Particle orientation distribution in a rotating, dilute suspension of rod-shaped particles

Abstract

We consider a theoretical model for the settling of rod-shaped particles of a dilute, initially homogeneous, suspension in rapid rotation. The particle Reynolds number and the particle Taylor number of the detailed flow around the particles are assumed small, representing a relevant limit for an industrial centrifugal separation process. By applying a statistical approach using the Fokker–Planck equation, and neglecting particle–particle interactions, we obtain an explicit, analytical solution for the time dependent, spatially uniform particle orientation distribution function. Not only does the volume fraction in the bulk of the suspension decrease with time due to the divergent centrifugal field, as similarly described in the literature for suspensions of spherical particles, the orientation of the rod particles also changes with time from an initially uniform distribution to one where the particles tend to align with a plane perpendicular to the axis of rotation. The corresponding particle trajectories, as also influenced by first-order effects from the Coriolis acceleration and gyroscopic effects, are obtained numerically for different initial particle orientation angles.