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Some problems in acoustics of emulsions

Abstract

The authors study small vibrations of a mixture (emulsion) of two weakly viscous compressible fluids, construct a macroscopic (homogenized) model of emulsion, and establish convergence (with respect to a small parameter) of solutions of the original boundary value problem for a two-phase fluid to solutions of the corresponding homogenized problem. The paper also describes the results of qualitative analysis of the spectrum of the macroscopic acoustic equation (the dynamical Darcy’s law), as well as typical spectral pictures obtained by numerical experiments.

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Correspondence to A. A. Gavrikov.

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Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 28, Part I, pp. 114–146, 2011.

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Gavrikov, A.A., Shamaev, A.S. Some problems in acoustics of emulsions. J Math Sci 179, 415–436 (2011). https://doi.org/10.1007/s10958-011-0601-6

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  • DOI: https://doi.org/10.1007/s10958-011-0601-6

Keywords

  • Elastic Material
  • Homogenize Problem
  • Complex Part
  • Convolution Kernel
  • Spectral Structure