On the velocity of a rigid sphere in a sound wave

Temkin, Samuel; Leung, Carlin

doi:10.1016/0022-460x(76)90758-6

Cited by 51 publications

(12 citation statements)

References 16 publications

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“…Thus we take the translational velocity in all cases to be equal to the velocity which rigid, spherical particles would acquire in the sound wave. This was obtained some time ago by Temkin and Leung, 31 and may be expressed as…”

Section: Particle-fluid Ratiosmentioning

confidence: 95%

“…These ratios are the particle-to-fluid translational velocity, temperature, and pressure, and are known from earlier work for single spherical particles. Thus the translational velocity ratio is obtained from the work of Temkin and Leung, 31 whereas the pressure and temperature ratios are provided by the author's recent work on compressible particles. 32 Use of these ratios in the theory developed here results in explicit forms for the attenuation and the sound speed for the basic suspension types mentioned earlier.…”

Section: List Of Symbols B B Imentioning

confidence: 99%

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Attenuation and dispersion of sound in dilute suspensions of spherical particles

Temkin

2000

The Journal of the Acoustical Society of America

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This paper considers sound propagation in dilute suspensions of constant-mass particles that can translate and pulsate under the effects of a small amplitude sound wave. A new theory for sound attenuation and dispersion is developed on the basis of the changes of the suspension's compressibility produced by the relative motions between host fluid and particles. The approach, used earlier to treat propagation in rigid-particle suspensions, decouples the propagation problem from the more difficult problem of obtaining accurate descriptions for the fluid-particle interactions. In this work the role of the pulsational motion is included in the theoretical framework. The resulting theory is thus applicable to aerosols, bubbly liquids, emulsions, and hydrosols composed of elastic particles, and includes, as a special limit, rigid-particle suspensions. The results are expressed in terms of three complex quantities that describe, respectively, the particles' translational velocity, temperature, and pressure, relative to their counterparts in the fluid. Theoretical results for these quantities, applicable in wide frequency ranges, are available from previous studies [Temkin and Leung, J. Sound Vib. 49, 75-92 (1976), Temkin, J. Fluid. Mech. 380, 1-38 (1999)]. Together with the compressibility theory presented here, they provide a more general description of propagation in dilute suspensions than presently available. In the case of aerosols and hydrosols, the theory produces known results for the attenuation and the sound speed. For bubbly liquids and emulsions the new results presented here differ from those available in the literature. The differences are traced to the neglect in the existing theories of the acoustic pressure disturbance produced by the pulsations of the particles.

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Section: Particle-fluid Ratiosmentioning

confidence: 95%

Section: List Of Symbols B B Imentioning

confidence: 99%

Attenuation and dispersion of sound in dilute suspensions of spherical particles

Temkin

2000

The Journal of the Acoustical Society of America

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“…The first work relevant to our goal appears to be that of Zwanzig and Bixon [7] (also see Metiu et al [8]), who investigated the velocity-correlation function of an atom immersed in a compressible visco-elastic liquid. Temkin and Leung [9] and Guz [10] have presented solutions that are essentially identical except for differences due to simplifying assumptions and some typographical mistakes.…”

Section: Introductionmentioning

confidence: 99%

Generalized Basset-Boussinesq-Oseen Equation for Unsteady Forces on a Sphere in a Compressible Flow

2011

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Viscous compressible flow around a sphere is considered in the limit of zero Reynolds and Mach numbers. An exact expression for the force on the sphere undergoing arbitrary motion with compressibility effects is presented. Quasisteady, inviscid-unsteady, and viscous-unsteady force components are identified. Numerical results are in excellent agreement with the theory. The present formulation offers an explicit expression for the unsteady force in the time domain and can be considered as a generalization of the Basset-Boussinesq-Oseen equation to compressible flow.

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“…Then Temkin and Leung [19] generalized the solution to all wavelengths, taking into account the viscosity and compressibility of the fluid. They showed that for the particular case of an inviscid fluid in 3D, the velocity ratio becomes:…”

Section: Analytic Solutionmentioning

confidence: 99%

Fictitious domain method to model a movable rigid body in a sound wave

Imbert

McNamara

2012

Journal of Numerical Mathematics

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Motivated by experiments on the acoustics of submerged granular media, we have developed a new fictitious domain method that combines the acoustic wave equation with the equations of motion of a rigid body. The coupling is realized through the natural boundary conditions of the wave equation on the surface of the body and enforced with boundary Lagrange multipliers. The method is validated using analytic solutions for a movable rigid sphere in a sound wave. Results show that the method is promising because numerical results and analytic solutions are close for long wavelengths, although some deviations occur when the wavelength is smaller to the sphere radius. This method permits us to use a discrete element method for particle motion and interaction, and finite elements for wave propagation in the fluid.

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On the velocity of a rigid sphere in a sound wave

Cited by 51 publications

References 16 publications

Attenuation and dispersion of sound in dilute suspensions of spherical particles

Attenuation and dispersion of sound in dilute suspensions of spherical particles

Generalized Basset-Boussinesq-Oseen Equation for Unsteady Forces on a Sphere in a Compressible Flow

Fictitious domain method to model a movable rigid body in a sound wave

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