Acoustic radiation force of attraction, cancellation and repulsion on a circular cylinder near a rigid corner space

• Published in: Applied Mathematical Modelling Vol. 64; p. 688
• Main Author: Mitri, F G
• Format: Journal Article
• Language: English
• Published: New York Elsevier BV 01-12-2018
• Subjects: Acoustic noise; Acoustics; Addition theorem; Attraction; Circular cylinders; Cylindrical coordinates; Design optimization; Incidence angle; Light; Method of images; Noise control; Plane waves; Sound waves; Theorems; Vibration control; Viscous fluids; Visibility
• ISSN: 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2018.07.056

The purpose of this study is to derive exact partial wave series expansions for the longitudinal and transverse radiation force components, for a circular cylinder in the proximity of a rigid corner space, and illuminated by incident plane waves with arbitrary orientation in the polar plane. Based on the multipole expansion method in cylindrical coordinates, the method of images as well as the translational addition theorem, an effective incident field (resulting from the primary waves as well as the multiple scattered fields from the image sources) is determined first, and used subsequently with the scattered field to derive the mathematical expressions for the radiation force components, stemming from the integration of the radiation stress in a non-viscous fluid. Numerical computations illustrate the analysis for rigid and soft cylinders with particular emphasis on the distances from the particle edges to the neighbouring walls, the size of the cylinder and the angle of incidence. Depending on the choice of these parameters, the radiation force components can vanish, rendering complete “invisibility”; i.e., the cylinder becomes unresponsive to the transfer of linear momentum carried by the incident effective field. Moreover, the radiation force components alternate between positive and negative values, suggesting a force of repulsion or attraction. The results find potential applications in acoustofluidics design and optimization as they shed light on the anechoic radiation force effect on a particle nearby a rigid corner. Other applications in noise and vibration control could also benefit from the results of the present investigation along with further related topics.