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.

中文翻译：

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瑞利极限中近距离声相互作用的广义势理论

在外部声场下，粒子会受到辐射力的作用，将其带到特定的捕获位置，例如平面驻波情况下的压力或速度节点。由于声学相互作用，粒子在到达那些捕获位置时会形成簇。在这项工作中，通过使用散射场的远场评估，制定了广义力势，该力势给出了大小远小于波长（瑞利极限）的粒子的主力和相互作用力。主力的广义势与戈尔科夫势相同。对于平面和非平面（贝塞尔）驻波的两种情况，研究了零主力位置处一对粒子之间的相互作用势和力。发现相互作用力主要取决于外部声场和来自相邻粒子的散射场的乘积。除了线条的形成，对于在平面驻波下聚结的三个固体颗粒，其他簇形状也被证明是合理的。发现具有不同材料特性的粒子之间的相互作用力通常不相等且相反，表明它们没有形成作用和反应对。从由于贝塞尔驻波的非平面场引起的相互作用模式，可以推断出许多簇构型是可能的，因为靠近稳定俘获位置的粒子从一个以上的方向相互吸引。