Forced oscillations of two gas bubbles in a fluid in the vicinity of bubble contact

For a theoretical derivation of bubble coalescence conditions, nonlinear forced oscillations of two closely spaced spherical bubbles subjected to the action of a periodic external pressure field are considered. The equations, asymptotic with respect to a small distance between the bubble surfaces, are derived to describe the approach of the bubbles under the action of (i) the Bjerknes attraction force averaged over the oscillation period and (ii) the viscous drag. It is shown that due to nonlinear interaction of the viscous drag with the radial and translational oscillations of the bubbles a unidirectional repulsive force is generated, which prevents the approach of the bubbles. The coalescence of the bubbles is possible when the nondimensional parameter combined from the amplitude and frequency of the external pressure field, the bubble radius, and the fluid viscosity is greater than a certain critical value. The obtained coalescence condition is qualitatively confirmed by experiments.     

Lift Force Acting on a Heavy Solid in a Rotating Liquid-Filled Cavity with a Time-Varying Rotation Rate

The dynamics of a heavy cylindrical body in a liquid-filled horizontal cylindrical cavity with a time-varying rotation rate is experimentally investigated. The body is near the cavity boundary under a centrifugal force and undergoes solid-body rotation together with the liquid and the cavity at a fixed rotation rate. The dependence of the body dynamics on the amplitude and frequency of modulation of the rotation rate is investigated. It is found that at a critical amplitude of modulation (at definite frequency), the heavy body repulses from the cavity boundary and comes into a steady state at some distance from the wall. It is found that the average lift force (repulsive one) is generated by the azimuthal oscillation of the body in the rotating frame of reference and manifests itself at a distance comparable to the thickness of the viscous boundary layer. In the experiments, we observed azimuthal drift of the body due to asymmetric azimuthal oscillations of the body. In the limit of high frequency of the rotation rate modulation, the dependence of the lift force coefficient on the gap between the body and the wall is determined.     

电解质吸附对水基带电表面黏着的影响

为研究界面黏着,利用表面力仪在高离子强度电解质水溶液中测量负电云母表面之间的法向力. 在纯水中,因范德华吸引,两表面跳跃至直接接触(间距0 ?),分离两表面时测得界面黏着力为?46.7 mN/m. 在0.1 mol/L K₂SO₄中,因K+离子牢固吸附于云母,表面间距稳定于5 ?,黏着力仅?2.9 mN/m;在0.1 mol/L Ca(NO₃)₂中,云母表面吸附的Ca2+离子产生显著短程水合排斥,但在较低载荷下解吸附,导致两表面直接接触,黏着力高达?40.7 mN/m. 加入Ca(OH)₂于0.1 mol/L K₂SO₄仅产生微弱短程排斥,黏着状态几乎与纯K₂SO₄水溶液中相同. 聚电解质PCE从0.1 mol/L K₂SO₄中吸附于云母表面且诱导远程空间位阻排斥,但在中等载荷下解吸附,导致两表面轻度黏着(间距5 ?);牢固吸附于云母表面的PNS高分子薄膜之间的空间位阻完全阻止云母界面黏着. 牢固吸附是电解质吸附层稳定阻止界面黏着的必要条件.      

MHD控制超声速边界层的理论研究和数值分析

对MHD(mechanisms of magnetohy drodynamics)控制超声速平板湍流边界层的机理进行了理论研究和数值模拟. 理论上,采用等离子体低频近似碰撞频率模型,建立等离子体中电子和离子的力平衡方程,得到等离子体速度、极化电场以及边界层速度. 数值上,通过空间HLLE格式、LU--SGS时间推进求解时均磁流体动力学湍流方程,其中湍流模型采用sst--k\omega双方程模型. 研究结果表明:(1)边界层速度的理论结果和数值结果误差在7%范围内;(2)只有磁场而电场为零时,洛仑兹力起到减小摩阻的作用. 施加电场后,洛仑兹力能够加速边界层低速区流体;(3) 在边界层外层,越靠近壁面,作用参数越小;而在边界层近壁区黏性底层,虽然惯性力减小, 但黏性力却迅速增加,因此越靠近壁面,作用参数反而越大,加速低速流的代价增加.      

Dynamics of a rigid cylinder near a plane boundary in the radiation field of an acoustic wave

An approach is described for investigation of the interaction between a rigid body and a viscous fluid boundary under acoustic wave propagation. The influence of the liquid on the rigid body is determined as a mean force, which is a constant in the time component of the hydrodynamic force. This enables the use of a previously developed technique for calculation of pressure in a compressible viscous liquid. The technique takes into account the second-order terms with respect to the wave field parameters and is based on investigation of a system of initially nonlinear hydromechanics equations that can be simplified with respect to the wave motion parameters of the liquid. It has proven possible to retain the second-order terms for determination of stresses in the liquid without having to solve the system of nonlinear equations. The stresses can be expressed in terms of parameters found in the solution of the linearized equations of the compressible viscous liquid. In this way, the solution of linearized equations is expressed in terms of a scalar and vector potentials. The problem statement is derived for a rigid cylinder located near a rigid flat wall under the effects of a wave propagating perpendicular to the wall. The solution for this particular example is obtained.     

Mechanics of physisorption on elastomer surface

Mechanical aspects of physisorption on elastomeric substrates are studied via a continuum model in combination with the Lennard-Jones potential. In light of the incompressibility of elastomers, it is shown that the presence of a zero-dimensional adsorbate gives rise to a distributed force on the surface of the substrate. The induced surface deformation is determined, and the adsorption force and energy which depend on the substrate stiffness are derived. The results are then used to examine mutual interaction between two like adsorbates with small spacing, showing complicated attraction and repulsion arising from elastic deformation of the substrate. The dipole and quadruple moments of an adsorbate are also calculated, and the multipole approximation is adopted to quantify the interaction when the two adsorbates are separated remotely.     

Force interaction of a sphere and a viscous liquid in the presence of a wall

The problem of the force interaction of a vibrating sphere and a viscous liquid bounded from outside by a rigid wall at rest is studied under the assumption that the largest displacement of the sphere is small compared to its radius and the radius of the sphere is small compared to the distance between the sphere and the wall surface. The liquid flow and the force exerted by the liquid on the sphere are determined. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol 41, No. 1, pp. 57–62, January–February, 2000.     

On the interaction forces between evaporating drops in charged liquid-drop systems

The pairwise hydrodynamic and electrostatic interaction between micrometer-sized water droplets at small distances between them due to their evaporation and the presence of an electric charge on at least one of them is considered. The velocities of the steady-state motion of charged water drops with radii of 1 and 10 μm evaporating in air are calculated. It is shown that at small distances between the drops the joint action of hydrodynamic attraction and polarization interaction, always of attraction type, favor the coalescence of the drops (or drops and solid particles), leading to the displacement of the maximum of the function of drop distribution over size to the region of greater sizes and the gravity sedimentation of large drops. At large distances between the drops, when the short-distance hydrodynamic and polarization attractive forces become smaller than the long-distance Coulomb repulsion forces between likely charged particles, this distance tends to increase. These phenomena give a microphysical explanation to the phenomenon of electrostatic blooming in optically dense smokes and mists.     

A light cylinder under horizontal vibration in a cavity filled with a fluid

The behavior of a light cylindrical body of circular cross-section under horizontal vibration in a rectangular cavity filled with a fluid is experimentally investigated. At critical vibration intensity the body is repelled from the upper side of the cavity and takes up a stable suspended position, in which the gravity field is balanced by the vibrational repulsive force, executing longitudinal oscillations. As the vibrations are intensified, the gap between the cylinder and the wall widens. A new form of instability, namely, the excitation of the tangential motion of the body along the vibration axis, is found to exist on the supercritical range. The cylinder is at a finite distance from the upper side of the cavity and the tangential motion is due to the loss of symmetry of the oscillating motion. The transition of the cylinder to the suspended state and its return to the wall, as well as the excitation of the average longitudinal motion and its cessation, occur thresholdwise and have a hysteresis. The body dynamics are studied as a function of the dimensionless vibration frequency.     

Modeling of friction at different scale levels

We construct a model for studying the common influence of the imperfect elasticity of actual bodies, the microgeometry of their surfaces, and their adhesive interaction on the contact characteristics (the contact pressure distribution, the region of actual contact) and on the sliding friction force. The model is based on the solution of a plane contact problem of sliding of a rigid body with a regular relief on the boundary of a viscoelastic foundation with surface molecular attraction in the gap between the surfaces taken into account. We analyze the influence of the surface microgeometry parameters at different scale levels on the character of the surface interaction (the saturated or discrete contact) and the friction force for different sliding velocities of the contacting bodies.     

Two-dimensional Green's functions in anisotropic multiferroic bimaterials with a viscous interface

We derive, by virtue of the unified Stroh formalism, the extremely concise and elegant solutions for two-dimensional and (quasi-static) time-dependent Green's functions in anisotropic magnetoelectroelastic multiferroic bimaterials with a viscous interface subjected to an extended line force and an extended line dislocation located in the upper half-plane. It is found for the first time that, in the multiferroic bimaterial Green's functions, there are 25 static image singularities and 50 moving image singularities in the form of the extended line force and extended line dislocation in the upper or lower half-plane. It is further observed that, as time evolves, the moving image singularities, which originate from the locations of the static image singularities, will move further away from the viscous interface with explicit time-dependent locations. Moreover, explicit expression of the time-dependent image force on the extended line dislocation due to its interaction with the viscous interface is derived, which is also valid for mathematically degenerate materials. Several special cases are discussed in detail for the image force expression to illustrate the influence of the viscous interface on the mobility of the extended line dislocation, and various interesting features are observed. These Green's functions can not only be directly applied to the study of dislocation mobility in the novel multiferroic bimaterials, they can also be utilized as kernel functions in a boundary integral formulation to investigate more complicated boundary value problems where multiferroic materials/composites are involved.     

Lift force exerted on a spherical particle in a laminar boundary layer

A spherical particle moving in an unbounded viscous shear flow is acted upon by a lift force [1, 2] which results from taking the inertial terms into account in the equations of motion. When the particle moves at the bottom of a laminar boundary layer the magnitude of the force differs from that obtained in [1, 2], The problem of determining the lift force exerted on the particle as a function of its distance from the wall has been solved by matched asymptotic expansions. The magnitude of the force is expressed in terms of a multiple integral which can be evaluated numerically.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 66–71, September–October, 1989.In conclusion, the author wishes to thank M. N. Kogan, N. K. Makashev, and A. Yu. Boris for useful discussions.     

Liquid flow in a simplex swirl nozzle

Pressure-swirl nozzles are widely used in applications such as combustion, painting, air-conditioning, and fire suppression. Understanding the effects of nozzle geometry and inlet flow conditions on liquid film thickness, discharge coefficient and spray angle is very important in nozzle design. The nozzle-internal flow is two-phase with a secondary flow which makes its detailed analysis rather complex. In the current work, the flow field inside a pressure-swirl nozzle is studied theoretically. Using the integral momentum method, the growth of the boundary layer from the nozzle entry to the orifice exit is investigated and the velocity through the boundary layer and the main body of the swirling liquid is calculated. A numerical modeling and a series of experiments have also been performed to validate the theoretical results. The effect of various geometrical parameters is studied and results are compared for viscous and inviscid cases. In addition, the condition in which the centrifugal force of the swirling flow overcomes the viscous force and induces an air core is predicted. The theoretical analysis discussed in this paper provides better criteria for the design and the performance analysis of nozzles.     

An Embedding Method for Bluff Body Flows: Interactions of Two Side-by-Side Cylinder Wakes

We introduce a simple method for the numerical simulation of bluff body flows where the solid object is represented by a distributed body force in the Navier–Stokes equations. The body force density is found at every time step to reduce the velocity within the computational cells occupied by the rigid body to a prescribed value. The method combines certain ideas from the immersed boundary method which was developed to treat biofluid mechanical flows and the volume-of-fluid method for simulating flows with fluid–fluid interfaces. The main advantage of this embedding method is that the computations can be effected on a regular Cartesian grid, without the need to fit the grid to the bluff body surfaces. Thus, flow past several complex bodies can be treated as easily as flow past a single body. The method is validated by reproducing well-established results for vortex shedding from a stationary cylinder. The flow past two side-by-side cylinders is then investigated. When the distance between the cylinders is small, they are seen to shed vortices in-phase, whereas for larger distances, the shedding occurs in anti-phase. For intermediate distances, various shedding patterns are observed, including quasi-periodic, asymmetric and chaotic regimes. Mean values and phase portraits associated with the cylinder lift and drag coefficients, as well as spectral analysis of the same data, are used to describe the flow. A transition diagram that can be compared with experiments or models outlines the various dynamical regimes as a function of the distance between the cylinders and the Reynolds number.     

A NONLINEAR FLUID–STRUCTURE INTERACTION ANALYSIS OF A NEAR-BED SUBMARINE PIPELINE IN A CURRENT

A negative lift force (attraction) can be induced on a near-bed pipeline in a horizontal current due to asymmetric flow. This negative lift force has a significant influence on the behaviour of the near-bed pipeline, causing two remarkable failure patterns. One failure pattern is due to stability loss, and the pipeline fully rests on the seabed. The other is due to the excessive stress or deformation even if the pipeline is stable in a position between the original equilibrium position and the seabed. A quantitative method to assess these two failure patterns by combining boundary element and finite element methods is proposed in this paper. This is a nonlinear fluid–structure interaction problem, and an iteration procedure is used herein to solve it. Numerical examples reveal that there exists a critical current velocity, above which the pipeline fails. The relationship between the critical velocity and the distance from the pipeline to the seabed is given.     

Role of the pressure gradient in flows controlled by a near-wall body force

Steady two-dimensional flows of a viscous incompressible fluid over a plane boundary in the presence of a near-wall body force are studied. The calculations are performed for a very simple one-parameter force distribution simulating the action of a single plasma actuator. The important role played by the pressure gradient in the flows controlled by body forces is shown.     

Elastic interaction of point defects in crystals with cubic symmetry

The energy of elastic mechanical interaction between point defects in cubic crystals is analyzed numerically. The finite-element complex ANSYS is used to investigate the character of interaction between point defects depending on their location along the crystallographic directions 〈100〉, 〈110〉, 〈111〉 and on the distance from the free boundary of the crystal. The numerical results are compared with the results of analytic computations of the energy of interaction between two point defects in an infinite anisotropic medium with cubic symmetry. The interaction between compressible and incompressible defects of general type is studied. Conditions for onset of elastic attraction between the defects, which leads to general relaxation of the crystal elastic energy, are obtained.     

Motion of a cylinder in a viscous electroconductive medium with a magnetic field

The method of force sources is used to consider the planar problem of the motion of a circular cylinder in a viscous electroconductive medium with a magnetic field. The conventional and magnetic Reynolds numbers are assumed to be small. Expressions are obtained for the hydrodynamic reaction forces of the medium, acting on the moving cylinder. It is shown that as a result of the flow anisotropy in the medium, caused by the magnetic field, in addition to the resistance forces on bodies moving at an angle to the field, there are deflecting forces perpendicular to the velocity vector. The velocity field disturbances at great distances from the moving cylinder are determined.The problems of viscous electroconductive flow about solid bodies in the presence of a magnetic field constitute one of the divisions of magnetohydrodynamics. Motion of an electroconductive medium in a magnetic field gives rise to inductive electromagnetic fields and currents which interact with the velocity and pressure hydrodynamic fields in the medium [1, 2]. Under conditions of sufficiently strong interaction, the number of independent flow similarity parameters in MHD is considerably greater than in conventional hydrodynamics. This circumstance complicates the theoretical analysis of MHD flow about bodies, and therefore we must limit ourselves to consideration of individual particular flow cases.Here we consider the linear problem of the motion of an infinite circular cylinder in a viscous incompressible medium with finite electroconductivity located in a uniform magnetic field.There are many studies devoted to the flow of a viscous electroconductive medium with a magnetic field about solid bodies (see, for example, [3–5]). Because of this, some of the results obtained here include previously known results, which will be indicated below. In contrast to the cited studies, the examination is made by the method of force sources, suggested in [6]. This method permits obtaining integral equations for the distribution of the forces acting on the surface of the moving body. Their solution is obtained for small Reynolds and Hartmann numbers. Then the nature of the velocity disturbances at great distances from the body are determined. These results are compared with conventional viscous flow about a cylinder in the Oseen approximation.