Particle dynamics and pattern formation in a rotating suspension

Abstract

A rotating suspension of non-neutrally buoyant particles, confined by a horizontal cylinder, can be unstable to axial perturbations in concentration. A highly regular pattern of particle density and fluid flow then coexists in a non-equilibrium stationary state. The density profile along the cylinder axis is roughly sinusoidal, with a well-defined wavelength close to the cylinder diameter, and has a magnitude of approximately 30% of the average number density. We have used numerical simulations within the Stokes-flow approximation to investigate the mechanism underlying axial-band formation. Our results show that bands develop from an inhomogeneous particle distribution in the radial plane, which is itself driven by the competition between gravity and the viscous drag of the rotating fluid. We have discovered that the mean angular velocity of the particles is an order parameter which distinguishes between a low-frequency segregated phase and a high-frequency dispersed phase, where the particles fill the whole volume uniformly. The order parameter is a function of a single dimensionless frequency, with a characteristic length that is the mean interparticle separation. As the rotational frequency increases, the particle distribution becomes more homogeneous and the band structure disappears. Hydrodynamic diffusion stabilizes the suspension against centrifugal forces, allowing for a uniformly dispersed phase that can be used to grow three-dimensional cell cultures in an artificial microgravity environment.