Acoustic levitation of axisymmetric Mie objects above a transducer array by engineering the acoustic radiation force and torque.

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.