Natural oscillation frequencies of a solid Rayleigh sphere suspended in a three-axis acoustic levitation system

In this formalism, we investigate the oscillation dynamics and levitation stability for a solid Rayleigh sphere suspended in a three-axis standing wave levitation system. In the limit of particles much smaller than the acoustic wavelength, the Gor'kov potential theory can be employed to calculate the three-dimensional acoustic radiation force induced on the sphere. With the acoustic field expanded into a series with respect to the displacements, linearized equations of motion are obtained for the deviating sphere, yielding the natural angular frequencies for the small-amplitude harmonic oscillations around its equilibrium position. Without loss of generality, the sphere oscillations along the wave axis, on the coordinate plane and in any direction are all considered, with their natural frequencies equal to each other if the three pairs of emitters generate identical standing wave fields. A specific computational example of a three-axis levitator composed of three Gaussian standing wave fields is also presented. The dynamic model paves the way to understand the oscillatory behaviors of suspended particles in a three-axis standing wave levitation system and achieve a more stable suspension as well as the parametric inversion under a container-free condition. Potential applications also include the development and optimization of acoustic radiation force experiments involving precise control of particles in materials science, ultrasound biomedicine and space utilization to name some examples.