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1.
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
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.
The capillary oscillations of a charged drop of a viscous liquid are calculated in terms of the boundary layer theory in an
approximation linear in oscillation amplitude. Calculation is accompanied with the estimation of a relative error that arises
when the exact solution is replaced by an approximate one. It is shown that, for the calculation accuracy in the framework
of the boundary layer theory to be about several percent, the thickness of the boundary layer near the free surface of the
drop must be several times larger than that at which the intensity of the eddy flow caused by the oscillating surface decreases
by e times. As the viscosity of the liquid grows, so does the thickness of the boundary layer. 相似文献
4.
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
5.
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
6.
Analytical calculation of a nonlinear periodic wave flow on the free surface of a charged layer of an ideal incompressible
conducting liquid resting on a solid substrate is carried out for the case when fluctuation-induced forces (the dispersion
component of the wedging pressure) have a decisive effect on the system. It is shown that wave flows emerge in the liquid
in calculations of the second order of smallness in the wave amplitude, which is assumed to be small compared with the thickness
of the liquid layer. These flows result from nonlinear interaction as nonlinear corrections to the waves set at the zero time.
The field of fluctuation-induced forces displaces these flows toward the periphery of the area of influence of these forces.
This effect takes place both in the presence of an external electric field near the free surface and in its absence. The sign
and value of the nonlinear corrections depend on whether an electric field is present near the free surface of the liquid.
In the presence of an electric field, the curvature of the crest of the nonlinear waves increases; in its absence, the curvature
decreases. 相似文献
7.
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. 相似文献
8.
I. V. Marchuk 《Journal of Engineering Thermophysics》2009,18(3):227-237
In this paper, steady thermocapillary flow in a thin horizontal layer of a viscous incompressible liquid with a free surface
is considered. An axially symmetric steady problem with a localized thermal action on a horizontal liquid layer with a deformable
free surface is solved in a thin-layer approximation. In addition to the thermocapillary effect, the model takes into account
the capillary pressure caused by the free surface variable curvature and the convective mechanism of heat transfer in the
liquid. Analytical expressions for the velocity vector components as functions of the liquid layer thickness and surface temperature
are obtained. The free surface and velocity profiles caused by various kinds of heating are calculated. The influence of convective
heat transfer on the flow pattern is analyzed. 相似文献
9.
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
10.
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
11.
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
12.
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
13.
O. N. Mel’nikova V. N. Semenyuk 《Bulletin of the Russian Academy of Sciences: Physics》2010,74(12):1666-1668
The bottom layer of a dam break flow is experimentally studied. It is shown that the thickness of the viscous layer exceeds
the diameter of a bottom particle (d
p
< 1.2 cm). Small particles d
p
< 0.05 cm are captured by single satellite eddies that occur under main eddies periodically formed in the viscous layer.
Two satellite eddies approach each other and merge into one eddy capable of capturing a large particle if the flow velocity
is higher than the critical value U
dip. The particle is captured for large U
cr > U
dip which provides particle rotation without slipping. 相似文献
14.
V. A. Koromyslov A. I. Grigor’ev S. O. Shiryaeva Yu. N. Zhigalko 《Technical Physics》2011,56(4):464-473
The contribution of aerodynamic pressure acting on the surface of a water layer to a total electric field near the free surface
of the layer is considered. The layer covers a charged melting hailstone moving parallel to the external electrostatic field
vector. An asymptotic analytical expression for the electric field strength near a water-covered hailstone is derived in an
approximation that is quadratic in the amplitude of capillary oscillations of a charged conducting liquid layer on the surface
of the hailstone. It is found that the motion of the hailstone in ambient air influences the total electric field near the
hailstone only slightly but noticeably enhances energy exchange between neighboring oscillation modes. An air flow about the
hailstone is shown to have an appreciable effect on the possibility of nonlinear resonance energy exchange between initially
excited modes and modes due to the nonlinear interaction. 相似文献
15.
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. 相似文献
16.
A problem on the excitation of seismoacoustic waves in a system of a homogeneous isotropic elastic halfspace covered with a liquid layer is solved in the case of action of a source of point harmonic force on the surface of an elastic medium. Integral expressions are obtained for the radiation powers averaged over a wave period for longitudinal and transverse waves in a solid. Mode excitation is analyzed in detail. Expressions describing parts of the mode powers radiated into a liquid layer and an elastic medium are obtained. Numerical analysis of radiation powers is conducted for spherical longitudinal and transverse waves as well as for the radiation powers of seismoacoustic modes in a solid halfspace and a liquid layer. It is determined that in the conditions characteristic of bottom rocks in the case, where the basin depth is several times and more larger than the sound’s wavelength, about 2/3 of the total power is radiated into a liquid. 相似文献
17.
《中国科学:物理学 力学 天文学(英文版)》2015,(7)
The molecular coating on the surface of microvascular endothelium has been identified as a barrier to transvascular exchange of solutes. With a thickness of hundreds of nanometers, this endothelial surface layer(ESL) has been treated as a porous domain within which fluid shear stresses are dissipated and transmitted to the solid matrix to initiate mechanotransduction events. The present study aims to examine the effects of the ESL thickness and permeability on the transmission of shear stress throughout the ESL. Our results indicate that fluid shear stresses rapidly decrease to insignificant levels within a thin transition layer near the outer boundary of the ESL with a thickness on the order of ten nanometers. The thickness of the transition zone between free fluid and the porous layer was found to be proportional to the square root of the Darcy permeability. As the permeability is reduced ten-fold, the interfacial fluid and solid matrix shear stress gradients increase exponentially two-fold. While the interfacial fluid shear stress is positively related to the ESL thickness, the transmitted matrix stress is reduced by about 50% as the ESL thickness is decreased from 500 to 100 nm, which may occur under pathological conditions. Thus, thickness and permeability of the ESL are two main factors that determine flow features and the apportionment of shear stresses between the fluid and solid phases of the ESL. These results may shed light on the mechanisms of force transmission through the ESL and the pathological events caused by alterations in thickness and permeability of the ESL. 相似文献
18.
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
19.
An asymptotic analytical solution to an initial boundary-value problem considering (i) the time evolution of the capillary
oscillation amplitude as applied to a viscous spheroidal liquid drop placed in a uniform electrostatic field and (ii) the
liquid flow velocity field inside the drop is found. The problem is solved in an approximation that is linear in two small
parameters: the dimensionless oscillation amplitude and the dimensionless field-induced constant deformation of the equilibrium
(spherical) shape of the drop. Terms proportional to the product of the small parameters are retained. In this approximation,
interaction between oscillation modes is revealed. It is shown that the intensity of the eddy component of the oscillation-related
velocity field depends on the liquid viscosity and the external uniform electrostatic field strength. The intensity of the
eddy component decays rapidly with distance from the free surface. The depth to which the eddy flow (which is caused by periodical
flows on the free surface) penetrates into the drop is a nonmonotonic function of the polar angle and increases with dimensionless
viscosity and field strength. 相似文献
20.
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. 相似文献