  Acoustic fields effect steady transport of suspended particles by rectifying
the inertia of primary oscillations. We develop a fully analytic theory that
relates this steady particle motion to incident oscillatory (acoustic) flow and
the time-averaged force acting on the particle, systematically spanning the
entire range between inviscid acoustofluidics and viscous particle
hydrodynamics. By applying the Lorentz reciprocal theorem, we obtain a
Fax\'{e}n-like relationship that includes nonlinear inertial forces, which
depend on (i) the thickness of the oscillatory Stokes layer around the
particle, and (ii) the density and compressibility contrast between the
particle and the fluid. The framework recovers secondary radiation forces for
thin Stokes layers, and predicts a reversal of the motion when the thickness of
the Stokes layer is comparable to the particle size. We quantitatively validate
the theory using numerical simulations of the timescale-separated
hydrodynamics.
