3D inertial migration of microspheres in a microchannel flow: transition from radial to angular focusing

Particles suspended in a square channel flow tend to be focused near the centers of each channel face due to the inertial migration. We found a transition in the particle focusing mode, from radial to angular, using digital holographic microscopy technique. 3D positions of microspheres (d=7, 15$\mu $m) in a square microchannel (H=100$\mu $m) were measured at channel Reynolds number R$_{C}$=4.7$\sim $120. With increasing R$_{C}$, the particles migrated in radial direction in advance and then started to focus angularly toward the four equilibrium positions at around $R_{C}>$60. The degree of angular focusing was also found to be linearly increased as the product of shear-rate and particle diameter increases.