Acoustic radiation force on a cylindrical particle near a planar rigid boundary

Abstract

The aim of this investigation is to provide improved mathematical series expansions of the longitudinal and transverse acoustic radiation forces for a rigid cylindrical particle in 2D of arbitrary cross-section located near a planar rigid wall. Incident plane progressive waves with variable angle of incidence are considered in a non-viscous fluid. The multiple scattering effects occurring between the particle and the rigid boundary are described using the partial-wave decomposition in cylindrical coordinates, the method of images and the translational addition theorem. Initially, an effective acoustic field incident on the particle is defined, which includes the primary incident field, the reflected waves from the flat wall and the scattered field from the image object. Subsequently, the incident effective field along with the scattered field from the object are utilized to obtain closed-form mathematical expressions for the longitudinal and transverse radiation force functions, based on a scattering approach in the far-field. The radiation force vector components are formulated in partial-wave series in cylindrical coordinates, which involve the incidence angle, 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 rigid circular cylinder are considered. Computations for the longitudinal and transverse non-dimensional radiation force functions are performed. Emphasis is given on varying the size of the particle, the incidence angle of the source field and the particle-wall distance. Depending on the particle-wall distance and incidence angle, zero-longitudinal and transverse force components arise, thus, the particle becomes unaffected by the linear momentum transfer. Moreover, pushing or pulling forces between the particle and wall are predicted depending on the particle-wall distance, the incidence angle and size parameter. The results may find possible applications in the development of acousto-fluidic devices, acoustic levitation of particles nearby a boundary, cloaking/invisibility, and underwater acoustics to name a few areas, where most investigations resort initially to numerical simulations to guide the experimental design processes.