Particles or cells in suspension and exposed to ultrasonic waves experience an acoustic radiation force (${\mathit{F}}_R$) which, under certain conditions, drives them toward positions of acoustic equilibrium. In this paper, we present a three-dimensional model of the particle motions within the acoustic field generated by ultrasonic standing waves. This model allows a theoretical study of the three-dimensional ${\mathit{F}}_R$ induced by a standing acoustic wave in a microfluidic chamber with rectangular geometry on micrometer-sized spherical particles. The approach models the agglomeration process and the behavior of particle clusters in the acoustic field. To achieve this, expressions for the 3D ${\mathit{F}}_R$ are obtained as the time-average of a gradient of the acoustic potential established within the chamber with two different sets of boundary conditions. The particle motion under the action of this force was analyzed assuming a non-viscous fluid and a particle size much smaller than the acoustic wavelength. The 3D force expressions were used in a simulation employing an optimized Forest–Ruth algorithm to derive the dynamics of $N$ spherical particles. This work provides novel results that predict some particle motion toward chamber or channel walls and the formation of pearl-chain aggregates within channels. These particle movements and the aggregate formation process were observed experimentally in an acoustic device built to assess the validity of the theoretical predictions.

悬浮并暴露于超声波的颗粒或细胞会受到声辐射力（${\mathit{F}}_{\mathrm{[R}}$），在某些条件下，将它们驱向声学平衡位置。在本文中，我们提出了由超声驻波产生的声场内质点运动的三维模型。该模型可以对三维进行理论研究${\mathit{F}}_{\mathrm{[R}}$在微米大小的球形粒子上具有矩形几何形状的微流体腔室中，由驻声波引起的感应。该方法模拟了声场中的团聚过程和粒子团簇的行为。为此，请使用3D表达式${\mathit{F}}_{\mathrm{[R}}$作为在具有两组不同边界条件的室内建立的声势的梯度的时间平均，获得了Δθ。假定非粘性流体且其粒径远小于声波波长，则分析了在此力作用下的粒子运动。在优化的Forest-Ruth算法的仿真中使用了3D力表达式，以得出动力学$ñ$球形颗粒。这项工作提供了新颖的结果，预测了一些粒子向室壁或通道壁运动以及通道内珍珠链聚集体的形成。这些声音运动和聚集体形成过程是在为评估理论预测的有效性而设计的声学装置中通过实验观察到的。