Outer acoustic streaming

Abstract

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.

Acoustic/steady streaming from a motionless boundary and related phenomena: generalized treatment of the inner streaming and examples

“…The flow pattern is not only axisymmetric, but also symmetric with respect to the equatorial plane. The second diagram is similar to one of those of Lee & Wang (1990), except that they had the sphere displaced above the antinode (K < 0 in our terms), so that their flow pattern appears vertically inverted as compared to ours. At K = ∞, when the sphere is at the velocity node, the results of Zhao et al (1999b) are recovered.…”

“…Nonetheless, the final result for the outer streaming (and thus for the effective slip velocity, although they do not work in such terms) happens to be correct in the sense that one comes up with the same result if the primary oscillatory flow in the Stokes layer is treated as compressible and adiabatic. In fact, it is considered compressible and adiabatic by Nyborg (1958) and Lee & Wang (1990), as well as by Zhao, Sadhal & Trinh (1999b). However, there comes another issue.…”

“…What we eventually come up with in § 3.2 generalizes certain results from the literature. In particular, as compared to Lee & Wang (1990) and Zhao et al (1999b), the non-adiabatic effects are taken into account and besides a leading-order result for the streaming which is uniformly valid for all positions of the sphere within the standing wave (including the velocity node) is constructed. As compared to Gopinath & Trinh (2000), the viscosity variability (non-adiabatic) is additionally taken into account, even though fewer terms of the expansion are eventually retained.…”

On the acoustic levitation stability behaviour of spherical and ellipsoidal particles

“…For the axial force, the streaming patterns are not symmetric about the horizontal axis of the particle. For rigid bodies, the drag force of the streaming acts in favour of the radiation force and increases the total force (Lee & Wang 1990). For droplets in a highly viscous fluid, the internal liquid flow will be coupling with the external acoustic streaming (Rednikov et al 2006).…”

Ablation of Chronic Total Occlusions Using Kilohertz-Frequency Mechanical Vibrations in Minimally Invasive Angioplasty Procedures

“…Atar et al (27) suggested that the ultrasonic longitudinal vibration of the wire waveguide distal-tip results in four major potentially disruptive events; direct contact ablation, pressure wave components, cavitation and acoustic micro-streaming and all these appear to be related to the distal-tip displacement amplitude, frequency and geometry (39)(40)(41)(42). A diagram of the distal section of the wire waveguide and location of disruption mechanisms is shown in Figure 3.…”