Mechanisms for the attracting acoustic radiation force on a rigid sphere placed freely in a spherical sound field

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It is well known that the mean force due to the Langevin radiation pressure on a sphere freely placed in a plane progressive sound field is always positive force (i.e., repulsive force). In the case of spherical diverging field, however, the situation is quite different. At very large distances from the source the radiation force obeys an inverse square law of repulsion. As the source of the field is approached, the repulsion decreases to zero and then becomes a force of attraction [T. F. W. Embleton, J. Acoust. Sot: Am., 26, 40-45 (1954)]. The present paper discusses the mechanisms for the attracting force acting on a rigid sphere placed freely in a spherical diverging sound field. The distribution of the three components of the radiation force on a sphere (i.e., kinetic energy density K, potential energy density U, and tensor term T that includes momentum flux density) is investigated and compared with the case of plane progressive sound field. In the cases of grazing incident of plane waves and spherical waves, it is shown theoretically that the contribution of the tensor term vanishes and the Lagrangean density L = K - U becomes the only cause of radiation force. In the case of incident plane waves, the effect of <L> vanishes because <K> - <U> where the symbol < > denotes the time-averaging operation, while attracting force arises because <K> > <U> in the case of incident spherical waves.
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