OUTER ACOUSTIC STREAMING

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. © 1990, Acoustical Society of America. All rights reserved.