A model for inertial particle trapping locations in hydrodynamic tweezers arrays

Abstract

We present a model for the trapping of particles with finite inertia in the microscale viscous steady streaming flow of hydrodynamic tweezers. Devices containing a square array and an offset array of cylindrical posts of radius 25 µm were fabricated. As water is oscillated at small amplitude (s < 5 µm) and audible frequency (5000 Hz), highly symmetric microeddies form causing the fluid and particles suspended in the fluid to transport through the device. We image the flows by using 0.5 µm radius fluorescent polystyrene particles, and demonstrate trapping with larger 5 µm radius polystyrene particles. The streaming flow fields are simulated numerically using a fast analytic-numeric approach, and inertial particle motion is determined using the well-known Maxey–Riley equation for small Stokes number (St) particle motion. The St-dependent period-averaged particle velocity is used to describe the effects of inertia on particle trapping locations. We find the St-dependence of trapping location depends on the underlying symmetry of the flow. Only traps located near eddy centers are affected by particle inertia.