Unsteady particle motion in an acoustic standing wave field

The acoustic-based separation has attracted considerable attention in biomedical research, such as sorting of cells and particles. Current design principles used for acoustic systems are based on the steady Stokes theory, equating the Stokes drag with the primary radiation force. However, this approach is not valid for large cells/particles or in the presence of particle-particle interaction. In this work, we analytically examine unsteady inertial affects and particle-particle hydrodynamic interaction on the particle motion in a viscous fluid in the presence of an acoustic standing wave field. Comparing our results to the steady Stokes theory, we find that the unsteady inertial force decreases the particle's velocity, while particle-particle interaction enhances it. For a particular acoustic-based separation approach 'tilted-angle standing surface acoustic waves (taSSAW)', we find that both effects of unsteady inertial force and particle-particle interaction are evident and should be considered for O(10 mu m) particles or larger. Our study improves the current predictions of particle trajectory in acoustic-based separation devices.