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

The problem of interaction of a rigid body and a boundary of a viscous fluid under acoustic wave propagation is investigated. An example of the motion of a cylinder in the vicinity of a flat rigid wall caused by acoustic field forces is examined. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 10, pp. 74–79, October, 1999.     

Oscillations of a gas bubble in a non-Newtonian liquid under the action of an acoustic field

The evolution of the radius of a spherical cavitation bubble in an incompressible non-Newtonian liquid under the action of an external acoustic field is investigated. Non-Newtonian liquids having relaxation properties and also pseudoplastic and dilatant liquids with powerlaw equation of state are studied. The equations for the oscillation of the gas bubble are derived, the stability of its radial oscillation and its spherical form are investigated, and formulas are given for the characteristic frequency of oscillations of the cavitation hollow in a relaxing liquid. The equations are integrated numerically. It is shown that in a relaxing non-Newtonian liquid the viscosity may lead to the instability of the radial oscillations and the spherical form of the bubble. The results obtained here are compared with the behavior of a gas bubble in a Newtonian liquid.     

Trajectories of charged solid particles in an air jet under the influence of an electrostatic field

Among modern coating techniques electrostatic powder spraying is one of the most attractive. In this method the plastic particles are charged by a high voltage electrode inside a coating gun. The charged particles are entrained by an air jet and directed towards the object to be coated, which is electrically grounded.In the present paper experimental trajectories of particles emerging from an electrostatic gun are determined. The equations of motion of particles in a jet are written in Lagrangean coordinates and solved numerically. Results are compared with the experimental data.     

Suspension of solid particles in a newtonian fluid

We consider the motion of a Newtonian fluid containing solid particles in the case of high concentration (the partial volume of solid is comparable to that of fluid) by using a homogeniztion technique associated with the small parameter ? (the ratio of the particle length to the characteristic macroscopical length). The limit behaviour as ? → 0 is that of fluid with anisotropy properties associated with a microstructure. The evolution equations for the limit flow and for the microstructure are given.     

Calculation of the motion in the near field of an explosion in a solid medium

Some results are presented of calculations of motions in the near field of an explosion in a solid body for which a previously obtained equation of state is employed. The corresponding theoretical and experimental results are compared.     

Dynamic simulation of sedimentation of solid particles in an Oldroyd-B fluid

In this paper we present a two-dimensional numerical study of the viscoelastic effects on the sedimentation of particles in the presence of solid walls or another particle. The Navier-Stokes equations coupled with an Oldroyd-B model are solved using a finite-element method with the EVSS formalism, and the particles are moved according to their equations of motion. In a vertical channel filled with a viscoelastic fluid, a particle settling very close to one side wall experiences a repulsion from the wall; a particle farther away from the wall is attracted toward it. Thus a settling particle will approach an eccentric equilibrium position, which depends on the Reynolds and Deborah numbers. Two particles settling one on top of the other attract and form a doublet if their initial separation is not too large. Two particles settling side by side approach each other and the doublet also rotates till the line of centers is aligned with the direction of sedimentation. The particle-particle interactions are in qualitative agreement with experimental observations, while the wall repulsion has not been documented in experiments. The driving force for lateral migrations is shown to correlate with the pressure distribution on the particle's surface. As a rule, viscoelasticity affects the motion of particles by modifying the pressure distribution on their surface. The direct contribution of viscoelastic normal stresses to the force and torque is not important.     

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.     

Grouping of suspended particles in a standing acoustic wave field

Assuning a snall difference in phase densities averaged equations have been obtained for the motion of a two-phase medium in a standing acoustic wave field. The force causing the relative motion of the phases has been determined. On the basis of the averaged equations obtained the dynamics of the redistribution of particles in the suspension in a plane standing acoustic wave has been studied.Translated from Izvestiya Akadenii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 81–88, September–October, 1984.The authors wish to thank S. A. Regirer for his interest in this work and for useful advice.     

Derivation of a segregation-mixing equation for particles in a fluid medium

The main purpose of this work is to show that the gravity term of the segregation-mixing equation of fine mono-disperse particles in a fluid can be derived from first-principles （i.e., elementary physics）. Our derivation of the gravity-driven flux of particles leads to the simplest case of the Richardson and Zaki correlation. Stokes velocity also naturally appears from the physical parameters of the particles and fluid by means of derivation only. This derivation from first-principle physics has never been presented before. It is applicable in small concentrations of fine particles.     

Three-dimensional linearized stability theory for stratified rock (continuum theory and model of a piecewise-homogeneous medium)

Conclusions Thus, the probability of applying rigorous three-dimensional linearized stability theory to stability problems of stratified rock has been demonstrated in the present work. New qualitative and quantative results have been obtained.This is the complete text of a paper presented at the International Conference on the Mechanical Instability of Rock and Tectonics (Montpelier, France, September 5, 1991 and at the First European Conference on the Mechanics of Deformable Solids (Munich, Germany, 1991). Only the abstract of this article was published in the conference proceedings, not the complete text.Institute of Mechanics, Ukrainian Academy of Sciences, Kiev. Translated from Prikladnaya Mekhanika, Vol. 29, No. 1, pp. 3–18, January, 1993.     

Some properties of far field patterns of acoustic waves in an inhomogeneous medium

In this paper, the step reduction method is discussed, which was advanced by Prof, Yeh Kai-yuan for calculating a non-uniform beam with various sections. The following result is proved. The approximate solution by this method approaches the true solution if the number of the steps approaches the infinity. However, the measure of the error between the limit solution and the ture solution is not认the pure mathematics sense but in the mechanics sense.     

Dynamics of shell structures under impulsive loading (review)

Institute of Geophysics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 26, No. 8, pp. 3–20, August, 1990.     

On the stability of a thermally stratified conducting fluid under the action of aligned magnetic field

The stability of a thermally stable stratified viscous electrically conducting shear flow is investigated in the presence of an impressed uniform aligned magnetic field. Only two-dimensional disturbances are studied in this paper because Squire's theorem does not apply in general, owing to the presence of the aligned magnetic field. The analysis is partly analytical and partly numerical. The asymptotic solutions for non-viscous fluid are first obtained analytically and they are then improved by introducing viscous and thermal diffusion terms (but only for =1) to get a uniformly valid solution. The neutral stability curves are numerically computed for a range of values of Richardson and Stuart numbers, which show that the flow is completely stabilized when a Stuart number exceeds a certain value for a given R _i>0. It is shown that the combined effects of magnetic field and stratification is to make the system stable to two-dimensional disturbances at lower Stuart number than the one given by Stuart (1954) in the absence of thermal stratification.