Convective flows in a layer of a viscous liquid with the uniformly charged free surface

It is found theoretically that the critical conditions under which a charged liquid surface becomes unstable against the electric charge relax as a result of interaction between capillary-gravitational and convective flows in the liquid. As the surface charge density approaches a value critical in terms of development of Tonks-Frenkel instability, convection in the liquid arises at a temperature gradient however small, this effect depending on the liquid layer thickness.     

Morphological stability analysis of partial wetting

We develop a macroscopic static theory of the morphological stability of partial wetting. The system we studied consist of a smooth horizontal solid surface and some non-volatile liquid on it. A necessary condition for the stable equilibrium of such systems is known as the Young condition on the contact angle made at the contact line where the free surface of liquid meets the solid surface. But this condition is local and is not sufficient for the stability. We present a formulation for studying the stability of systems which satisfy the Young condition. Then we apply this to several morphologies of wetting. We find that there are at least two fundamental morphologies that we call a hole and a ridge, which are thermodynamically unstable against certain infinitesimal deformations of the contact lines. The hole type instability has also been found recently [D. J. Srolovitz and S. A. Safran, J. Appl. Phyys., 60 (1986), 1]. We also derived a reduced expression for the wetting energy as a functional of the contact line positions under the assumption of almost flat free surface of the liquid. This serves us to understand the characteristic length scale which appears in the ridge type instability. Besides these instabilities there is another category of morphological instability in which the system becomes unstable against an infinitesimal deformation of the free surface of liquid. We show this by an illustrating example in which the instability is described as the so-called tangent bifureation in nonlinear systems.     

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.     

Instability and reconstruction of a thin fluid film under inversion conditions

The development of mechanical instability of a neutral fluid film (liquid helium or hydrogen) under inversion conditions (it does not lie on a solid substrate but hangs from a ceiling) is discussed. Critical parameters of such an instability and the character of surface reconstruction under the action of van der Waals forces, bubble pressure, and gravitational forces are determined. The interrelation with the well-known Frenkel problem of a drop on a solid substrate is pointed out. An electrostatic mechanism is proposed for the stimulation of instability of a thin helium film. This mechanism is promising for the problem of superfluid helium leakage.     

Mass transfer due to nonlinear capillary-gravitational waves on the surface of a viscous liquid

An analytical expression of the second order of smallness in wave amplitude-to-wavelength ratio is derived for a horizontal flow arising in a finite-depth layer of a viscous liquid under the action of a periodic nonlinear capillary wave. It is found that the liquid flow is determined by the nonlinear component of the velocity field vortex part and the flow rate increases with increasing viscosity and decreasing wavelength irrespective of the layer thickness. In thin layers, the flow rate rapidly drops from its maximal value with increasing viscosity, wavelength, and surface charge density. If the liquid surface is charged, the horizontal liquid flow decreases rapidly as the surface charge density approaches the threshold of the Tonks-Frenkel instability.     

液体横向射流在气膜作用下的破碎过程

为了研究液体横向射流在气膜作用下的破碎过程,采用背景光成像技术及VOF TO DPM方法进行了实验研究和仿真研究,模拟介质为水和空气.研究结果表明,液体射流在气膜作用下主要存在两种破碎过程:柱状破碎和表面破碎.Rayleigh-Taylor(R-T)不稳定性产生的表面波是液体射流发生柱状破碎的主要原因,气流穿透表面波的波谷导致射流柱破碎,破碎后的液丝沿流向逐渐发展呈带状分布.Kelvin-Helmholtz(K-H)不稳定性产生的表面波是液体射流发生表面破碎的主要原因,液丝和液滴从射流表面剥离.局部动量比对液体横向射流的破碎过程具有重要影响,当局部动量比较低时,液体射流的破碎由K-H不稳定性主导;随着局部动量比的增大液体射流的破碎逐渐由R-T不稳定性主导.液体射流的破碎长度及穿透深度均随局部动量比的增大而增大.     

Electrostatic stability of the liquid layer surface on a hard wettable cylindrical substrate

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.     

Electrostatic instability of a heavily charged conducting liquid jet

The effect of electric charge on the jet surface on the capillary instability of the jet and its disintegration into drops is analyzed. A theoretical explanation is given for the electrostatic mechanism of instability development and jet disintegration that is akin to the mechanisms behind the instability of a heavily charged drop (Rayleigh instability) and flat uniformly charged liquid surface (Tonks-Frenkel instability) but differs qualitatively from the conventional capillary mechanism of instability and disintegration.     

Electrostatic instability of the lateral surface of a viscous liquid finite-conductivity jet in a collinear electrical field

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.     

Instability of equilibrium of the liquid dielectric surface and formation of regular cellular structures in the field of a corona discharge

It has been established experimentally that the equilibrium of the plane surface of transformer oil under a corona electrode (needle) becomes unstable when the critical voltage, which increases with the oil layer thickness, is attained at the corona point. When the voltage at the needle exceeds the critical value, regular static cells are formed on the oil surface with characteristic sizes decreasing upon an increase in voltage. The theoretically estimated parameters of the experiment are found to be close to the experimental data. Comparison of the parameters corresponding to the occurrence of instability in the equilibrium of the oil surface in the field of the corona discharge with the parameters of instability in the equilibrium of the charged surface of liquid helium in a uniform electric field [7] demonstrates the similarity of the effects.     

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.     

Capillary vibrations of a viscoelastic medium under the action of a constant external force

A layer of a viscoelastic liquid was found to exhibit two types of instabilities, aperiodic and vibrational, when its free surface was subjected to an external force. For the aperiodic instability, the critical condition and increment value were derived analytically. If the angle between the force direction and external normal to the free surface of the liquid is smaller than 45 degrees, only the vibrational instability sets up in the system; if the angle is larger, the aperiodic one alone is observed.     

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.     

Measurements of Rayleigh–Taylor instability growth of laser-shocked iron–silicon alloy

The Rayleigh–Taylor (RT) instability of liquid iron alloys is important for understanding the core formation mechanism in the Earth. Here we first report the measurement of RT instability growth for a liquid iron–silicon (Fe–Si) alloy, which is one of the major candidate for the material of the Earth’s core, using a high power laser. We optimized the measurement setup and analytical technique to observe the growth of perturbation on an Fe–Si sample surface. The growth of perturbation amplitude on the Fe–Si alloy under high pressure and temperature was successfully observed using in situ X-ray radiography. The growth rate of the RT instability for the Fe–Si alloy on about 1000?GPa was estimated to be 0.3 ns^?1.     

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).     

Thickness of a boundary layer attributed to the wave motion on the charged free surface of a viscous liquid

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.     

垂直排液过程不稳定性的数值模拟

为分析线框排液实验中液膜表面出现的不稳定现象及其成因,针对含有不溶性活性剂的线框液膜排液过程,模拟液膜底部的不稳定现象,分析Marangoni效应、膨胀黏性和扰动波数因素的影响。结果表明：底部扰动在排液开始比较剧烈,而后快速减弱,到排液后期又逐渐增强。排液开始的扰动是由初始扰动引起,而排液后期的扰动与活性剂分布有关。较弱的Marangoni效应可增强表面扰动,而较强的Marangoni效应则减弱底部扰动,使液膜呈刚性,发生表面逆流现象;较高的膨胀黏性减慢液膜排液进程,降低表面速度,且能抑制Marangoni效应引起的逆流现象;波数较大的扰动使液膜在排液初期的扰动变强,但对排液后期的稳定性不产生影响。     

Exact solutions of the equations of motion of liquid helium with a charged free surface

The dynamics of the development of instability of the free surface of liquid helium, which is charged by electrons localized above it, is studied. It is shown that, if the charge completely screens the electric field above the surface and its magnitude is much larger than the instability threshold, the asymptotic behavior of the system can be described by the well-known 3D Laplacian growth equations. The integrability of these equations in 2D geometry makes it possible to describe the evolution of the surface up to the formation of singularities, viz., cuspidal point at which the electric field strength, the velocity of the liquid, and the curvature of its surface assume infinitely large values. The exact solutions obtained for the problem of the electrocapillary wave profile at the boundary of liquid helium indicate the tendency to a change in the surface topology as a result of formation of charged bubbles.     

Nonlinear capillary vibration of a charged bubble in an ideal dielectric liquid

The problem of nonlinear radial pulsations and surface vibrations of a charged bubble placed in an ideal incompressible dielectric liquid is asymptotically solved up to the second order of smallness by the method of many scales. It is shown that, in the case of nonlinear vibrations, resonance energy exchange may take place not only between surface modes but also between the radial mode and a surface mode. A new type of instability (other than Rayleigh instability against the self-charge), instability against the excess vapor pressure in the bubble, is discovered. The new type of instability shows up as energy transfer from the centrosymmetric pulsation mode to all initially excited surface vibration modes simultaneously.     

Dynamic stability of liquid-filled cylindrical shells under horizontal excitation,part I: Experiment

Experimental studies have been carried out on the dynamic stability of a cantilever cylindrical shell partially filled with liquid, under horizontal excitation. The test cylinder was harmonically excited with constant acceleration or displacement amplitude. It was found that a combination instability resonance of sum type could occur, involving two natural vibrations with the same axial mode of vibration number but with the circumferential wave numbers differing by one. By varying the dimensionless water height from 0 to 1·0 stepwise by 0·25 increments, the instability regions and vibration modes were determined for two polyester test cylinders. The response waves, axial and circumferential vibration modes, and behavior of the free liquid surface were also observed.