Tang Tianquan, Silva Glauber T, Huang Lixi, Han Xue
Department of Mechanical Engineering, University of Hong Kong, Pokfulam, Hong Kong SAR 999077, China.
Physical Acoustics Group, Instituto de Física, Universidade Federal de Alagoas, Maceió, Alagoas 57072-970, Brazil.
Phys Rev E. 2022 Oct;106(4-2):045108. doi: 10.1103/PhysRevE.106.045108.
Transducer arrays are a versatile tool for the contactless manipulation of spherical Rayleigh objects. Here we propose an analytical model for stable levitation of axisymmetric Mie objects through directly engineering the desired radiation force and torque. Acoustic contributions from multiple transducers are superimposed through the translation addition theorem, and the nonspherical objects are mapped into a sphere using the conformal transformation technique so that the scattered field can be asymptotically obtained. Then we give the acoustic radiation force and torque applied to a rigid nonspherical Mie object, which can be reconstructed as a series of quasiexplicit functions of the transducer (amplitude and phase) parameters. Through specifying the desired radiation force and torque exerted on the objects, a system of nonlinear equations is produced, which could be iteratively solved to retrieve appropriate transducer parameters that stabilize the object in an equilibrium position. Practically, we demonstrate several examples of stable levitation of a sphere, a spheroid, and a disk with an averaged radius of a=7mm (size parameter of ka≈5.18) above a transducer array. The absolute acoustic pressure field surrounding the objects simulated by the finite-element method is illustrated to verify the trapping results. The developed analytical model provides an alternative approach to retrieve the transducer parameters for levitating macroscopic nonspherical rigid objects, which may help design the systematic dynamical manipulation of Mie particles.
换能器阵列是用于对球形瑞利物体进行非接触式操控的多功能工具。在此，我们提出一种解析模型，通过直接设计所需的辐射力和扭矩来实现轴对称米氏物体的稳定悬浮。多个换能器的声学贡献通过平移叠加定理进行叠加，并且使用共形变换技术将非球形物体映射到一个球体上，以便渐近地获得散射场。然后，我们给出施加在刚性非球形米氏物体上的声辐射力和扭矩，它们可以被重构为换能器（幅度和相位）参数的一系列准显式函数。通过指定施加在物体上所需的辐射力和扭矩，会产生一个非线性方程组，可以通过迭代求解该方程组来获取能使物体稳定在平衡位置的合适换能器参数。实际上，我们展示了在换能器阵列上方稳定悬浮球体、椭球体和平均半径(a = 7mm)（尺寸参数(ka≈5.18)）的圆盘的几个示例。通过有限元方法模拟的物体周围的绝对声压场被展示出来以验证捕获结果。所开发的解析模型为获取用于悬浮宏观非球形刚性物体的换能器参数提供了一种替代方法，这可能有助于设计米氏粒子的系统动态操控。
