Abstract
Acoustic fields are widely used to manipulate suspended particles, by rectifying the inertia of rapid oscillations into steady transport. We develop an analytic theory of this particle motion, systematically unifying inviscid acoustophoresis with viscous streaming effects. By applying the Lorentz reciprocal theorem, we obtain a Faxén-like relationship that relates particle motion to a generalized version of the secondary radiation force that depends on the thickness of the oscillatory Stokes layer around the particle, and the density and compressibility contrast between the particle and the fluid. The theory identifies a reversal of particle motion when inertial and viscous forces are comparable, which we validate quantitatively with numerical solutions of the timescale-separated hydrodynamics. We discuss the implications of our findings for practical applications seeking to sort or focus particles by size or material properties.
