Theory of acoustophoresis in counterpropagating surface acoustic wave fields for particle separation

Acousotophoretic particle separations in counterpropagating surface acoustic wave (SAW) fields, e.g., standing SAWs (SSAWs), phase modulated SSAWs, tilted angle SSAWs, and partial standing SAWs, have proven successful. But there still lacks analytical tools for predicting the particle trajectory and optimizing the device designs. Here, we study the acoustophoresis of spherical Rayleigh particles in counterpropagating SAW fields and find that particle motions can be characterized into two distinct modes, the drift mode and the locked mode. Through theoretical studies, we provide analytical expressions of particle trajectories in different fields and different moving patterns. Based on these, we obtain theory-based protocols for designing such SAW acoustofluidic particle separation chips, which are demonstrated through finite-element simulations. The results here provide theoretical guidelines for designing high throughput and high efficiency particle separation devices.