A numerical study of the behaviour of a gas–liquid interface subjected to periodic vertical motion

A numerical study has been undertaken to examine the behaviour of a gas liquid interface in a vertical cylindrical vessel subjected to a sinusoidal vertical motion. The computational method used is based on the simplified marker‐and‐cell method and includes a continuum surface model for the incorporation of surface tension. The numerical results indicate that the surface tension has very little effect on the period and amplitude of oscillations of the interfacial waves. The stability of the interfacial waves has been found to depend on the initial pressure pulse disturbance, and exponential growth of the interfacial wave has been observed in some cases. The influence of the amplitude and frequency of the forcing oscillations has also been investigated. The results are in good agreement with available experimental and analytical solutions. Copyright © 2002 John Wiley & Sons, Ltd.     

Temperature fluctuations in a two-phase superheated layer in the boiling of a liquid

One of the basic parameters defining the intensity of heat transfer on the boundary separating liquid and vapor phases is the superheating of the liquid during boiling. In a two-phase boundary layer superheating constitutes a variable (fluctuating) quantity, which depends on several parameters of the system and is of a statistical nature. This paper is devoted to a study of the statistical nature of the fluctuations in the superheating of a liquid. Starting from experimental data, obtained in measuring temperature fluctuations in a two-phase boundary layer during the boiling of water in contact with a heated surface, we carry out a statistical analysis of the amplitude of the fluctuations. Based on this analysis, we determine the average and the maximum superheating as a function of the distance to the heated wall. To determine the microstructure of the temperature fluctuations and to study their origin, we took high-speed pictures of the head of a thermocouple in contact with the two-phase medium. We established that the presence of various size amplitudes is associated, in the main, with two effects: the existence of a superheated layer on a bubble in the course of its growth and the convection of the liquid close to the bubble.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 62–69, September–October, 1973.     

Mechanism of wave formation at the interface in explosive welding

Some of the main progress on the investigation of the mechanism of the wave formation in explosive welding at the Institute of Mechanics is summarized and others' previous works are reviewed. Our systematic experiments and analysis do not substantiate the theory of wave formation based on Karman vortex-street analogy or Helmholtz instability. On the contrary, they show that material strength insensitive to strain rate plays an important role. A simple hydro-plastic model is presented to explain the main features regarding the interfacial wave formation and to estimate the magnitude of wave length. The result is in broad agreement with experiment.     

Gyroscopic waves in a rotating liquid layer

The dispersion characteristics of gyroscopic waves in an incompressible liquid layer in a cavity of a rapidly rotating cylinder are studied. It is shown that in a viscous incompressible liquid layer, an inertial wave can be represented as the sum of six helical harmonics. The effects of the liquid viscosity and the ratio of the wave frequency to the angular velocity of rotation of the cylinder on the real and imaginary parts of the wavenumber are studied. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 15–20, March–April, 2008.     

The vapour–liquid interface and stresses in dried bodies

The paper presents a contribution to modelling the problem of vapour–liquid interface receding into dried body and stresses induced by drying of capillary-porous bodies. A complex algorithm comprising the specific mechanisms of drying in the first and second periods of drying is constructed. It enables calculation and drawing of the body temperature and drying curves for the whole drying process and identification of the vapour–liquid interface receding into the body. The drying induced stresses caused by the receding vapour–liquid interface and the non-uniform distribution of moisture content and/or temperature are analyzed. Numerical calculations of the temperature and drying curves and the drying induced stresses are carried out for the example of a finite dimensional kaolin cylinder dried convectively.     

Growth rates of the Marangoni instability in a layer of elastic liquid

The problem of thermocapillary (Marangoni) convection in a layer of viscoelastic liquid is considered. The stability boundary for this problem has been previously calculated in various cases by a number of authors. Here attention is fixed on the magnitude of the growth rate in the parameter regime corresponding to instability. Two noteworthy features are pointed out. First, there are anomalously large values of the growth rate at or near the limiting special case of a Maxwell fluid. Second, the complex values of the growth rate (corresponding to overstability, or the onset of instability via oscillatory motion) coalesce into real (positive) values at moderately supercritical values of the Marangoni number, suggesting that overstability might be elusive to observation.     

气体速度对液膜在预膜板表面流动形态影响的LBM模拟

为了探究气流剪切作用对航空燃油在气动雾化喷嘴预膜板上流动形态的影响,首先对基于相场理论的两相流格子Boltzmann模型进行修正,并通过经典算例验证了修正后模型的准确性和可靠性.随后利用该模型模拟了同向气流驱动下液膜在水平预膜板表面上的流动,分析了气流速度对液膜流动形态的影响规律.研究表明,该模型可准确追踪具有大密度比...     

The boundary layer solutions of the interface problem considering the strain gradient

According to the classical elastic theory, there is always a discontinuity of rotation angle on the interface between different materials. This illogic result can be overcome by the strain gradient plasticity theory. In the light of this theory, there is a group of boundary layer solutions near the interface, which have made important adjustment of the classical results. This project is supported by National Natural Science Foundation of China (19891180).     

Two-dimensional problem of the impact of a vertical wall on a layer of a partially aerated liquid

The two-dimensional unsteady problem of the impact of a vertical wall on a layer of a liquid which is mixed with air near the wall and does not contain air bubbles away from the wall is solved in a linear approximation. The gas-liquid mixture is modeled by a homogeneous, ideal, and weakly compressible medium with a reduced sound velocity dependent on the air concentration in the gas-liquid mixture. Outside the gas-liquid layer, the liquid is considered ideal and incompressible. During the initial stage of the impact, the liquid flow and the hydrodynamic pressure are determined using the linear theory of the potential motion of an inhomogeneous liquid. The dependence of the amplitude of the impact pressure along the wall on the air concentration in the gas-liquid layer and on the thickness of this layer is investigated. For a small relative thickness of the layer, the thin-layer approximation is used. It is shown that the solution of the original problem tends to the approximate solution as the thickness of the layer decreases. It is shown that the presence of the gas-liquid layer leads to wall pressure oscillations. Estimates are obtained for the pressure amplitude and the oscillation period. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 34–46, September–October, 2006.     

Response of a viscous annular liquid layer in zero-gravity to different axial excitations of the rigid boundary plates

A cylindrical annular liquid layer between two plates and around a rigid center-core consisting of incompressible and viscous liquid is subjected to different axial excitations, such as one-sided, counter-directional and double-sided unequal excitations. The response of the free liquid surface, the velocity- and pressure-distribution has been determined.

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Zusammenfassung Eine zylindrische Flüssigkeitsschicht bestehend aus inkompressibler und viskoser Flüssigkeit wurde verschiedenen harmonischen Anregungsformen ausgesetzt. Dabei wurden die Fälle einseitiger, doppelseitiger entgegengesetzter und ungleicher doppelseitiger Anregung mit Phase behandelt. Die Vergrößerungsfunktionen für die freie Flüssigkeitsoberfläche, für die Geschwindigkeits- und Druckverteilung wurden bestimmt.

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List of symbols a radius of liquid layer - b radius of inner cylindrical core - (a–b) thickness of layer - e _r , e , k unit vectors in the radial, angular and axial direction resp. - h length of layer - I _m , K _m modified Bessel functions of first and second kind and order m - diameter ratio - p pressure - q 2na/h - q* na/h - r, , z cylindrical coordinates - complex frequency - S sa ²/ - t time - u, w velocity components in the radial- and axial direction - ₀ excitation amplitude - abbreviation - surface tension parameter - surface tension - dynamic viscosity - kinematic viscosity - density of liquid - free liquid surface elevation - dimensionless time - _rz shear stress - reduced forcing frequency - forcing frequency - stream function - _mn natural frequency of non-viscous liquid     

Evolution of the joint motion of two viscous heat-conducting fluids in a plane layer under the action of an unsteady pressure gradient

A study is made of an invariant solution of the equations of a viscous heat-conducting fluid, which is treated as unidirectional motion of two such fluids in a plane layer with a common boundary under the action of an unsteady pressure gradient. A priori estimates of the velocity and temperature are obtained. The steady state is determined, and it is shown (under some conditions on the pressure gradient) that, at larger times, this state is the limiting one. For semiinfinite layers, a solution in closed form is obtained using the Laplace transform. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 94–107, July–August, 2008.     

液体环轴对称抛洒首次破碎的理论分析

对于水和无水乙醇环形轴对称抛洒实验的首次破碎结果的分析表明，在给定实验条件下，液体密度大约是气体的1000倍，液体首次破碎的过程分2个阶段:首先，界面不稳定性非线性发展，液体尖钉在惯性力和空气阻力的作用下，拉伸变细变长；然后在射流不稳定性的作用下，断裂成液体珠串。这个理论分析给出的首次破碎的平均液体直径与实验结果基本一致。理论分析表明，无水乙醇破碎液滴的平均直径比水液滴小，是无水乙醇表面张力值仅为水的1/3的一个必然结果。     

Unsteady flow in the Ekman layer of an elastico-viscous liquid

The transient flow in the Ekman layer of an elastico-viscous liquid near a flat plate is discussed. Initially the fluid and the plate were rotating together and the plate then suddently starts moving with a uniform velocity in its own plane relative to the rotating frame of reference. It is shown that the ultimate steady state is reached through decay of inertial oscillations whose frequency decreases with increase in the elastic parameter.     

The onset of convection in a viscoelastic liquid saturated anisotropic porous layer

The linear stability of a viscoelastic liquid saturated horizontal anisotropic porous layer heated from below and cooled from above is investigated by considering the Oldroyd type liquid. A generalized Darcy model, which takes into account the viscoelastic properties, the mechanical and thermal anisotropy is employed as momentum equation. The critical Rayleigh number, wavenumber, for stationary and oscillatory states and frequency of oscillation are determined analytically. It is shown that oscillatory instabilities can set in before stationary modes are exhibited. The effect of the viscoelastic parameter, the mechanical and thermal anisotropy parameters and specific heat ratio on the linear stability of the system is analyzed and presented graphically.     

Steady thermocapillary motion in a horizontal layer of liquid metal locally heated from above

The article considers stationary thermocapillary convection in a thin horizontal layer of fluid with Prandtl number Pr < 1 when it is being locally heated from above in conditions in which the curvature of the free surface is small. It is shown that the motion has a cellular structure. The size of the convective cell is determined from the solution to the spectral problem to which the integration of the free convection system of equations reduces. If the Maragoni (Péclet) number is sufficiently high, the length of the convective cell turns out to be large in comparison with the thickness of the layer. The convection picture is considered and an expression obtained for the velocity of the developing flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 146–152, November–December, 1984.     

Stability of motion in a planar layer of inhomogeneous ideal incompressible liquid having free boundaries

Research performed with financial support from the Krasnoyarsk Scientific Fund (Project Code 2F0059).     

单侧摩擦梯度非均匀双半平面的反平面运动

研究了二个半平面的反平面运动，二个半平面都是剪切弹性模量与材料密度为梯度的非均匀介质，它们之间的界面是具有Coulomb摩擦的单侧界面. 当介质的梯度参数按二次幂规律变化时，求得了这一问题的解析解，给出了界面上粘着区与滑移区以及相应的界面剪应力与相对滑移量的分布. 通过抛物线脉冲入射下的数值计算发现：界面上的剪应力呈反双峰形分布，正、反滑移区出现在峰值点附近，其范围随界面上施加的外压力σ=fsp∞/μ0的增加而减小，当外压力达到某一数值时，滑移区消失，整个界面将完全粘着在一起.     

Effect of fillers on the steady state rheological behaviour of liquid crystalline polymers

The effect of fillers on the flow curves of polymeric liquid crystals is investigated. Suspensions of polystyrene particles in liquid crystalline solutions of hydroxypropylcellulose (HPC) in water are used. By reducing the HPC concentration an isotropic solution can be prepared. It serves as a reference to isolate the effect of the isotropic/anisotropic structure of the suspending medium on the rheological behaviour. Suspensions in the isotropic solution behave as expected for filled viscoelastic matrices in general. In the anisotropic medium the shear rate rather than the shear stress seems to govern the changes in the relative viscosity. This behaviour is clearly different from isotropic viscoelastic media. The most dramatic effect however is that even small amounts of particles eliminate or drastically shift the region of negative normal stress differences. As far as the structure is concerned, microscopic observations show that particles align in anisotropic as well as in isotropic media. At rest or at relatively low shear stresses the liquid crystalline structure is, in the present case, hardly affected by the presence of the particles. If anything, it becomes more homogeneous. Received: 28 April 1998 Accepted: 28 July 1998     

Bifurcation of the solution to the problem of steady traveling waves in a layer of viscous liquid on an inclined plane

Traveling waves in a viscous liquid flowing down an inclined plane can be described at small and moderate Reynolds numbers by an ordinary differential equation in the thickness of the layer [1, 2]. As the Reynolds number tends to zero, this equation goes over into an equation of third order with quadratic nonlinearity [3]. Periodic solutions of this last equation bifurcating from the plane-parallel solution have been investigated by Nepomnyashchii and Tsvelodub [3–6]. In the present paper, a study is made of the bifurcation of periodic solutions from periodic solutions, namely, an investigation is made of the values of the wave number for which a periodic solution is not unique; a bifurcation equation is derived, the number of bifurcating solutions is found, and their behavior near a bifurcation point is considered; and the bifurcating solutions are continued numerically with respect to a parameter (the wave number) from the neighborhoods of the bifurcation points.