Acoustic Streaming due to Attenuated Plane Waves

Abstract

Theories for calculating steady streaming associated with sound fields are reviewed, comparing the methods and approximations of various authors. Two illustrative problems are worked out, both for rectilinear flow due to irrotational sound fields. The first deals with a single attenuated plane wave traveling down a tube, as in Cady's quartz wind experiments. In the second, a pair of crossed plane waves is treated, giving rise to a quite different kind of streaming. In obtaining solutions, attention is given to boundary conditions; here, gradients of She excess static pressure, another second-order quantity, come into consideration. Significantly, streaming speeds depend critically upon α, the attenuation constant, where α may be due to any common cause, such as heat conduction, scattering, thermal relaxation, etc. From these results it appears that streaming measurements cannot be used to distinguish between absorption mechanisms. Numerical values are given for a few cases; high flow speeds may be expected in a bubbly medium.

Ultrasound–biophysics mechanisms

“…Other than those responses related to macrostreaming (Nyborg, 1953(Nyborg, ,1965, there is a limited association, possibly only speculative, between the response and radiation force.…”

Modal Rayleigh-like streaming in layered acoustofluidic devices

“…Following Rayleigh's early work, a series of modifications to his solution have been proposed. [17][18][19] The boundary-driven streaming vortices both inside and outside of the acoustic boundary layer can be modelled by considering Reynolds stresses, the volume forces representing the time-averaged acoustic momentum flux due to the acoustic dissipation near the no-slip walls. 20 Alternatively, the streaming field in the bulk of the fluid can be effectively modelled using the a) m.hill@soton.ac.uk…”

Finite-element analysis of acoustic streaming generated between a bending transducer and a reflector through second-order approximated forces

“…First of all, in the nonlinear acoustic field, acousticrelated variables, density &, pressure p and velocity u, can be expanded in series as [6,8] …”

“…In particular, streaming fields of air in an acoustic resonant domain have been a target of study from the 19th century [1,5]. Many theoretical [2,[6][7][8] and numerical approaches [9][10][11][12] have been reported up to now in efforts to understand the phenomena. At the same time, acoustic streaming plays an important role in several applications of high-power ultrasound [13][14][15][16][17].…”

“…On the other hand, the driving force of streaming, introduced by Nyborg [6], and derived from the time average and the conservation of the second-order static term, has been used for the theoretical approach. Although it is still difficult to solve fluid equations analytically using the driving force, the calculation cost of simulating streaming with the driving force is far lighter than that of simulating all phenomena numerically.…”