54 CHAPTER 6. STREAMING STUDIES
Figure 6.2: Particle trajectories illustrating the cross-over from streaming-induced drag force dominated
motion to radiation force dominated motion as a result of increasing particle size. (a) The starting positions
(dots) of 144 evenly distributed particles at t = 0 s. The following ve panels show the trajectories (colored
lines) and positions (dots) that the particles have reached by acoustophoresis at t = 10 s for ve dierent
particle diameters: (b) 0.5 m, (c) 1 m, (d) 2 m, (e) 3 m, and (f) 5 m. The colors indicate the
instantaneous particle speed u ranging from 0 m/s (dark blue) to 44 m/s (dark red). The lengths of the
trajectories indicate the distance covered by the particles in 10 s. Streaming-induced drag dominates the
motion of the smallest particles, which consequently are being advected along the acoustic streaming rolls.
In contrast, the acoustic radiation force dominates the motion of the larger particles, which therefore are
forced to the vertical nodal plane at y = 0 of the rst-order pressure p1. Figure adapted from Ref. 28
Appendix A.
6.3 Numerical modeling of acoustophoretic particle motion
Even with the improved analytical analysis and numerical model of acoustic streaming,
there was still a gab between the theoretical predictions of uid velocities and the experimental
measurements of particle velocities, as the drag force from the acoustic streaming
ow is not the only force acting on the suspended particles. This gab was closed by the
numerical particle tracking scheme presented in Ref. 28 Appendix A. Previously, experimental
studies of radiation force dominated particle motion was often neglecting the
small contribution from the streaming-induced drag force, and studies of drag force dominated
particle motion was neglecting the small contribution from the radiation force. In
Ref. 28 Appendix A this interplay between the radiation force and the streaming-induced
drag force was treated, and the particle motion was visualized, see Fig. 6.2. This provided
an intuitive understanding of the critical particle size and how the transition from radia