共查询到20条相似文献,搜索用时 62 毫秒
1.
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
2.
The theory of a boundary layer that is adjacent to the surface of an indefinitely deep viscous liquid and caused by its periodic
motion is modified for analysis of finite-amplitude flow motion on the charged surface of a viscous conductive finite-thickness
liquid layer resting on a hard bottom (the thickness of the layer is comparable to the wavelength). With the aim of adequately
describing the viscous liquid flow, two boundary layers are considered: one at the free surface and the other at the hard
bottom. The thicknesses of the boundary layers are estimated for which the difference between an exact solution and a solution
to a model problem (stated in terms of the modified theory) may be set with a desired accuracy in the low-viscosity approximation.
It is shown that the presence of the lower (bottom) boundary layer should be taken into account (with a relative computational
error no more than 0.001) only if the thickness of the viscous layer does not exceed two wavelengths. For thicker layers,
the bottom flow may be considered potential. In shallow liquids (with a thickness of two tenths of the wavelength or less),
the upper (near-surface) and bottom layers overlap and the eddy flow entirely occupies the liquid volume. As the surface charge
approaches a value that is critical for the onset of instability against the electric field negative pressure, the thicknesses
of both layers sharply grow. 相似文献
3.
S. O. Shiryaeva 《Technical Physics》2008,53(12):1541-1550
The existent concepts of the boundary layer near the free surface of a viscous liquid, which is related to its periodic motion,
are modified with the aim of analyzing the finite-amplitude wave motion on the surface of a thick charged jet of a viscous
conducting liquid. To describe the flow in the boundary layer, a model problem is proposed that is simpler in statement compared
with the complete problem and the solution of which uses the governing properties of the exact solution obtained in the low-viscosity
asymptotics: the form of the dispersion relation, wave profile, and rate of velocity field viscous damping with time. An estimate
is made of the boundary layer thickness at which the discrepancy between the exact solution and solution to the model problem
(stated in terms of the theory proposed) falls into a given interval in the low-viscosity asymptotics. The domain of applicability
of the modified theory is determined. 相似文献
4.
The existing concepts of the boundary layer arising near the free surface of a viscous liquid, which is related to its periodic motion, are revised with the aim to calculate finite-amplitude linear oscillations of a viscous liquid charged drop. Equations complementing the boundary layer theory are derived for the vicinity of the oscillating free spherical surface of the drop. An analytical solution to these equations is found, comparison with an exact solution is made, and an estimate of the boundary layer thickness is obtained. The domain of applicability of the modified theory is defined. 相似文献
5.
The prevailing concepts concerning the boundary layer near the free surface of a viscous liquid associated with oscillatory
motion are modified for calculating finite-amplitude linear oscillations of a charged bubble in this liquid. Equations of
the boundary layer theory for the neighbourhood of the oscillating free spherical surface of a charged bubble in a dielectric
liquid are derived, their analytic solution is obtained and compared with the exact solution, and the thickness of the boundary
layer is assessed. The range of applicability of the modified theory is determined. 相似文献
6.
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
7.
《Journal of sound and vibration》1987,115(2):339-349
Parametric instabilities of a horizontal liquid layer with a finite depth covered by a thin elastic plate under a vertical periodic motion are investigated with account taken of the viscosity of the liquid layer. The primary regions and the secondary ones of dynamic instabilities are determined by using the equation of a thin elastic plate including the normal component of the viscous stress, but not the tangential component of it. The critical amplitude of the imposed oscillation, beyond which a parametric instability occurs (that is, the neutral stability curves) is found in the space of the frequency and amplitude of the imposed vertical oscillation. These results are confirmed by experimental ones for a liquid layer of glycerine covered with a thin rubber plate. 相似文献
8.
A modified theory of a boundary layer associated with a periodic capillary-gravitational motion on the free surface of an infinitely deep viscous liquid is proposed. The flow in the boundary layer is described in terms of a simplified (compared with the complete statement) model problem a solution to which correctly reflects the main features of an exact asymptotic solution: the rapid decay of the flow eddy part with depth of the liquid and insignificance of some terms appearing in the complete statement. The boundary layer thickness at which the discrepancy between the exact asymptotic solution and model solution is within a given margin is estimated. 相似文献
9.
Analytical calculations show that the time-periodic decay of the double electric layer near the free surface of a viscous
polar liquid causes periodic variation of the surface tension coefficient of the liquid and may be a reason for parametric
buildup of capillary-gravitational finite-amplitude wave motion. 相似文献
10.
A heavy sphere is free to move inside a rotating horizontal cylinder filled with viscous liquid. The steady motion is essentially Stokesian, and the sphere rotates at a fixed location with a lubrication layer between the ball and the wall. The symmetry of the flow field suggests there will be no force to balance the normal component of the ball's weight. However, we show that a normal force can arise when a cavitation bubble is present. The bubble size was measured as a function of the cylinder rotation rate and agrees well with a model which uses the force and torque balances on the sphere. 相似文献
11.
To probe the microscopic balance of forces close to a moving contact line, the boundary conditions around viscous drops sliding down an inclined plane are investigated. At first, the variation of the contact angle as a function of the scale of analysis is discussed. The dynamic contact angle is measured at a scale of 6 mum all around sliding drops for different volumes and speeds. We show that it depends only on the capillary number based on the local liquid velocity, measured by particle tracking. This velocity turns out to be normal to the contact line everywhere. It indirectly proves that, in comparison with the divergence involved in the normal direction, the viscous stress is not balanced by intermolecular forces in the direction tangential to the contact line, so that any motion in this last direction gets damped. 相似文献
12.
《Journal of sound and vibration》1987,119(2):249-265
The coupled frequencies of hydroelastic systems in zero gravity consisting of an elastic shell and a viscous liquid layer with a free surface have been treated. The system exhibits either an annular liquid layer around an elastic cylindrical center shell or a liquid layer inside an elastic infinitely long container. The first case has been evaluated numerically, where the influence of the liquid surface tension parameter, the elasticity parameter of the shell, its axial deflection wave length l and the thickness of the layer have been determined. In contrast to the hydroelastic system with an ideal liquid, the system with viscous liquid exhibits instability of the liquid surface as well as the shell. 相似文献
13.
K. I. Morozov 《Journal of Experimental and Theoretical Physics》1997,85(4):728-733
Unique capabilities for modeling the bulk motion of one liquid in another arise from the use of droplets made of a magnetic
liquid. In this paper the low-frequency rotational motion of a magnetic droplet suspended in a viscous liquid is investigated.
In this frequency range, the shape of the droplet does not depend on the field frequency and is determined only by its amplitude.
An analytic solution has been found in the Stokes approximation to the problem, which generalizes the classic problem of Jeffrey
to the case of a liquid ellipsoidal particle. This solution makes it possible to determine the velocity field inside and outside
the liquid particle, the moments of the viscous forces acting on the droplet, its coefficient of rotational mobility.
Zh. éksp. Teor. Fiz. 112, 1340–1350 (October 1997) 相似文献
14.
The dispersion relation for the spectrum of capillary waves of a spherical layer of a viscous liquid coating a solid spherical
core with a layer of finite thickness is introduced and analyzed. It is shown that the existence of two mechanisms for the
viscous dissipation of the energy of the capillary-wave motions of the liquid, viz., damping in the bulk of the layer and
on the solid core, leads to restriction of the spectrum of the realizable capillary waves of the liquid on both the high-and
low-mode sides. At a fixed value of the system charge which is supercritical for the first several capillary modes, the maximum
growth rates in the case of a small solid core are possessed by modes from the middle of the band of unstable modes, while
in thin liquid layers the highest of the unstable modes have the largest growth rates. This points out differences in the
realization of the instability of the charged surface of the spherical layer for small and large relative sizes of the solid
core.
Zh. Tekh. Fiz. 67, 8–13 (September 1997) 相似文献
15.
The theory of a boundary layer near the periodically oscillating free surface of a spherical viscous liquid layer over a solid
core (bottom) is modified. Two boundary layers are considered to adequately describe a liquid viscous flow in the system:
one at the free surface of the liquid and the other at the solid bottom. The thicknesses of the boundary layers are estimated,
which provide any given discrepancy between an exact solution to the model problem and a solution obtained in the small viscosity
approximation. Taking into account the boundary layer near the solid bottom is shown to be significant only for lower oscillation
modes. For higher modes, the flow near the core can be considered potential. In the case of lower modes and shallow liquid,
the surface and bottom boundary layers overlap and an eddy flow occupies the entire volume of the liquid. 相似文献
16.
Doklady Physics - The axisymmetric motion of a viscous incompressible fluid in a layer bounded by a solid plane and the free surface parallel to it is considered. There are three regimes of motion... 相似文献
17.
Elvira-Segura L 《Ultrasonics》2000,37(8):537-547
This paper deals with the study of the velocity and the attenuation of an acoustic wave propagating inside a cylindrical elastic tube filled with a viscous liquid. A theory describing the propagation of the axisymmetrical modes in such waveguides is presented, with special attention given to the absorption produced by the viscous mechanisms in the liquid. One of these mechanisms is related to the momentum transfer between the compression and rarefaction regions of a propagating wave. The other viscous mechanism is due to the momentum transport inside the viscous boundary layer, close to the tube wall. Numerical calculations were carried out to investigate the influence of different parameters (frequency, tube radii, viscosity coefficient) on the propagation of acoustic waves. 相似文献
18.
Bogoyavlenskiy VA 《Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics》1999,60(1):504-508
The present work is devoted to a model of bubble collapse in a Newtonian viscous liquid caused by an initial bubble wall motion. The obtained bubble dynamics described by an analytic solution significantly depends on the liquid and bubble parameters. The theory gives two types of bubble behavior: collapse and viscous damping. This results in a general collapse condition proposed as the sufficient differential criterion. The suggested criterion is discussed and successfully applied to the analysis of the void and gas bubble collapse. 相似文献
19.
The temporal evolution of the three-dimensional pattern of perturbations superposed on a radialrotational spread or sink of a viscous layer the parameters of which depend on the radial coordinate and time has been studied. The motion of the layer boundaries is specified both in the main motion and in the perturbed motion. Based on the integral relations method applied to the linearized problem in perturbations, sufficient estimates of exponential stability (in particular, on a finite time interval) of the main motion have been derived. 相似文献