The inhomogeneous structure of a bidisperse sedimenting gas–solid suspension

Abstract

We consider a model of a bidisperse gas–solid suspension in which the particles are subject to gravitational and Stokes drag forces and undergo elastic solid-body collisions. Dynamic simulations of many interacting particles in a unit cell with periodic boundary conditions indicate that the suspension has an inhomogeneous structure on the length scale of the cell. A linear stability analysis of averaged equations of motion for the particulate phase is used to predict the values of the Stokes number, particle volume fraction, and unit cell length for which the homogeneous suspension is unstable and these results are compared with the numerical simulations. The suspension is subject to long horizontal wave instabilities at sufficiently high particle volume fractions and low Stokes numbers. The mechanism of instability involves a coupling between the shear flow induced by particle volume fraction variations and the collisional exchange of momentum between the particles. Solutions of the averaged equations successfully capture the particle velocity fields induced by the inhomogeneous structure in the unstable suspensions. These velocity fields are characterized by the mean and variance of the particle velocity and by momentum-density correlation functions. When the total particle volume fraction is small, the simulated suspensions are stable but still exhibit long-range structure. This structure may be attributed to a pair probability, corresponding to an excess of neighbors of the same species, and a deficit of neighbors of the other species, which decays like 1/r with radial distance r.