Analysis of the resonance frequency shift in cylindrical cavities containing a sphere and its prediction based on the Boltzmann-Ehrenfest principle

It is known that forces generated by high-level acoustic waves can compensate for the weight of small samples, which can be suspended in a fluid. To achieve this, a standing wave is created in a resonant enclosure, which can be open or closed to the external medium. This phenomenon, called Acoustic levitation, has numerous applications in containerless study and processing of materials. Although it is possible to levitate a sample for long periods of time, instabilities can appear under certain conditions. One of the causes of oscillational instabilities is the change of the resonance frequency of the cavity due to the presence of the levitated object. The Boltzmann-Ehrenfest principle is used to find an analytical expression for the resonance frequency shift in a cylindrical cavity produced by a small sphere, with kr < 1, where k is the wavenumber and r is the radius of the sphere. The validity of this expression has been investigated by means of the Boundary Element Method and experiments. In addition, the effect of the dispersion of the sound field by the sphere and the boundaries of the cavity on the resonance frequency shift has been analyzed using the BEM.