Stability analysis of an acoustically levitated disk

In this paper, a model is developed for the stability analysis of an acoustically levitated disk on the basis of analyzing eddy acoustic streaming and acoustic viscous stress. In the model, the effect of the acoustic streaming outside the boundary layer that is on the surface of the levitated disk is properly taken into account. Also, the calculation of sound field and acoustic viscous stress is limited to the range that has a dominant effect on the stability. By this method, we obtain a quite accurate solution of the stability coefficient. For the small horizontal shift of a large levitated disk, the model is verified by the good agreement between the experimental and theoretical results. By means of this model and relevant experiments, some factors that affect the stability of the levitated disk are investigated, and useful guidelines for design and application are obtained. It is found that the range from the edge to the outermost nodal circle of the disk-shaped vibrator has a large effect on the stability of the levitated disk. To stabilize the levitated disk by acoustic viscous force, the distance between the edge and the outermost nodal circle of the vibrator must be larger than a critical value, which is determined by the driving frequency and the sound velocity of the fluid between the levitated disk and the vibrator. When this condition is satisfied, increasing the distance between the edge and the outermost nodal circle leads to a decrease in the stability. It is also found that the property of the fluid between the levitated disk and the vibrator has a large effect on the stability. It is easier to stabilize the levitated disk in steam than in air, but more difficult to do so in carbon dioxide and hydrogen. In addition, theoretical results show that increasing the weight per unit area of the levitated object increases the stability for a given vibrator velocity. The distribution of the acoustic viscous stress and the dependence of the stability coefficient and the holding force on the horizontal shift of the levitated disk, which are obtained by this study, also are useful to a better understanding of the stability of the levitated disk.