Extrinsic and intrinsic acoustical cross-sections for a viscous fluid particle near a planar rigid boundary: circular cylinder example

Abstract

The objective of this investigation is to derive closed-form partial-wave series expansions for the extrinsic and intrinsic acoustical scattering, extinction and absorption cross-sections of a fluid viscous cylindrical particle of arbitrary geometrical cross-section, located nearby a flat rigid boundary. Plane progressive waves with arbitrary incidence angle are considered in a non-viscous fluid. The multiple scattering between the particle and the boundary is described using the multipole expansion in cylindrical coordinates, the method of images and the translational addition theorem. The extrinsic cross-sections are determined by integrating the associated power flow densities over a virtual surface of large radius enclosing the object and its image, stemming from far-field expressions of the incident and scattered pressure fields. The expressions for the intrinsic cross-sections are established after defining an effective acoustic field incident on the particle, which includes the primary incident field, the reflected waves from the boundary and the scattered field from the image object. Subsequently, the incident effective field is used with the scattered field from the object to derive closed-form analytical expressions for the intrinsic cross-sections, based on a far-field scattering approach, which does not introduce any approximation in the evaluation of the expressions. The obtained expressions involve the angle of incidence, the expansion coefficients of the scatterer and its image, and the distance from the center of mass of the particle to the boundary. Numerical examples for a viscous fluid circular cylindrical cross-section are considered, and computations illustrate the analysis with particular emphasis on varying the size of the particle, the angle of incidence and the particle-wall distance. The results find potential applications in the quantitative predictions of the acoustical cross-sections from fluid/soft/compressible objects nearby a boundary, such as contrast agents in biomedicine, oceanography, sonochemistry, marine science, and (borehole) geophysical applications to name a few examples.

Local cross-sections and energy efficiencies in the multiple electromagnetic/optical scattering by two perfect electrically-conducting cylindrical particles

“…Practically, in an experimental setting, extrinsic cross-sections are measured in the far-field [22,23]. The extrinsic cross-sections are different from the local/intrinsic cross-sections, as shown in the acoustical context [27,28,37]. Extending the scope of the previously analysis for the extrinsic acoustical cross-sections [27], the EM extrinsic crosssections (denoted by the superscript e) are obtained similarly as,  …”

Radiation force and torque on a two-dimensional circular cross-section of a non-viscous eccentric layered compressible cylinder in acoustical standing waves

“…A system of four equations with four unknowns (i.e., C n , C int n,1 , D int n,1 , and C int n,2 ) are derived in the following, which can be computed numerically by matrix inversion procedures. [44,45] The coupled system of equations is expressed at r = a (> d) and r = b, respectively, as,…”

Acoustic radiation force and torque on a lossless eccentric layered fluid cylinder

“…[25] The boundary conditions lead to a system of four equations with four unknowns (i.e., C n , C int n,1 , D int n,1 , and C int n,2 ) that are determined by matrix inversion as in Refs. [26,27], obtained as…”