Effective Equations for Multiphase Flows—Waves in a Bubbly Liquid

Miksis, Michael J.; Ting, Lu

doi:10.1016/s0065-2156(08)70155-8

Cited by 40 publications

(12 citation statements)

References 62 publications

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“…However, the results are usually given in terms of a complex dispersion relation that usually requires numerical computation, making it difficult to interpret them. Furthermore, these conservation equations are based for specific suspensions, e.g., dusty gases, 10 bubbly liquids, [11][12][13][14] hydrosols, 15 but these do not exist for general types of suspensions. Fortunately, the two-phase model is not needed for acoustic motions, because, for them, one is usually interested in the propagation constants in the vicinity of an equilibrium condition.…”

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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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: 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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“…In the following we employ the conservation equations of mass and momentum in a homogeneous mixture approximation to describe the propagation of one-dimensional pressure waves in a foam (Miksis and Ting 1991).…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…Introduction The main difference between gas-liquid foams and the well known and investigated bubbly liquids is in the high (close to unity) gas content which characterizes gas-liquid foams. Propagation of pressure disturbances in foams can be described by the method developed for analyzing bubbly liquid flows (Miksis and Ting 1991). The structure of foams can be well described by a polyhedral model whereby an elementary foam cell represents an irregular polyhedron (Bikerman 1973, ( §41, §42) and Kraynik 1988).…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…In the present investigation the cellular model of the multiphase media (see, e. g., Miksis and Ting 1991) is employed, whereby the foam is modeled by a regular cellular structure. Each cell consists of a spherical gas bubble surrounded by a thin liquid film.…”

Section: Derivation Of Conservation Equations For Gas-liquid Foamsmentioning

confidence: 99%

“…Then, after some algebra, using basic relations from the theory of homogeneous mixtures (Miksis and Ting 1991), we arrive at the following relation for the velocity of sound in foams: In the derivation of Eq.2, the liquid phase is considered incompressible.…”

Section: Derivation Of Conservation Equations For Gas-liquid Foamsmentioning

confidence: 99%

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