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

TL;DR

This study uses direct numerical simulation to analyze circular band formation in fluid-rigid particle mixtures within a rotating cylinder, revealing that particle interactions and gravity influence band compactness.

Contribution

It demonstrates that circular band formation results from particle interactions and gravity effects, not from inertial waves, providing new insights into the dynamics of such mixtures.

Findings

Particle interactions are key to band formation.

Gravity affects the compactness of the bands.

Sufficient particle density is necessary for stable band formation.

Abstract

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 not resulted by mutual interaction between the particles and the periodic inertial waves in the cylinder axis direction (as suggested in Phys. Rev. E, 72, 021407 (2005)), but due to the interaction of particles. When a circular band is forming, the part of the band formed by the particles moving downward becomes more compact due to the particle interaction strengthened by the downward acceleration from the gravity. The part of a band formed by the particles moving upward is always loosening up due to the slow down of the particle motion by the counter effect of the gravity. To form a compact circular band (not a loosely one), enough particles are needed to interact among themselves continuously through the entire circular band at a rotating rate so that the upward diffusion of particles can be balanced by the compactness process when these particles moving downward.