This article studies the acoustic streaming pattern near a small sphere due to two orthogonal standing waves, which have the same frequency but, in general, are out of phase. The results indicate a new kind of acoustic streaming arising from the circular motion in the medium caused by the two waves.
There is a general formulation by Nyborg that accounts for the streaming inside the viscous boundary layer on a solid surface in the presence of a sound wave [W. L. Nyborg, J. Acoust. Soc. Am. 30, 329 (1958)]. Using the streaming velocity at the edge of the viscous layer from Nyborg’s theory as a slip boundary condition, the streaming pattern at large outside the layer for various geometries is calculated. Compressibility of the first-order wave motion is retained, such that its effect is reflected in the boundary condition for the secondary flow, although the latter is considered as incompressible. For the case of a cylinder or a sphere situated at a velocity antinode of a plane standing wave, it is found that the streamlines are closed loops as a consequence of compressibility. If the solid body is displaced from the antinode, the vortex pattern becomes asymmetric. A weak viscous drag acts on the object in the direction opposing the displacement. As a reaction, a weak net flow arises in the direction of the displacement. These findings are consistent with observations, and are absent in previous theoretical treatments of the problem, in which the oscillating flow is assumed to be uniform and incompressible.
In this investigation, our previous theoretical result on the subject of the acoustic radiation force on a heated sphere [Lee and Wang, J. Acoust. Soc. Am. 75, 88-96 (1984) ] is reexamined. For a more complete understanding, effects of heat transfer and acoustic streaming are taken into consideration. Essentially, it was found that at high sound-pressure levels in a steady situation, the force is not affected significantly by the temperature profile, consistent with the result of an experimental work [Leung and Wang, J. Acoust. Soc. Am. 77, 1686-1691 (1985) ]. This resolves the earlier apparent contradiction between the theory and the experiment. But our previous result is reaffirmed that, if excessive hot air is accumulated around the sphere, which can happen in transient situations, the force can be weakened or reversed in sign. As a by-product of our study, a heat transfer model due to acoustic streaming was also found.
PACS numbers: 43.25.Uv
INTRODUCTION
Background information on the acoustic force was men-
The physical mechanism governing the centring of a hollow liquid shell in capillary oscillations, which has been observed in experiments, is investigated theoretically. First, the shell is assumed to be inviscid and to have a thickness that is much less than its spherical radius. A system of one-dimensional nonlinear equations of motion is derived using a thin-sheet model. From a numerical study the nonlinear effects of the wave are found to cause the core to oscillate slowly relative to the shell while the centre of mass of the whole system remains stationary. The effects of small viscosity are then considered in an approximation. Finally the strength of the centring mechanism is compared with that of the decentring effect due to buoyancy. The findings are consistent with the limited experimental information available.
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