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1.
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) 相似文献
2.
S. O. Shiryaeva 《Technical Physics》2011,56(3):335-344
A dispersion relation is derived for capillary waves with an arbitrary symmetry on the surface of a charged jet of a finite-conductivity
viscous liquid placed in an electric field collinear with the axis of the jet. Analytical calculations are carried out in
an approximation that is linear in dimensionless wave amplitude. In the case of axisymmetric waves, the instability of which
causes disintegration of the jet into drops, the finiteness of the potential equalization rate has a noticeable effect only
for jets of poorly conducting liquids. The charge relaxation shows up in that “purely relaxation” periodic and aperiodic liquid
flows arise. When the conductivity of the liquid declines, the instability growth rates for unstable waves increase and their
spectrum extends toward short waves. A charge present on the surface of the jet enhances its instability. An increase in the
charge surface diffusion coefficient variously influences the capillary and relaxation branches of the solution: the damping
ratio increases in the former case and decreases in the latter. As the diffusion coefficient rises, relaxation flows may become
unstable. 相似文献
3.
A. I. Grigor’ev S. O. Shiryaeva V. A. Koromyslov D. F. Belonozhko 《Technical Physics》1997,42(8):877-883
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) 相似文献
4.
S. O. Shiryaeva 《Technical Physics》2011,56(6):782-787
The influence of the finiteness of the charge transfer rate on the electrostatic instability of the lateral surface of a viscous
liquid jet is studied. The study is based on the analysis of a dispersion relation for flexural-deformation capillary waves
on the surface of the jet with allowance for charge relaxation. The jet is subjected to a superposition of two electrostatic
fields one of which is collinear with the jet’s axis and the other is directed radially to the former. It is found that the
finiteness of the potential equalization rate influences jets of a poorly conducting liquid most strongly. The charge relaxation
shows up in the appearance of both periodic and aperiodic “purely relaxation” flows. Relaxation flows give rise to electrostatic
instability in low-permittivity liquids. When the conductivity of the liquid drops, the instability growth rate of relaxation
waves grows and their spectrum expands toward shorter waves. An increase in the charge surface diffusion coefficient introduces
destabilization into the relaxation flows of the liquid, which may eventually become unstable. 相似文献
5.
On the stability of capillary waves on the surface of a charged jet moving relative to the environment 总被引:1,自引:0,他引:1
A dispersion relation is derived for capillary waves with arbitrary symmetry (arbitrary azimuthal numbers) on the surface
of a charged cylindrical jet of an ideal incompressible conducting liquid moving relative to an ideal incompressible dielectric
medium. It is shown that a tangential discontinuity in the velocity field on the surface of the jet leads to periodic instability
of waves (similar to the Kelvin-Helmholtz instability) at the interface and destabilizes both axisymmetric and flexural waves.
The wavenumber range for unstable waves and the instability growth rate increase with the field strength and relative speed
of motion, varying as the square of these parameters. In the case of the neutral jet, the flexural instability is of the threshold
character and sets in starting from a certain finite value of the speed rather than at an arbitrary small speed. 相似文献
6.
An analytical expression for the profile of a finite-amplitude wave on the free charged surface of a deep low-viscosity conducting liquid is derived in an approximation quadratic in wave amplitude-to-wavelength ratio. It is shown that viscosity causes the wave amplitude to decay with time and makes the wave profile asymmetric at surface charge densities subcritical in terms of Tonks-Frenkel instability. At supercritical values of the surface charge density, taking account of viscosity decreases the growth rate of emissive protrusions on the unstable free surface, slightly broadens them for short waves, and narrows for long ones. Analytical expressions for the wave frequencies, damping rates, and instability growth rates with regard to viscosity are found. 相似文献
7.
An asymptotic solution to the problem of analyzing the nonlinear stage of the Rayleigh-Taylor instability at the uniformly charged interface between two (conducting and insulating) immiscible ideal incompressible liquids is derived in the third order of smallness. It is found that the charge expands the range of waves experiencing instability toward shorter waves and decreases the length of the wave with a maximum growth rate. It turns out that the characteristic linear scale of interface deformation, which arises when the heavy liquid flows into the light one, decreases as the charge surface density increases in proportion to the square root of the Tonks-Frenkel parameter characterizing the stability of the interface against the distributed self-charge. 相似文献
8.
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. 相似文献
9.
An analytic expression for the electrostatic field strength at the free surface of a thin layer of a uniformly charged viscous
incompressible liquid is obtained in second-order asymptotic calculations in the amplitude of a periodic capillary-gravity
wave propagating over the liquid surface. It is shown that a corona discharge at the crests of the waves can be initiated
at subcritical values of the field strength (in the sense of possible realization of the Tonks-Frenkel instability). The electrostatic
field strength at the crests of nonlinear waves increases with the wavenumber and the wave amplitude. 相似文献
10.
S. O. Shiryaeva 《Technical Physics》2010,55(2):204-209
A dispersion relation is derived for capillary waves with arbitrary symmetry (with arbitrary azimuthal numbers) on the surface
of a cylindrical jet of an ideal incompressible dielectric liquid subjected to an electrostatic field aligned with the symmetry
axis of the jet. It is shown that only long axisymmetric waves can experience capillary instability in such a system. The
wavenumber range into which unstable waves fall begins with a zero value, and its width depends on the permittivities of the
liquid and ambient and on the electrostatic field strength squared. As the field strength grows, the wavenumber range for
unstable waves rapidly narrows and the capillary instability growth rate, as well as the wavenumber of the wave with the greatest
growth rate, decreases. 相似文献
11.
It is shown that the analytical estimator for the boundary layer thickness that contains the wave frequency in the denominator and is proposed for approximate calculation of the wave motion on the free surface of a viscous liquid cannot be formally applied to the wave motion on the uniformly charged liquid surface. The fact is that, when the surface charge density attains a value critical in terms for the Tonks-Frenkel instability, the wave frequency tends to zero. From the analysis of liquid motions near the electric charge critical density, a technique is proposed for calculating the thickness of a boundary layer attributed to flows of various kinds. It is found that the thickness of the boundary layer due to aperiodic flows with amplitudes exponentially growing with time (such flows take place at the stage of instability against the surface charge) does not exceed a few tenths of the wavelength, whereas the thickness of the boundary layer due to exponentially decaying liquid flows is roughly equal to the wavelength. 相似文献
12.
The thermal instability of discharge plasma in air is analyzed. The contributions of specific mechanisms of instability are examined, including VT relaxation, the increase in the fractional energy dissipation via rapid heating due to an increase in reduced field strength, and ionization thermal instability. The effects of acoustic wave generation caused by heating and of charged particle motion relative to the neutral gas on both the length scale and the growth rate of unstable fluctuations are taken into account. 相似文献
13.
The spectrum of capillary-relaxational motions of a charged free liquid surface is analyzed. The analysis takes into account the effect of surface-tension relaxation and the existence of two relaxation times due to different physical mechanisms. Each relaxation mechanism is associated with certain liquid wave motions. Motions due to different relaxation processes interact with each other and with capillary-gravity waves through nonlinear mechanisms. 相似文献
14.
The problem of the stability of capillary waves on the surface of a charged jet of an ideal incompressible electroconducting liquid, which moves with respect to a material dielectric medium, is considered. There is a tangential discontinuity of the velocity field on the interface between the media. Solutions to the problem in two idealized models have been compared, i.e., when the jet has a finite and infinite length. It has been shown that the instability increments and the wave numbers of the most unstable waves, computed in both models, are linearly related, and velocity of motion of the jet acts as a coefficient of proportionality. 相似文献
15.
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. 相似文献
16.
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) 相似文献
17.
The wave motion in a cylindrical layer of an ideal conducting liquid on a hard rod kept at a constant electrical potential is calculated accurate to the first order of smallness in dimensional perturbation of the free surface. The instability of the free surface is also considered. A dispersion relation is derived. It is shown that the range of instability waves depends on only the electric field strength near the free surface and the instability increments of capillary waves decrease as the layer gets thinner. The influence of the hard rod becomes tangible only when its radius becomes comparable to the thickness of the liquid layer. 相似文献
18.
The propagation of surface acoustic waves in a system composed of two piezoelectric crystals moving with respect to each other and separated by a vacuum gap is considered. The waves are localized on different sides of the gap and coupled only through the electrostatic interaction. It is shown that when the velocity of the relative motion of crystals is close to some value, there occurs a wave instability resulting in a resonant generation of these surface waves. The rate of growth of Bleustein-Gulyaev waves in piezoelectric crystals of 6mm symmetry class is determined analytically. 相似文献
19.
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. 相似文献
20.
G. L. Komissarova 《Acoustical Physics》2009,55(3):319-328
The properties of harmonic surface waves in an elastic cylinder filled with a liquid are studied. The case of elastic material for which the shear wave velocity is higher than the sound velocity in a liquid is considered. The wave motion is described based on the complete system of equations of the dynamic theory of elasticity and the equation of motion of an ideal compressible liquid. The asymptotic analysis of the dispersion equation in the region of large wave numbers and qualitative analysis of the dispersion spectrum showed that in such a waveguiding system there exist two surface waves, the Stoneley and the Rayleigh waves. The lowest normal wave forms the Stoneley wave on the internal surface of the cylinder. In this waveguide phase, velocities of all normal waves, except for the lowest one, have the velocity of sound in the liquid as their limit. Therefore, the Rayleigh wave on the external surface of the cylinder is formed by all normal waves in the range of frequencies and wave numbers in which phase velocities of normal waves of the composite waveguide and the lowest normal wave of the elastic hollow cylinder coincide. 相似文献