Effect of surfactant on bubble motion close to a solid wall

Numerical analysis is used to study the effect of surfactants on the parameters of gas-bubble motion close to a solid wall under the influence of abrupt pressure change at infinity.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 34, No. 1, pp. 84–88, January, 1978.     

Near-wake flow characteristics of two side-by-side circular cylinders close to a wall

Flow characteristics in the near wake of two identical side-by-side circular cylinders located close to a fully developed turbulent boundary layer are investigated experimentally using the particle image velocimetry (PIV) and the pressure sensor. The Reynolds number based on the cylinder diameter (D) is 1,696, the boundary layer thickness is 6.6 D, the cylinder center-to-center spacing (T) is varied from T/D = 1 to 1.906, and the gap spacing between the lower cylinder and the wall (G) is varied from G/D = 0 to 1.811. To study the effects of changing the gap ratios of T/D and G/D on the wake flow, various wake characteristics such as averaged streamlines, Reynolds stress and vorticity contours as well as other key flow features including the length scales and the Strouhal number are investigated for different ratios of T/D and G/D. According to these wake characteristics, five basic flow patterns have been identified.     

Between two limits: Flow separation behind a bluff body close to a wall

There are two classical cases of a considerable flow separation:?A body in a flow without limits is leading to a separation behind the body, a wall with a remarkable change of contour is leading to a separation region at the wall. Here, both situations are considered for the two-dimensional case of a flow past a cylinder with a triangle cross section. The free flow case and the flow at a cylinder directly placed at a wall is investigated. An intermediate situation can be observed, when the cylinder is placed close to the wall. The occurring complex separation region can be interpreted in that way, that both separation regions, body and wall related, are existing. Es gibt zwei “klassische” Fälle der massiven Strömungsablösung: An einem frei umströmten Körper entsteht ein Ablösegebiet hinter dem Körper, an einer Wand mit starker Konturänderung entsteht ein Ablösegebiet an der Wand. Beide Situationen werden für den zweidimensionalen Fall der Umströmung eines Zylinders mit dreieckegem Querschnitt gezeigt. Dabei handelt es sich einmal um die freie Umströmung und zum anderen um die Strömung längs einer Wand, auf der dieser Zylinder angebracht ist. Eine Situation zwischen diesen Grenzfällen entsteht, wenn der Zylinder nahe der Wand positioniert wird. Das komplexe Ablösegebiet kann dann so interpretiert werden, daß beide Ablösegebiete, d.h. das zylinder- und das wandgebundene Gebiet vorhanden sind.     

壁面形貌对磁流变液滑移特性的影响

为了分析传动壁面形貌对磁流变液滑移特性的影响规律,建立磁流变传动性能实验台,分析了传动壁面沟槽形状、沟槽密度、沟槽深度、纹理类型等对滑移强度的影响规律,研究发现,滑移强度与传动壁面表面形貌有关,壁面沟槽形状对滑移强度影响并不明显,三角形截面形状略优于矩形;增加沟槽密度可提升磁流变液的传动能力,沟槽深度在0～0.5mm范围内存在最优值;同心圆、光滑、凹坑及径向辐射条纹4种壁面形貌中,滑移强度由大到小依次是:径向辐射条纹、凹坑、光滑、同心圆,改变壁面形貌可使滑移强度提高10%。     

Generalized squirming motion of a sphere

A number of swimming microorganisms, such as ciliates (Opalina) and multicellular colonies of flagellates (Volvox), are approximately spherical in shape and swim using beating arrays of cilia or short flagella covering their surfaces. Their physical actuation on the fluid may be mathematically modeled as the generation of surface velocities on a continuous spherical surface—a model known in the literature as squirming, which has been used to address various aspects of the biological physics of locomotion. Previous analyses of squirming assumed axisymmetric fluid motion and hence required all swimming kinematics to take place along a line. In this paper we generalize squirming to three spatial dimensions. We derive analytically the flow field surrounding a spherical squirmer with arbitrary surface motion and use it to derive its three-dimensional translational and rotational swimming kinematics. We then use our results to physically interpret the flow field induced by the swimmer in terms of fundamental flow singularities up to terms decaying spatially as \({\sim } 1/r^3\) . Our results will make it possible to develop new models in biological physics, in particular in the area of hydrodynamic interactions and collective locomotion.     

Stokes flow with slip caused by the axisymmetric motion of a sphere bisected by a free surface bounding a semi-infinite micropolar fluid

The first part of this paper investigates the motion of a solid spherical particle in an incompressible axisymmetric micropolar Stokes flow. A linear slip, Basset-type, boundary condition has been used. Expressions for the drag force and terminal velocity has been obtained in terms of the parameter characterizing the slip friction. In the second part, we consider the flow of an incompressible axisymmetrical steady semi-infinite micropolar fluid arising from the motion of a sphere bisected by a free surface bounding a semi-infinite micropolar fluid. Two cases are considered for the motion of the sphere: perpendicular translation to the free surface and rotation about a diameter which is also perpendicular to the free surface. The speed of the translational motion and the angular speed for the rotational motion of the sphere are assumed to be small so that the nonlinear terms in the equations of motion can be neglected under the usual Stokesian approximation. Also a linear slip, Basset-type, has been used. The analytical expressions for velocity and microrotation components are determined in terms of modified Bessel functions of second kind and Legendre polynomials. The drag for the translation case and the couple for the rotational motion on the submerged half sphere are calculated and expressed in terms of nondimensional coefficients whose variation is studied numerically. The variations of the drag and couple coefficients with respect to the micropolarity parameter and slip parameter are tabulated and displayed graphically.     

Resistance to the free steady-state motion of a sphere in a viscous medium

An approximate method is proposed for calculating the drag and velocity of spherical particles in a viscous medium.     

Study of the collapse of a cavitation cavity close to a solid wall

The dynamics of cavitation cavities are affected by the presence of a wall. An expression is obtained for the pressure fluctuations acting on the wall.     

A note on impulsive sphere motion beneath a free-surface

A general framework is presented for solving the impulsive oblique motion of a spherical body in close proximity and below a free-surface. The fluid is considered to be impulsive and the flow as incompressible. The irrotational flow field is deduced from a velocity potential. The full nonlinear problem is reduced to a sequence of boundary-value problems by employing a small-time expansion technique. The mixed boundary conditions are of a Dirichlet type on the undisturbed free-surface and of a Neumann type on the equilibrium spherical shape. The solution is obtained by employing a Green's function and the method of multipoles expansions. General expressions, correct to each order in the small-time, are given for the free-surface deflections and the pressure force experienced by the moving sphere.     

Simulation of random close packed discs and spheres

Random packing is a phenomenon which is observed on a regular basis but which currently lacks any constructive mathematical formalism. Consequently, much of our understanding of packing structures comes from experimental physics and mathematical modeling. Using Monte Carlo simulations as a model of real sphere aggregates, estimates of contact distributions are obtained for various binary mixtures of spheres. We find that the number of contacts can be described by a single algebraic function of two variables: the ratio of radii, and the concentration of small spheres.     

Hot-wire anemometer measurement of mean velocity very close to a wall

This paper analyzes the errors arising in the use of a hot-wire anemometer for measurements in flow near the wall and associated with proximity to a heat-conducting surface and large velocity gradients.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 36, No. 6, pp. 985–990, June, 1979.     

Transformation of sliding motion to rolling during spheres collision

In this research, we have investigated the three-dimensional elastic collision of two balls, based on friction in the tangential plane. Our aim is to offer analytical closed form relations for post collision parameters such as linear and angular velocities, collision time and tangential and normal impulse in three dimensions. To simplify the problem, stick regime is not considered. In other words, balls have a low tangential coefficient of restitution. Sliding, sliding then rolling, and rolling at the beginning of contact are three cases that can occur during impact which have been considered in our research. The normal interaction force is described by the Hertz contact force and dimensionless analysis is used for investigating normal interaction force; furthermore, Coulomb friction is considered during sliding. Experimental data for collisions show when sliding exists through the impact, tangential impulses can be taken as frictional impulses using the Coulomb law if the dynamic regime is not stick regime. To identify transformation of sliding motion to rolling or sticking during the impact process, linear and trigonometric functions are considered as an approximation for the normal interaction force. Afterwards, we have obtained the condition for the possibility of this transformation; moreover, we can estimate the duration of sliding and rolling or sticking. We have obtained an analytical solution for maximum force and deformation, collision time, impulses and post-collision linear and angular velocities in three dimensions.     

Numerical study of the effects of slip and a temperature discontinuity on the surface of a sphere in a supersonic flow

This article examines the effect of boundary conditions for slip and temperature discontinuity on drag and heat-transfer characteristics. Numerical solutions of the Navier-Stokes equations are used to analyze the dependence of these effects on the governing parameters of the flow.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 53, No. 3, pp. 446–450, September, 1987.     

Study of the axially symmetric motion of an incompressible viscous fluid between two concentric rotating spheres

The research reported herein involves the study of the steady state and transient motion of a system consisting of an incompressible, Newtonian fluid in an annulus between two concentric, rotating, rigid spheres. The primary purpose of the research is to study the use of an approximate analytical method for analyzing the transient motion of the fluid in the annulus and the spheres which are started suddenly due to the action of prescribed torques. The problems include cases where: (a) one (or both) spheres rotate with prescribed constant angular velocities and (b) one sphere rotates due to the action of an applied constant or impulsive torque.In this research, the coupled solid and fluid equations of motion are linearized by employing the perturbation technique. The meridional dependence in these equations is removed by expanding the dependent variables in a series of Gegenbauer functions with variable coefficients and employing the orthogonality property of these functions. The equations for the variable coefficients are solved by separation of variables and Laplace transform methods. Results for the stream function, circumferential function, angular velocity of the spheres and torque coefficient are presented as a function of time for various values of the dimensionless system parameters.     

The effect of the slip boundary condition on the flow of fluids in a channel

Summary The assumption that a liquid adheres to a solid boundary (no-slip boundary condition) is one of the central tenets of the Navier-Stokes theory. However, there are situations wherein this assumption does not hold. In this paper we investigate the consequences of slip at the wall on the flow of a linearly viscous fluid in a channel. Usually, the slip is assumed to depend on the shear stress at the wall. However, a number of experiments suggests that the slip velocity also depends on the normal stress. Thus, we investigate the flow of a linearly viscous fluid when the slip depends on both the shear stress and the normal stress. In regions where the slip velocity depends strongly on the normal stress, the flow field in a channel is not fully developed and rectilinear flow is not possible. Also, it is shown that, in general, traditional methods such as the Mooney method cannot be used for calculating the slip velocity.     

On the slow motion of a sphere in fluids with non-constant viscosities

We study a slowly moving sphere in fluids where the viscosity depends upon factors such as shear-rate, temperature and pressure, with the flow field approximated by the Stokes flow past a sphere. We derive an expression for the stresses generated in the fluid due to these various factors. This gives us information about both, the force imposed by the fluid upon the sphere and also the reaction force due to the sphere upon the fluid, referred to as the stress density. The values of the force and stress density are numerically computed in each of the cases and analyzed for various values of the flow and material parameters. Our computations show interesting variations in the distribution of stress density in the fluid for the various cases and also give us valuable information about the effect of walls. Our calculations also indicate that particle heating or cooling can serve as a significant control parameter since the drag force upon the sphere increases dramatically for a cold particle and can be reduced considerably upon heating it.     

Turbulent wall motion of a viscoelastic fluid

Qualitative agreement between the theoretically calculated parameters and published experimental data is obtained for turbulent wall flow of a drag-reducing aqueous polymer solution treated as a viscoelastic medium.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 30, No. 1, pp. 109–114, January, 1976.     

The effect of a penny-shaped crack on the distribution of stress in an elastic sphere

The paper presents an analysis of the distribution of stress in an elastic sphere when it is deformed by the application of pressure to the inner surfaces of a penny-shaped crack, which is situated in a diametrical plane. Three problems are discussed. By application of transform method and the theory of dual integral equations each problem is reduced to that of solving a Fredholm integral equation of second kind. Expressions for various quantities of physical interest are derived for small values of the ratio of radius of crack to that of sphere by finding an iterative solution of this equation. For values of this ratio near unity the integral equations have been solved numerically.     

The unsteady hydrodynamic force during the collision of two spheres in a viscous fluid

The time-dependent Stokes equations were solved in the vicinity of two spheres colliding in a viscous fluid with viscosity ν to determine the rate of change of the hydrodynamic forces during large accelerations associated with Hertzian mechanical contact of small duration \({\tau_{\rm c}}\). It was assumed that the gap clearance remains finite during contact and is approximately equal to the height σ of surface micro-asperities. The initial condition corresponds to the steady-state axisymmetric solution of Cooley and O’Neill (Mathematika 16:37–49, 1969), and the initial value problem for the time-dependent Stokes streamfunction was solved using Laplace transform methods. Assuming that σ is small compared to the sphere radius a, we used singular perturbation expansions and tangent-sphere coordinates to obtain an asymptotic solution for the viscous flow in the gap and around the moving sphere. The solution provides the dependence of the resistance, added mass and history forces on σ, the sphere velocity and acceleration, and the ratio of the sphere diameters. We found that the relative importance of viscous and mechanical forces during contact depends on a new Stokes number \({St_{\rm c}=\sigma^2/\nu \tau_{\rm c}}\). Integration of Newton’s equation for the motion of the sphere during mechanical contact showed that there is a critical \({St_{\rm c}=O(\sigma/a)}\) for which there is no rebound at the end of contact.     

A numerical model for determining the motion of a bubble close to a fixed rigid structure in a fluid

This paper is concerned with the problem of modelling the motion of a bubble close to a rigid structure in an infinite fluid. It is well known that the boundary integral method is a powerful technique for modelling the motion of a single bubble in a fluid. In this paper we shall present a modified boundary integral method for modelling the motion of a bubble close to a fixed finite rigid structure, and discuss a numerical scheme for solving the resulting integral equation for three-dimensional problems. Finally, we illustrate our method with some typical numerical results.