The stable levitation of an analyte sample in an acoustic levitator is a primary requirement for accurate x-ray characterization of its scientific structure. A rigid particle oscillates in an under-damped manner when introduced into the node of established standing acoustic waves. This investigation has employed the lattice Boltzmann method (LBM), a computational fluid dynamics technique, for the analysis of such rigid particle dynamics in acoustic levitation. The simulation uses the two dimensional and nine velocity (D2Q9) Bhatnagar–Gross–Krook formulation to levitate a rigid 1.6 mm diameter nylon (ρ = 1150 kg/m³) particle in the air at standard pressure and temperature conditions. The presented work is the first reported simulation of realistic acoustic levitator boundary conditions using the LBM. The simulation can capture the particle–fluid interactions that produce dynamic levitation at less than one-period timescale in the ultrasonic frequency regime. An experiment was conducted by levitating a 1.6 mm-diameter nylon sphere to estimate the oscillations, and the oscillating frequency was found to be 50 Hz. The dynamic simulation results are consistent with experimental results for particle oscillations within the same order of magnitude, indicating that LBM formulation can be successfully used to study acoustic levitation to understand and mitigate particle jitter. The distortion of the acoustic field due to a levitating particle’s presence was also analyzed to demonstrate how the presence of the particle can disrupt adjacent levitating nodes.

中文翻译：

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晶格玻尔兹曼方法研究和验证声悬浮粒子的动力响应

声学悬浮器中分析物样品的稳定悬浮是对其科学结构进行精确X射线表征的主要要求。刚性粒子在引入已建立的驻声波节点时会以阻尼不足的方式振荡。这项研究采用了格子玻尔兹曼方法（LBM），一种计算流体动力学技术，来分析声悬浮中的这种刚性粒子动力学。该模拟使用二维和九速度（D2Q9）Bhatnagar–Gross–Krook公式悬浮1.6 mm直径的刚性尼龙（ρ = 1150 kg / m ³）在标准压力和温度条件下空气中的颗粒。提出的工作是第一个使用LBM的真实声悬浮物边界条件的模拟报告。该模拟可以捕获在超声频率范围内小于一周期时间尺度上产生动态悬浮的粒子-流体相互作用。通过使直径为1.6 mm的尼龙球悬浮来进行实验，以估计振荡，发现振荡频率为50 Hz。动态仿真结果与相同数量级内颗粒振动的实验结果一致，表明LBM公式可以成功地用于研究声悬浮以理解和减轻颗粒抖动。