  Based on the analyses of the wave front and the wave vector of an
acoustic-vortex (AV) spanner generated by a circular array of point source, the
principle of object rotation is investigated through the calculation of the
orbital angular momentum (OAM) and the radiation torque for AVs with various
topological charges. It is demonstrated theoretically that the rotation of the
axisymmetric disk centered on an AV spanner is mainly driven by the exerted
radiation torque without the contribution of the OAM transfer. The radiation
torque on a small-radius object is inversely associated with the topological
charge in the center of the AV spanner, and it is enhanced significantly for a
larger AV with a higher topological charge. The special case of the radiation
torque proportional to the topological charge might be realized when the disk
radius is much larger than the wavelength, in which case the acoustic power of
the AV spanner can be absorbed as much as possible. With the established
sixteen-source experimental setup, the radial pressure distributions of AVs
with different topological charges measured at the frequency of 1.3 kHz in air
agree well with the simulations. The topological-charge dependence of the
radiation torque for AVs is also verified by the quantitative
laser-displacement (angle) measurements for disks with different radii. The
favorable results demonstrate that, for the object covering the vortex center
of an AV spanner, the total OAM transfer might be 0 and the object rotation is
contributed by the acting moments. Thus, the radiation torque of an AV spanner
is more applicable than the OAM for describing the driving capability of object
rotation, and it can be used as an effective tool in clinical applications to
noninvasively manipulate objects with a feature size at the wavelength-scale
(e.g. kidney stone in lithotripsy) inside body.
