Time-averaged acoustic forces acting on a rigid sphere within a wide range of radii in an axisymmetric levitator

Abstract

Acoustic levitation is a physical phenomenon that arises when the acoustic radiation pressure is strong enough to overcome gravitational force. It is a nonlinear phenomenon which can be predicted only if higher order terms are included in the acoustic field calculation. The study of acoustic levitation is usually conducted by solving the linear acoustic equation and bridging the gap with an analytical solution. Only recently, the scientific community has shown interest in the full solution of the Navier-Stokes' equation with the aim of deeply investigating the acoustic radiation pressure. We present herein a numerical model based on Finite Volume Method (FVM) and Dynamic Mesh (DM) for the calculation of the acoustic radiation pressure acting on a rigid sphere inside an axisymmetric levitator which is the most widely used and investigated type of levitators. In this work, we focus on the third resonance mode. The use of DM is new in the field of acoustic levitation, allowing a more realistic simulation of the phenomenon, since no standing wave has to be necessarily imposed as boundary condition. The radiating plate is modeled as a rigid cylinder moving sinusoidally along the central axis. The time-averaged acoustic force exerting on the sphere is calculated for different radii Rs of the sphere (0.025 to 0.5 wavelengths). It is shown that the acoustic force increases proportional to Rs3 for small radii, then decreases when the standing wave condition is violated and finally rises again in the travelling wave radiation pressure configuration. The numerical model is validated for the inviscid case with a Finite Element Method model of the linear acoustic model based on King's approximation.