Zaman Zafir, D'Ortona Umberto, Umbanhowar Paul B, Ottino Julio M, Lueptow Richard M
Department of Chemical & Biological Engineering, Northwestern University, Evanston, Illinois 60208, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Jul;88(1):012208. doi: 10.1103/PhysRevE.88.012208. Epub 2013 Jul 29.
Models of monodisperse particle flow in partially filled three-dimensional tumblers often assume that flow along the axis of rotation is negligible. We test this assumption, for spherical and double cone tumblers, using experiments and discrete element method simulations. Cross sections through the particle bed of a spherical tumbler show that, after a few rotations, a colored band of particles initially perpendicular to the axis of rotation deforms: particles near the surface drift toward the pole, while particles deeper in the flowing layer drift toward the equator. Tracking of mm-sized surface particles in tumblers with diameters of 8-14 cm shows particle axial displacements of one to two particle diameters, corresponding to axial drift that is 1-3% of the tumbler diameter, per pass through the flowing layer. The surface axial drift in both double cone and spherical tumblers is zero at the equator, increases moving away from the equator, and then decreases near the poles. Comparing results for the two tumbler geometries shows that wall slope causes axial drift, while drift speed increases with equatorial diameter. The dependence of axial drift on axial position for each tumbler geometry is similar when both are normalized by their respective maximum values.
部分填充的三维转鼓中，单分散颗粒流的模型通常假定沿旋转轴的流动可忽略不计。我们使用实验和离散元方法模拟，对球形和双锥转鼓检验了这一假设。通过球形转鼓颗粒床的横截面显示，经过几次旋转后，最初垂直于旋转轴的有色颗粒带会变形：靠近表面的颗粒向极点漂移，而流动层中较深处的颗粒向赤道漂移。对直径为8 - 14厘米的转鼓中毫米级表面颗粒进行追踪，结果显示每次通过流动层时，颗粒的轴向位移为一到两个颗粒直径，对应于轴向漂移，其为转鼓直径的1 - 3%。双锥转鼓和球形转鼓中的表面轴向漂移在赤道处为零，远离赤道时增加，然后在极点附近减小。比较两种转鼓几何形状的结果表明，壁面斜率会导致轴向漂移，而漂移速度随赤道直径增加。当将每种转鼓几何形状的轴向漂移对轴向位置的依赖性按各自的最大值进行归一化时，二者相似。
