Generalized potential theory for close-range acoustic interactions in the Rayleigh limit

Under an external acoustic field, particles experience radiation forces that bring them to certain trapping locations, such as pressure or velocity nodes for the case of plane standing wave. Due to acoustical interactions, particles form clusters on reaching those trapping locations. In this work, by using the far-field evaluation of scattered fields, a generalized force potential is formulated that gives both the primary and interaction forces for particles with size much smaller than the wavelength (Rayleigh limit). The generalized potential for the primary force is the same as the Gorkov's potential. The interaction potential and forces between a pair of particles at the zero-primary-force locations are studied for the two cases of planar and nonplanar (Bessel) standing waves. It was found that the interaction forces are predominantly dependent on the product of the external acoustic field and the scattered fields from the adjacent particles. Besides the line formation, other cluster shapes are shown to be plausible for three solid particles agglomerating under a plane standing wave. The mutual interaction force between particles of different material properties was found to be not equal and opposite in general, suggesting that they do not form an action and reaction pair. From the interaction patterns due to the nonplanar field of a Bessel standing wave, it is inferred that many cluster configurations are possible since particles near the stable trapping locations attract each other from more than one direction. The advantage of using the generalized force potential is that it provides physical insight for the acoustical manipulation of small particles in any external field with arbitrary wave front, such as those used in acoustic holography.