Circular band formation for incompressible viscous fluid-rigid-particle mixtures in a rotating cylinder

In this paper we have investigated a circular band formation of fluid-rigid-particle mixtures in a fully filled cylinder horizontally rotating about its cylinder axis by direct numerical simulation. These phenomena are modeled by the Navier-Stokes equations coupled to the Euler-Newton equations describing the rigid solid motion of the non-neutrally particles. The formation of circular bands studied in this paper is mainly caused by the interaction between particles themselves. Within a circular band, the part of the band formed by the particles moving from the front to the back through the upper portion of the cylinder becomes more compact due to the particle interaction strengthened by the speedup of the particle speeds first by the rotation and later by the rotation and the gravity. The part of a band formed by the particles moving from the back to the front through the lower portion of the cylinder is always loosening up and spreading out due to the slowdown of the particle motion first by the rotation and then by the rotation and the counter effect of the gravity. To have a compact circular band, particles have to interact among themselves continuously through the entire circular band at an angular speed so that the separation of particles can be balanced by their aggregation.