  We derive analytical expressions for the three-dimensional (3D)
acoustophoretic motion of spherical microparticles in rectangular
microchannels. The motion is generated by the acoustic radiation force and the
acoustic streaming-induced drag force. In contrast to the classical theory of
Rayleigh streaming in shallow, infinite, parallel-plate channels, our theory
does include the effect of the microchannel side walls. The resulting
predictions agree well with numerics and experimental measurements of the
acoustophoretic motion of polystyrene spheres with nominal diameters of 0.537
um and 5.33 um. The 3D particle motion was recorded using astigmatism particle
tracking velocimetry under controlled thermal and acoustic conditions in a
long, straight, rectangular microchannel actuated in one of its transverse
standing ultrasound-wave resonance modes with one or two half-wavelengths. The
acoustic energy density is calibrated in situ based on measurements of the
radiation dominated motion of large 5-um-diam particles, allowing for
quantitative comparison between theoretical predictions and measurements of the
streaming induced motion of small 0.5-um-diam particles.

Fluid Dynamics