Acoustic attraction, repulsion and radiation force cancellation on a pair of rigid particles with arbitrary cross-sections in 2D: Circular cylinders example

The acoustic radiation forces arising on a pair of sound impenetrable cylindrical particles of arbitrary cross-sections are derived. Plane progressive, standing or quasi-standing waves with an arbitrary incidence angle are considered. Multiple scattering effects are described using the multipole expansion formalism and the addition theorem of cylindrical wave functions. An effective incident acoustic field on a particular object is determined, and used with the scattered field to derive closed-form analytical expressions for the radiation force vector components. The mathematical expressions for the radiation force components are exact, and have been formulated in partial-wave series expansions in cylindrical coordinates involving the angle of incidence, the reflection coefficient forming the progressive or the (quasi)standing wave field, the addition theorem, and the expansion coefficients. Numerical examples illustrate the analysis for two rigid circular cross-sections immersed in a non-viscous fluid. Computations for the dimensionless radiation force functions are performed with emphasis on varying the angle of incidence, the interparticle distance, the sizes of the particles as well as the characteristics of the incident field. Depending on the interparticle distance and angle of incidence, one of the particles yields neutrality; it experiences no force and becomes unresponsive (i.e., “invisible”) to the linear momentum transfer of the effective incident field due to multiple scattering cancellation effects. Moreover, attractive or repulsive forces between the two particles may arise depending on the interparticle distance, the angle of incidence and size parameters of the particles. This study provides a complete analytical method and computations for the axial and transverse radiation force components in multiple acoustic scattering encompassing the cases of plane progressive, standing or quasi-standing waves of arbitrary incidence by a pair of scatterers. Potential applications concern the prediction of the forces used in acoustically-engineered metamaterials with reconfigurable periodicities, cloaking devices, and liquid crystals to name a few examples.