P. Vainshtein

Acoustic enhancement of heat transfer between two parallel plates

Abstract The paper considers a problem in which a steady-state sonic wave is propagated in the longitudinal direction in a fluid enclosed between two horizontal parallel plates which are kept at different temperatures. The distance between the plates is much smaller than the sound wavelength. Rayleighs vortical acoustic streaming that appears in the region between the plates as a result of the sound wave leads to forced heat convection. The effect of that forced convection on heat transferred between the plates is analyzed theoretically. An acoustic Peclet number, which represents the interaction between heat conduction and forced convection is introduced, and asymptotic relations expressing the mean Nusselt number in terms of this dimensionless group are derived. The results obtained demonstrate that acoustic streaming results in a marked enhancement of heat transfer between the plates.

The effect of centreline particle concentration in a wave tube

The interaction of sound waves with an aqueous suspension of solid particles was analysed experimentally and theoretically. A heretofore unreported effect of particle concentration in the vicinity of a wave-tube centreline was observed. The phenomenon is related to the combined effect of Rayleigh-type acoustic streaming, jet-like streaming (quartz wind) and drift forces occurring in the presence of a sonic wave in the suspension-filled tube.

ON THE DRIFT OF AEROSOL PARTICLES IN SONIC FIELDS

Abstract The drifting motion of aerosol particles enclosed in vessels subject to ultrasonic oscillations is analysed theoretically. The geometry considered here is of vessels with dimensions not exceeding the ultrasonic wavelength. This geometry is quite different from previously treated cases, where the flow field dimensions measured many times the ultrasonic wavelength and where the aerosol particles were found to move towards nodes and towards loci of maximum amplitudes, according to their sizes. The results obtained here are rather different and indicate that all particles move away from the oscillating wall and towards the stationary one. These results conform to the motivation of the investigation, which is to protect a clean site from settling particles. The analysis incorporates two-scale expansions methods applied to the multiphase flow equations for a one-dimensional flow model. The results are constructed by the superposition of a slow mean motion of the gas and a fast oscillatory motion associated with the eigenfunctions of the standing waves solution. The combined effect on the particles is a drift in the direction of the stationary wall.

On electroviscous effects in microchannels

This paper contains results of a theoretical investigation on the effect of the diffusive electric double layer (EDL) at the solid–liquid interface on liquid flow through a microchannel between two parallel plates. Unlike previous works, the electrical charge connected with the EDL at the inlet of a channel is accounted for. The Debye–Huckel linear approximation of the surface potential distribution is used to describe the EDL field near the solid–liquid interface. The electrokinetic distance is assumed to be arbitrary. The electrical body force resulting from the double layer field is considered in the equation of motion. This equation is solved for steady-state flow. Effects of the EDL field on the apparent viscosity are discussed.

Dynamics of suspended particles in a two-dimensional high-frequency sonic field

Abstract The interaction of two-dimensional standing sonic waves with particles suspended in a fluid is analyzed. The domain considered is bounded below by a plane plate which performs harmonic oscillations, and above by a stationary plate which is slightly curved. The size of the gap at the axis of symmetry exceeds the sonic wavelength, so that there is at least one velocity node of the standing wave inside the region. The domain is filled with a fluid which contains spherical particles. The steady sonic wave causes a steady particle drift. The curvature of the stationary upper wall produces a two-dimensional standing wave, which causes the suspended particles to move in a direction transverse to the wave front of the applied field. It is shown that in addition to the well known particle drift toward the fluid velocity nodes or antinodes there exists a side drift along the nodes and the antinodes. The direction of the drift depends on the sonic wave frequency and on the fluid-to-particle density ratio. The analysis employs a small parameter perturbation method.

Creeping flow past and within a permeable spheroid

Abstract Flow past and within an isolated permeable spheroid directed along its axis of symmetry is studied. The flow velocity field is solved using the Stokes creeping flow equations governing the fluid motion outside the spheroid, and the Darcy equation within the spheroid. Expressions for the hydrodynamic resistance experienced by oblate and prolate spheroids are derived and analyzed. The limiting cases of permeable circular disks and elongated rods are examined. It is shown that the spheroid’s resistance varies significantly with its aspect ratio and permeability, expressed via the Brinkman parameter.

Resonance gas oscillations in closed tubes

The problem of gas motion in a tube closed at one end and driven at the other by an oscillating poston is studied theoretically. When the piston vibrates with a finite amplitude at the first acoustic resonance frequency, periodic shock waves are generated, travelling back and forth in the tube. A perturbation method, based on a small Mach number. M and a global mass conservation condition, is employed to formulate a solution of the problem in the form of two standing waves separated by a jump (shock front). By expanding the equations of motion in a series of a small parameter e = M ½ , all hydrodynamic properties are predicted with an accuracy to second-order terms, i.e. to e 2 . It is found that the first-order solution coincides with the previous theories of Betchov (1958) and Chester (1964), while additional terms predict a non-homogeneous time-averaged pressure along the tube. This prediction compares favourably with experimental results from the literature. The importance of the phenomenon is discussed in relation to different transport processes in resonance tubes.

Rayleigh streaming at large Reynolds number and its effect on shear flow

A fluid contained between two parallel walls, one of which is at rest and the other moving in the longitudinal direction with a constant velocity, is examined when a standing sound wave is imposed in the transverse direction. Vortical acoustic streaming appears in the region between the walls. The streaming is not affected by the main flow. A qualitative analysis is presented for the Navier-Stokes equations governing the steady-streaming component of the motion. The study considers the case of flow with high streaming Reynolds number and makes an explicit determination of the vorticity in the inviscid core region. The effect of the streaming upon the shear flow in the longitudinal direction is then analysed asymptotically. A periodic structure of the wall shear stress in the transverse direction is detected in which vast areas of vanishing wall shear stress alternate with narrow regions where it increases significantly. A relation expressing the mean wall shear stress in terms of the streaming Reynolds number is derived. Results obtained show that acoustic streaming results in a marked enhancement of the mean wall shear stress at the walls

Side drift of aerosols in a two-dimensional slowly oscillating sonic field

The two-dimensional drifting motion of aerosol particles in vessels under the influence of slow sonic oscillations is analyzed theoretically using the asymptotic small parameter method. The vessel geometry is such that the dimension in the direction of wave propagation does not exceed the sonic wavelength. It was recently shown that in the case of one-dimensional sonic waves, particles move away from the oscillating wall and drift toward the stationary one. The domain considered here is quite different from those previously treated in one-dimensional cases in the sense that the stationary wall of the vessel is slightly curved. It is shown that this curvature causes a drift of aerosol particles in the longitudinal direction, normal to the propagation of the applied sonic field.

Fluidized bed in a confined volume

Coarse solid elastic enough particles form a packed bed in a vertical cylinder confined from below and from above by permeable elastic plates. A gas is forced through the lower plate with a velocity exceeding the terminal (transport) velocity. Adjacent to the lower plate the particles are entrained and impact on the upper plate. As a result, fluidization regimes of still unreported types take place in the confined cylinder. These regimes are analyzed qualitatively by a theoretical model proposed here. This model describes the mean motions of the gas and particles. It includes the mass and momentum equations for the gas and particle phases and the equation of the kinetic energy of particle fluctuations. The system of equations is supplemented by constitutive equations for the averaged drag force, granular pressure, kinetic energy dissipation due to inelastic particle collisions, and energy generation. It is assumed that generation of the kinetic energy is caused by the lateral Magnus force due to particle rotation. Steady state solutions of the equations are obtained, which describe the fluidization regimes in a confined cylinder, namely disperse for a fluidized bed with increasing or decreasing volume fraction and for an inverted packed bed. Experiments are performed to show the existence of the disperse regime of fluidization. Stability of the disperse bed with respect to small perturbations is considered. It is shown that a disperse fluidized bed is unstable for sufficiently concentrated dispersions where the bulk modulus of elasticity of the granular phase is negative. The effect of vibrations of the upper plate upon fluidization regimes is also studied. Resonant frequencies are detected in the concentration region where the bulk modulus of elasticity is positive.