  Three-dimensional harmless contactless manipulation and assembly of
micro-objects and micro-organisms would open new horizons in microrobotics and
microbiology, e.g. for microsystems assembly or tissue engineering. In our
previous work [Gong and Baudoin, Phys. Rev. Appl., 12: 024045 (2019)], we
investigated theoretically the possibility to trap and assemble in two
dimensions small particles compared to the wavelength with synchronized
acoustical tweezers based on cylindrical acoustical vortices. However, since
these wavefields are progressive along their central axis, they can only push
or pull (not trap) particles in this direction and hence are mainly limited to
2D operations. In this paper, we extend our previous analysis and show
theoretically that particles can be trapped and assembled in three-dimensions
with synchronized spherical vortices. We show that the particles can be
approached both laterally and axially and we determine the maximum assembly
speed by balancing the Stokes' drag force and the critical radiation force.
These theoretical results provide guidelines to design selective acoustical
tweezers able to trap and assemble particles in three dimensions.
