The inhomogeneous structure of a bidisperse sedimenting gas-solid suspension

We consider a model of a bidisperse gas-solid suspension in which the parti cles are subject to gravitational and Stokes drag forces and undergo elasti c solid-body collisions. Dynamic simulations of many interacting particles in a unit cell with periodic boundary conditions indicate that the suspensi on has an inhomogeneous structure on the length scale of the cell. A linear stability analysis of averaged equations of motion for the particulate pha se is used to predict the values of the Stokes number, particle volume frac tion, and unit cell length for which the homogeneous suspension is unstable and these results are compared with the numerical simulations. The suspens ion is subject to long horizontal wave instabilities at sufficiently high p article volume fractions and low Stokes numbers. The mechanism of instabili ty involves a coupling between the shear flow induced by particle volume fr action variations and the collisional exchange of momentum between the part icles. Solutions of the averaged equations successfully capture the particl e velocity fields induced by the inhomogeneous structure in the unstable su spensions. These velocity fields are characterized by the mean and variance of the particle velocity and by momentum-density correlation functions. Wh en the total particle volume fraction is small, the simulated suspensions a re stable but still exhibit long-range structure. This structure may be att ributed to a pair probability, corresponding to an excess of neighbors of t he same species, and a deficit of neighbors of the other species, which dec ays like 1/r with radial distance r. (C) 1999 American Institute of Physics . [S1070-6631(99)02810-X].