The development of the theory of multiple scattering of sound by discrete heterogeneities
The model of a two-phase medium in the form of gas bubbles in the liquid is a reference model when other, more complex problems of the wave propagation in structurally heterogeneous media are addressed. Search for exact solutions in the absence of restrictions on the concentration of the mixture components is of considerable interest from the point of view of both fundamental science and possible applications. Studies in this direction were started with an attempt to rethink the problems of sound scattering by a single particle. Transformation of the amplitude of the monopole sound scattering by a spherical particle was found in [1]. This made it possible to eliminate the radiation loss coefficient and determine, in particular, its impedance. An analogy between the sound scattering processes in a viscous compressible fluid and in an elastic medium at the level of boundary conditions was drawn in [2]. This permitted a transition from the problems of scattering in a fluid to similar problems for an elastic medium using a formal replacement of the wave numbers of the sound and viscous waves in a fluid by the wave numbers of the longitudinal and transverse waves in an elastic medium, respectively. Setting up spherical means for the fields around a spherical particle and representing its oscillations as the sum of monopole, dipole, and rotary types made it possible to solve the problem of the heterogeneous sound field scattering [2,3].
The equations of multiple scattering of sound by an arbitrary number of particles were obtained in [4] based on the formalism developed in the problems of sound scattering by a single particle. These equations are specific in that the effective or acting field is eliminated in them and the amplitudes of particle oscillations are introduced instead. It is important to note that these equations are valid up to a contact of particles whose vibrations are described by the sum of monopole, dipole, and rotary types. Based on these equations and taking into account only the monopole oscillations of particles, the problem of scattering of a plane harmonic wave by a plane layer of particles was solved in [5]. It is shown that in this case the compressibility of the fluid surrounding the particles is insignificant and the radiation losses are absent. Furthermore, in the case of a gas-liquid mixture of identical bubbles the resonant frequency of the particle oscillations increases with increasing concentration and tends to the infinity when the concentration is approximately 30%, whereas the sound speed becomes independent of the oscillation frequency. The solution derived requires the further analysis. In the near future, we intend to solve the problem of sound scattering by a layer of particles taking into account all the above-mentioned types of their oscillations. Also, it seems important to consider the nonlinear problem about the intersection and the probability of a collision between two liquid droplets in the field of a sound wave and a gravity wave [6], referring to a possible strengthening of the fields scattered by particles, as follows from [3].
References to Section 5
1. Kobelev Yu (2004) Parameters of Microparticles Responsible for the Monopole Sound Scattering in a Liquid. Acoustical Physics 50(6): 808–812.
2. Kobelev Yu (2008) Analogy Between Linear Sound Scattering Processes in a Viscous Liquid and in an Isotropic Elastic Medium. Acoustical Physics 54(6): 890–894.
3. Kobelev Yu (2009) Scattering of spatially inhomogeneous sound waves by a spherical particle. Acoustical Physics 55(1): 21–31.
4. Kobelev Yu (2011) On the Theory of Multiple Scattering of Sound Waves by Spherical Particles in Liquid and Elastic Media. Acoustical Physics 57(4): 447–453.
5. Kobelev Yu (2011) Multiple monopole scattering of sound waves from spherical particles in liquid and elastic media. Acoustical Physics 57(6): 731–740.
6. Kobelev Yu (1983) Nonlinear dipole oscillations of the spherical particle in a sound field. Acoustical Physics 29(6): 783–789.
