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.

中文翻译：

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非牛顿幂律流变学对通道流中颗粒惯性迁移的影响。

本文对幂律流体通道中颗粒的惯性迁移进行了数值研究。探索了幂律指数（n），雷诺数（Re），阻塞比（k）和通道纵横比（AR）对粒子惯性迁移和平衡位置的影响。结果表明，在方形通道的横截面上，存在两个阶段的粒子迁移和四个稳定的平衡位置。矩形通道中的颗粒平衡位置与方形通道中的颗粒平衡位置有很大不同。在剪切稀化流体中，在低Re处发现了长通道面平衡位置和两种粒子轨迹。随着Re的增加，短通道面平衡位置变为稳定，多平衡位置，长壁上的三种粒子轨迹开始形成。剪切增稠流体中仅存在两个稳定的平衡位置。随着n和k的增加以及Re的减小，平衡位置越来越靠近通道中心线。粒子迁移的第二阶段中的惯性聚焦长度L 2比第一阶段中的惯性聚焦长度L 1长得多。在方通道中，L 2随着Re和k以及n的减小而减小。在矩形通道中，L 2在剪切稀化流体中最短。粒子迁移的第二阶段中的惯性聚焦长度L 2比第一阶段中的惯性聚焦长度L 1长得多。在方通道中，L 2随着Re和k以及n的减小而减小。在矩形通道中，L 2在剪切稀化流体中最短。粒子迁移的第二阶段中的惯性聚焦长度L 2比第一阶段中的惯性聚焦长度L 1长得多。在方通道中，L 2随着Re和k以及n的减小而减小。在矩形通道中，L 2在剪切稀化流体中最短。