Near-boundary streaming around a small sphere due to two orthogonal standing waves

Lee, Chun P.; Wang, Taylor G.

doi:10.1121/1.397491

Cited by 79 publications

(61 citation statements)

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“…Thus, as a result of the recirculation, their signs are different. However, there is no such recirculation for the rotational part of the inner streaming, which was pointed out by Lee & Wang (1989) in different terms.…”

Section: A Y Rednikov and S S Sadhalmentioning

confidence: 99%

“…One possible interpretation is that the sphere is within two out-of-phase orthogonal acoustic standing waves with the wavelength much greater than the sphere radius (the incompressible limit). As compared to Lee & Wang (1989), where this problem has been originally treated, here one can fully appreciate the advantage of a vector-form representation. Besides, in what the extension of the analysis to the outer streaming is concerned, treated here is not only the problem of a "fixed" rigid sphere as in Lee & Wang (1989), but also a sphere free to rotate and its generalization to a spherical drop (although its dynamic viscosity is required in the analysis to be much greater than that of the medium, e.g.…”

Section: Introductionmentioning

confidence: 99%

“…Lee & Wang (1989) revisit Nyborg's generalized treatment, correct certain points, and apply it to describing the streaming from a rigid sphere fixed in two out-of-phase orthogonal acoustic standing waves. The treatment of Lee & Wang (1989), just as the original one of Nyborg (1958), explicitly represents it all in terms of an orthogonal curvilinear coordinate system introduced on the boundary. The result looks rather cumbersome.…”

Section: Introductionmentioning

confidence: 99%

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

Rednikov

Sadhal

2011

J. Fluid Mech.

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As originally realized by Nyborg (1958), the problem of the inner acoustic/steady streaming can be analyzed in quite general terms. The inner streaming is the one that develops in the high-frequency limit in a thin Stokes (shear-wave) layer at a boundary, in contrast with the outer streaming in the main bulk of the fluid. The analysis consists in expressing relevant inner-streaming characteristics through a given distribution of the acoustic amplitude along the boundary. Here such a generalized treatment is revisited for a motionless boundary. By working in terms of surface vectors, though in elementary notations, new compact and easy-to-use expressions are obtained. The most important ones are those for the effective (apparent) slip velocity at the boundary as seen from a perspective of the main bulk of the fluid, which is often the sole driving factor behind the outer streaming, and for the induced (acoustic) steady tangential stress on the boundary. As another novel development, non-adiabatic effects in the Stokes layer are taken into account, which become apparent through the fluctuating density and viscosity perturbations, and whose contribution into the streaming is often ignored in the literature. Important particular cases, such as the axisymmetric case and the incompressible case, are dealt with. As far as the application of the derived general inner-streaming expressions is concerned, a few examples provided here involve a plane acoustic standing wave, which either grazes a wall parallel to its direction (convenient for the estimation of the non-adiabatic effects), or into which a small (compared to the acoustic wavelength) rigid sphere is placed. If there are simultaneously two such waves, out-of-phase and, say, in mutually orthogonal directions, a disk placed coplanarly with them will undergo a steady torque, which is calculated here as another example. Two further examples deal with translational highfrequency harmonic vibrations of particles relative to an incompressible fluid medium, viz. of a rigid oblate spheroid (along its axis) and of a sphere (arbitrary 3-d). The latter can be a fixed rigid sphere, one free to rotate or even a (viscous) spherical drop, for which the outer streaming and the internal circulation are considered as well.

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Section: A Y Rednikov and S S Sadhalmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Rednikov

Sadhal

2011

J. Fluid Mech.

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“…Fluids 28, 012004 (2016) limiting velocity method, 21,22 in which the acoustic boundary layer with its non-slip boundary condition on the walls parallel to the axis of acoustic resonances is replaced by a slip boundary condition with a limiting velocity derived from the acoustic field. The former method is computationally expensive, especially for three-dimensional (3D) models, as tiny mesh elements near the no-slip walls are required to resolve the acoustic and streaming fields within the acoustic boundary layer.…”

Section: -2mentioning

confidence: 99%

“…In the second step, the limiting velocity method, introduced by Nyborg, 21 modified by Lee and Wang 22 and applied by Lei et al 28,35 for 3D simulations, was used to solve the acoustic streaming fields in these layered acoustofluidic devices. Driven by the limiting velocities, the COMSOL "Creeping Flow" interface was used to simulate the acoustic streaming fields.…”

Section: Modellingmentioning

confidence: 99%

Modal Rayleigh-like streaming in layered acoustofluidic devices

2016

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Classical Rayleigh streaming is well known and can be modelled using Nyborg’s limiting velocity method as driven by fluid velocities adjacent to the walls parallel to the axis of the main acoustic resonance. We have demonstrated previously the existence and the mechanism of four-quadrant transducer plane streaming patterns in thin-layered acoustofluidic devices which are driven by the limiting velocities on the walls perpendicular to the axis of the main acoustic propagation. We have recently found experimentally that there is a third case which resembles Rayleigh streaming but is a more complex pattern related to three-dimensional cavity modes of an enclosure. This streaming has vortex sizes related to the effective wavelength in each cavity axis of the modes which can be much larger than those found in the one-dimensional case with Rayleigh streaming. We will call this here modal Rayleigh-like streaming and show that it can be important in layered acoustofluidic manipulation devices. This paper seeks to establish the conditions under which each of these is dominant and shows how the limiting velocity field for each relates to different parts of the complex acoustic intensity patterns at the driving boundaries.

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A noncontact ultrasonic motor with the rotor levitated by axial acoustic viscous force

Nakamura

Ueha

1999

Electron. Comm. Jpn. Pt. III

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Near-boundary streaming around a small sphere due to two orthogonal standing waves

Cited by 79 publications

References 0 publications

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

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

Modal Rayleigh-like streaming in layered acoustofluidic devices

A noncontact ultrasonic motor with the rotor levitated by axial acoustic viscous force

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