Sepehrirhnama Shahrokh, Lim Kian-Meng
Mechanical Engineering Department, National University of Singapore, Singapore 117575.
Phys Rev E. 2020 Oct;102(4-1):043307. doi: 10.1103/PhysRevE.102.043307.
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.
在外部声场作用下，粒子会受到辐射力，这些力会将它们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，粒子在到达这些捕获位置时会形成团簇。在这项工作中，通过对散射场进行远场评估，制定了一种广义力势，它给出了尺寸远小于波长（瑞利极限）的粒子的初级力和相互作用力。初级力的广义势与戈尔科夫势相同。针对平面驻波和非平面（贝塞尔）驻波这两种情况，研究了在零初级力位置处一对粒子之间的相互作用势和力。结果发现，相互作用力主要取决于外部声场与相邻粒子散射场的乘积。除了形成线状外，还表明在平面驻波下三个固体粒子团聚时，其他团簇形状也是可能的。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不相反，这表明它们不构成作用力与反作用力对。从贝塞尔驻波的非平面场引起的相互作用模式可以推断，由于靠近稳定捕获位置的粒子会从多个方向相互吸引，所以可能存在许多团簇构型。使用广义力势的优点在于，它为在具有任意波前的任何外部场中对小粒子进行声学操纵提供了物理见解，例如用于声全息术的那些场。
