  A rigid spherical particle in an acoustic wave field oscillates at the wave
period but has also a mean motion on a longer time scale. The dynamics of this
mean motion is crucial for numerous applications of acoustic microfluidics,
including particle manipulation and flow visualisation. It is controlled by
four physical effects: acoustic (radiation) pressure, streaming, inertia and
viscous drag. In this paper, we carry out a systematic multiscale analysis of
the problem in order to assess the relative importance of these effects
depending on the parameters of the system that include wave amplitude,
wavelength, sound speed, sphere radius, and viscosity.
  We identify two distinguished regimes characterised by a balance among three
of the four effects, and we derive the equations that govern the mean particle
motion in each regime. This recovers and organises classical results by King,
Gor'kov and Doinikov, clarifies the range of validity of these results, and
reveals a new nonlinear dynamical regime. In this regime, the mean motion of
the particle remains intimately coupled to that of the surrounding fluid, and
while viscosity affects the fluid motion, it plays no part in the acoustic
pressure. Simplified equations, valid when only two physical effects control
the particle motion, are also derived. They are used to obtain sufficient
conditions for the particle to behave as a passive tracer of the
Lagrangian-mean fluid motion.
