Acoustic streaming generated by standing waves in two-dimensional channels of arbitrary width

Abstract

An analytic solution is derived for acoustic streaming generated by a standing wave in a viscous fluid that occupies a two-dimensional channel of arbitrary width. The main restriction is that the boundary layer thickness is a small fraction of the acoustic wavelength. Both the outer, Rayleigh streaming vortices and the inner, boundary layer vortices are accurately described. For wide channels and outside the boundary layer, the solution is in agreement with results obtained by others for Rayleigh streaming. As channel width is reduced, the inner vortices increase in size relative to the Rayleigh vortices. For channel widths less than about 10 times the boundary layer thickness, the Rayleigh vortices disappear and only the inner vortices exist. The obtained solution is compared with those derived by Rayleigh, Westervelt, Nyborg, and Zarembo.