Extrinsic extinction cross-section in the multiple acoustic scattering by fluid particles

Abstract

Cross-sections (and their related energy efficiency factors) are physical parameters used in the quantitative analysis of different phenomena arising from the interaction of waves with a particle (or multiple particles). Earlier works with the acoustic scattering theory considered such quadratic (i.e., nonlinear) quantities for a single scatterer, although a few extended the formalism for a pair of scatterers but were limited to the scattering cross-section only. Therefore, the standard formalism applied to viscous particles is not suitable for the complete description of the cross-sections and energy balance of the multiple-particle system because both absorption and extinction phenomena arise during the multiple scattering process. Based upon the law of the conservation of energy, this work provides a complete comprehensive analysis for the extrinsic scattering, absorption, and extinction cross-sections (i.e., in the far-field) of a pair of viscous scatterers of arbitrary shape, immersed in a nonviscous isotropic fluid. A law of acoustic extinction taking into consideration interparticle effects in wave propagation is established, which constitutes a generalized form of the optical theorem in multiple scattering. Analytical expressions for the scattering, absorption, and extinction cross-sections are derived for plane progressive waves with arbitrary incidence. The mathematical expressions are formulated in partial-wave series expansions in cylindrical coordinates involving the angle of incidence, the addition theorem for the cylindrical wave functions, and the expansion coefficients of the scatterers. The analysis shows that the multiple scattering cross-section depends upon the expansion coefficients of both scatterers in addition to an interference factor that depends on the interparticle distance. However, the extinction cross-section depends on the expansion coefficients of the scatterer located in a particular system of coordinates, in addition to the interference term. Numerical examples illustrate the analysis for two viscous fluid circular cylindrical cross-sections immersed in a non-viscous fluid. Computations for the (non-dimensional) scattering, absorption, and extinction cross-section factors are performed with particular emphasis on varying the angle of incidence, the interparticle distance, and the sizes, and the physical properties of the particles. A symmetric behavior is observed for the dimensionless multiple scattering cross-section, while asymmetries arise for both the dimensionless absorption and extinction cross-sections with respect to the angle of incidence. The present analysis provides a complete analytical and computational method for the prediction of cross-section and energy efficiency factors in multiple acoustic scattering of plane waves of arbitrary incidence by a pair of scatterers. The results can be used as a priori information in the direct or inverse characterization of multiple scattering systems such as acoustically engineered fluid metamaterials with reconfigurable periodicities, cloaking devices, liquid crystals, and other applications.