer allows to close the system of equations. A possible hypothesis, similar to that made for a fluid layer, but inspired from granular flow experiments, is presented. The force acting on the flowing layer is discussed. Averaging over the flowing depth, as in shallow water theory, then allows to transform these conservation laws into equations for the evolution of the profile of a granular pile. Apart from their interest for building models, these conservation laws can be used to measure experimentally the effective forces acting on a flowing layer. Received 25 July 1998 and Received in final form 14 January 1999     

Instability development on the charged free surface of a horizontal liquid layer with thermal convection

The instability of the charged free surface of a horizontal liquid layer heated from the solid bottom against excess electric charge is studied theoretically for the case in which this type of instability is combined with thermal-convective instability. The structure of the total spectrum of unstable wave flows and physical parameters influencing the structure of the spectrum are determined.     

电弧增材成形中熔积层表面形貌对电弧形态影响的仿真

电弧增材成形常采用单道多层或多道搭接的熔积方式,不同的熔积方式下对应的熔积层表面形貌不同,从而影响电弧的形态及其传热传质过程.本文建立了纯氩保护电弧增材成形的电弧磁流体动力学三维数值模型,以及不同表面形貌的熔积层模型,并在保持阳极与阴极之间距离和熔积电流不变的条件下,通过模拟计算获得增材成形特有的单道和多道搭接熔积条件下的不同表面形貌对应的电弧形态以及相应的温度场、流场、电流密度、电磁力、电弧压力分布.数值模拟结果表明:平面基板上起弧情况下电弧中心具有较高的温度、速度、电流密度以及压强;单道多层熔积情况下熔积层数对电弧的各个参量影响较小;多道搭接熔积情况下电弧呈非对称分布,电弧中心温度较前两者低,电流密度、电磁力和电弧压强的分布偏向熔积层一侧.     

Model of discontinuity surface in continuum physics

In this paper we adopt the division of the discontinuity surfaces into autonomous, nonautonomous and surfaces of jump. A uniform, general integral form of balance equations (conservation laws) is derived for all three types and its localisation to the point on the discontinuity surface is carried out. In the case of the surfaces of jump the local balance equation takes the form of the Kotchine condition. Local form of the balance equations is specified for the mass, momentum, energy (total, kinetic and internal) and entropy. The equation which expresses the hypothesis of local equilibrium for a discontinuity surface is derived. This equation reflects also the phase transitions that take place in equilibrium. The relations of the derived results to other theories are discussed.     

Formation of singularities on the charged surface of a liquid-helium layer with a finite depth

The dynamics of the development of an instability of a charged surface of a liquid-helium layer with a finite depth is investigated. The equations describing the evolution of the free surface are derived with the use of conformal variables for the case in which the charge completely screens the electric field above the liquid. A model of the evolution of a spatially localized perturbation of a liquid-helium surface is proposed for the strong-field limit where the dynamics of the liquid is predominantly determined by the effect of electrostatic forces. This model describes the development of an instability of the initially planar boundary to the point of the formation of cuspidal dimples. The limit of an infinitely deep liquid is considered. The stability of the previously revealed liquid flow regime described by the Laplacian growth equations is proved without significant constraints on the surface geometry.     

On surface elasticity theory for plane interfaces

A closed system of surface elasticity equations was derived in terms of surface quantities defined as integrals of respective excess bulk quantities normal to the interface. The equations were consistently linearized for the case of small strains. It is shown that these equations are more general than the Shuttleworth equations. Equations of this type were also derived for the particular case of an interface formed by a thin layer with constant properties. The derived equations were used to consider bending of a plate under pressure applied to both sides.     

Nonlinear oscillations of a charged jet of a conducting liquid under multimode initial deformation of its surface

The subject of consideration is a uniformly charged jet of an ideal incompressible conducting liquid moving with a constant velocity along the symmetry axis of an undisturbed cylindrical surface. An evolutionary expression for the jet shape is derived accurate to the second order of smallness in oscillation amplitude for the case when the initial deformation of the equilibrium surface is a superposition of a finite number of both axisymmetric and nonaxisymmetric modes. The flow velocity field in the jet and the electric field distribution near it are determined. The positions of internal nonlinear secondary combined three-mode resonances are found, which are typical of nonlinear corrections to the analytical expressions for the jet shape, flow velocity field potentials, and electrostatic field in the vicinity of the jet.     

Nonlinear oscillations of a charged layer of a conducting liquid on the surface of a solid spherical core

Nonlinear oscillations of a layer of an ideal incompressible perfectly conducting liquid on the surface of a charged melting hailstone (solid core) are studied using analytical asymptotic calculations of the second order of smallness in initial deformation amplitude. Specifically, it is shown that, when the thickness of the layer is much less than the characteristic linear size (radius) of the solid core, the size of the core considerably influences the amplitudes of capillary oscillation modes arising on the surface of the charged layer via nonlinear interaction. It is found that, as the liquid layer on the surface of the solid core gets thinner, the energy in the spectrum of nonlinearly excited modes is redistributed with its maximum shifting toward higher (larger number) modes.     

Size-dependent dispersion characteristics in piezoelectric nanoplates with surface effects

In this paper, surface effects on the dispersion characteristics of elastic waves propagating in an infinite piezoelectric nanoplate are investigated by using the surface piezoelectricity model. Based on the surface piezoelectric constitutive theory, the presence of surface stresses and surface electric displacements exerting on the boundary conditions of the piezoelectric nanoplate is taken into account in the modified mechanical and electric equilibrium relations. The partial wave technique is employed to obtain the general solutions of governing equations, and the dispersion relations with surface effects are expressed in an explicit closed form. The impacts of surface piezoelectricity, residual surface stress and plate thickness on the propagation properties of elastic waves are analyzed in detail. Numerical results show that the dispersion behaviors in piezoelectric nanoplates are size-dependent, and there exists a critical plate thickness above which the surface effects may vanish.     

Analysis of a combined influence of substrate wetting and surface electromigration on a thin film stability and dynamical morphologies

A PDE-based model combining surface electromigration and wetting is developed for the analysis of morphological stability of ultrathin solid films. Adatom mobility is assumed anisotropic, and two directions of the electric field (parallel and perpendicular to the surface) are discussed and contrasted. Linear stability analyses of small-slope evolution equations are performed, followed by computations of fully nonlinear parametric evolution equations that permit surface overhangs. The results reveal parameter domains of instability for wetting and non-wetting films and variable electric field strength, nonlinear steady-state solutions in certain cases, and interesting coarsening behavior for strongly wetting films.     

Influence of a thin surface layer on light scattering by spherical particles

The Mie problem with modified boundary conditions that take into account the influence of a thin surface layer on the scattering of an electromagnetic wave by a spherical particle is considered. Analytical equations are derived for the partial amplitudes of scattered waves and forced oscillations. These equations are applicable in the case of anisotropy and gyrotropy of an optical response from the surface layer.     

Effect of surface on phase modulation of light in a nematic layer

The nanorelief of orienting surfaces in a nematic layer is studied experimentally. The initial inclination angle of the director and the phase retardation of light in the crystal are determined, and the director reorientation dynamics in the crystal under SB deformation in an electric field is analyzed. It is shown that a thin layer of amorphous hydrogenated carbon (a-C: H) deposited on a GeO monoxide layer with an anisotropic nanorelief produced by the inclined deposition method smoothens the surface topography without changing the surface structure. Modification of the structure and physicochemical properties of the GeO surface alters the conditions of the anisotropic-elastic interaction at the interface with the liquid crystal, as evidenced by an increase in the S-effect threshold and a decrease in the initial inclination of the director from 22° (on the GeO surface) to 0–6°. Strong influence of the surface nanostructure on the dynamics of the director reorientation in the electric field and on the phase modulation of light is experimentally demonstrated. It is shown that the phase retardation of light in the GeO layer covered by an a-C: H film is twice as large as in the layer of the same thickness with a virgin surface.     

Peculiarities of evaporation of a thin water layer in the presence of a solvable surfactant

Evaporation of a thin layer of a polar liquid (water) having a free surface and located on a solid substrate is investigated. A solvable surfactant is placed on the free liquid-vapor interface. The surface tension is a linear function of the surface concentration of the surfactant. The surface energy of the solid-liquid contact line is a nonmonotonic function of the layer thickness and is the sum of the Van der Waals interaction and the specific interaction of the double electric layer on the interface. The effect of the solvable surfactant on the dynamics and stability of the propagation of the evaporation front in the thin liquid film is analyzed in the long-wave approximation in the system of Navier-Stokes equations.     

Two-parametric family of exact solutions for the profile of the surface of a conducting liquid in a nonuniform electric field

Possible equilibrium configurations of the free surface of a conducting liquid in an external nonuniform electric field are investigated. The liquid is at the tip of a wedge-shaped electrode, and the counter-elecrode is a thin straight conducting filament parallel to the edge of the wedge. The conformal mapping method is used to obtain a two-parametric family of exact solutions for the shape of the surface. The solutions describe the deformation of the surface right to separation of a drop from the electrode.     

Time delay temperature behaviour of surface acoustic waves propagation on crystal substrate

A method is described for the computation of the time delay temperature behaviour for surface acoustic waves propagated in a surface layer of piezoelectric crystals. The linear field equations for small vibration superposed on thermally induced deformation were employed in the determination of the time delay temperature behaviour. The computed time delay temperature dependence of the surface acoustic waves propagated in the digonal axis direction on the ZX-cut quartz plate is given as an example.     

SH surface acoustic wave propagation in a cylindrically layered piezomagnetic/piezoelectric structure

SH surface acoustic wave (SH-SAW) propagation in a cylindrically layered magneto-electro-elastic structure is investigated analytically, where a piezomagnetic (or piezoelectric) material layer is bonded to a piezoelectric (or piezomagnetic) substrate. By means of transformation, the governing equations of the coupled waves are reduced to Bessel equation and Laplace equation. The boundary conditions imply that the displacements, shear stresses, electric potential, and electric displacements are continuous across the interface between the layer and the substrate together with the traction free at the surface of the layer. The magneto-electrically open and shorted conditions at cylindrical surface are taken to solve the problem. The phase velocity is numerically calculated for different thickness of the layer and wavenumber for piezomagnetic ceramics CoFe₂O₄ and piezoelectric ceramics BaTiO₃. The effects of magnetic permeability on propagation properties of SH-SAW are discussed in detail. The distributions of displacement, magnetic potential and magneto-electromechanical coupling factor are also figured and discussed.