### Abstract

We investigate the attenuation and dispersion of sound waves in suspensions and emulsions caused by the thermal-transport process. They combine to constitute the effective compressibility of the system. We begin with an attempt to justify the Isakovich formula for calculating the effective compressibility. The formula is then rewritten in terms of the interfacial heat flux. Isakovich's analysis is simply an independent-particle approximation. It is the purpose of this paper to consider the effect of interparticle interactions. The effective compressibility is calculated for an array of spherical particles or droplets centered at the points of a periodic lattice, immersed in a fluid of different species. Ewald's method of fast-convergent lattice sums in electrostatics is extended to a technique for the heat-conduction problem in a periodic emulsion. The computation for cubic lattices reveals that the interparticle interactions act to reduce, in the lower-frequency range, both the attenuation coefficient and the departure of the sound velocity from its high-frequency limit. The striking feature is that a drastic change in attenuation occurs when the thermal conductivity of the particle is substantially larger than that of the ambient fluid.

Original language | English |
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Pages (from-to) | 4905-4921 |

Number of pages | 17 |

Journal | Physical Review A |

Volume | 46 |

Issue number | 8 |

DOIs | |

Publication status | Published - Jan 1 1992 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A*,

*46*(8), 4905-4921. https://doi.org/10.1103/PhysRevA.46.4905

**Thermal attenuation and dispersion of sound in a periodic emulsion.** / Fukumoto, Yasuhide; Izuyama, Takeo.

Research output: Contribution to journal › Article

*Physical Review A*, vol. 46, no. 8, pp. 4905-4921. https://doi.org/10.1103/PhysRevA.46.4905

}

TY - JOUR

T1 - Thermal attenuation and dispersion of sound in a periodic emulsion

AU - Fukumoto, Yasuhide

AU - Izuyama, Takeo

PY - 1992/1/1

Y1 - 1992/1/1

N2 - We investigate the attenuation and dispersion of sound waves in suspensions and emulsions caused by the thermal-transport process. They combine to constitute the effective compressibility of the system. We begin with an attempt to justify the Isakovich formula for calculating the effective compressibility. The formula is then rewritten in terms of the interfacial heat flux. Isakovich's analysis is simply an independent-particle approximation. It is the purpose of this paper to consider the effect of interparticle interactions. The effective compressibility is calculated for an array of spherical particles or droplets centered at the points of a periodic lattice, immersed in a fluid of different species. Ewald's method of fast-convergent lattice sums in electrostatics is extended to a technique for the heat-conduction problem in a periodic emulsion. The computation for cubic lattices reveals that the interparticle interactions act to reduce, in the lower-frequency range, both the attenuation coefficient and the departure of the sound velocity from its high-frequency limit. The striking feature is that a drastic change in attenuation occurs when the thermal conductivity of the particle is substantially larger than that of the ambient fluid.

AB - We investigate the attenuation and dispersion of sound waves in suspensions and emulsions caused by the thermal-transport process. They combine to constitute the effective compressibility of the system. We begin with an attempt to justify the Isakovich formula for calculating the effective compressibility. The formula is then rewritten in terms of the interfacial heat flux. Isakovich's analysis is simply an independent-particle approximation. It is the purpose of this paper to consider the effect of interparticle interactions. The effective compressibility is calculated for an array of spherical particles or droplets centered at the points of a periodic lattice, immersed in a fluid of different species. Ewald's method of fast-convergent lattice sums in electrostatics is extended to a technique for the heat-conduction problem in a periodic emulsion. The computation for cubic lattices reveals that the interparticle interactions act to reduce, in the lower-frequency range, both the attenuation coefficient and the departure of the sound velocity from its high-frequency limit. The striking feature is that a drastic change in attenuation occurs when the thermal conductivity of the particle is substantially larger than that of the ambient fluid.

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U2 - 10.1103/PhysRevA.46.4905

DO - 10.1103/PhysRevA.46.4905

M3 - Article

VL - 46

SP - 4905

EP - 4921

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 8

ER -