Interaction force and dynamics for a pair of Rayleigh spherical particles located in nodal or anti-nodal planes for Gauss standing wave

Abstract

The acoustic radiation force acting on a pair of spherical particles in a Gauss standing wave field is investigated, with the particle size considered to be much smaller than the wave length. Within the Rayleigh scattering limit, analytical expressions are presented for both the primary and secondary radiation forces using their corresponding potential functions. Force and dynamic analyses are performed for the particles located in nodal or anti-nodal planes where the axial primary radiation force vanishes. Two equal-sized rigid spheres in air and two highly compressible gas bubbles in water are selected as computational examples, whose corresponding equations of motion are solved using numerical methods to facilitate the analysis of their dynamic behaviors. The acoustic interaction force dominates only in the short-range limit for a pair of rigid spheres but without the range limit for a pair of gas bubbles. This study provides a theoretical guide for precise manipulation in standing acoustic waves, especially when there are several particles in the acoustic field.