Influence of non-Newtonian power law rheology on inertial migration of particles in channel flow.

In this paper, the inertial migration of particles in the channel flow of power-law fluid is numerically investigated. The effects of the power-law index (n), Reynolds number (Re), blockage ratio (k), and channel aspect ratio (AR) on the inertial migration of particles and equilibrium position are explored. The results show that there exist two stages of particle migration and four stable equilibrium positions for particles in the cross section of a square channel. The particle equilibrium positions in a rectangular channel are much different from those in a square channel. In shear-thinning fluids, the long channel face equilibrium position and two kinds of particle trajectories are found at low Re. With increasing Re, the short channel face equilibrium position turns to be stable, multiequilibrium positions, and three kinds of particle trajectories along the long wall start to form. Only two stable equilibrium positions exist in shear-thickening fluids. The equilibrium positions are getting closer to the channel centerline with increasing n and k and with decreasing Re. The inertial focusing length L 2 in the second stage of particle migration is much longer than inertial focusing length L 1 in the first stage. In the square channel, L 2 is decreased with increasing Re and k and with decreasing n. In the rectangular channel, L 2 is the shortest in the shear-thinning fluid.