Particle pressure and marginal stability limits for a homogeneous monodisperse gas-fluidized bed: kinetic theory and numerical simulations

A linear stability analysis is performed for the homogeneous state of a mon odisperse gas-fluidized bed of spherical particles undergoing hydrodynamic interactions and solid-body collisions at small particle Reynolds number an d finite Stokes number. A prerequisite for the stability analysis is the de termination of the particle velocity variance which controls the particle-p hase pressure. In the absence of an imposed shear, this velocity variance a rises solely due to the hydrodynamic interactions among the particles. Sinc e the uniform state of these suspensions is unstable over a wide range of v alues of particle volume fraction phi and Stokes number St, full dynamic si mulations cannot be used in general to characterize the properties of the h omogeneous state. Instead, we use an asymptotic analysis for large Stokes n umbers together with numerical simulations of the hydrodynamic interactions among particles with specified velocities to determine the hydrodynamic so urces and sinks of particle-phase energy. In this limit, the velocity distr ibution to leading order is Maxwellian and therefore standard kinetic theor ies for granular/hard-sphere molecular systems can be used to predict the p article-phase pressure and rheology of the bed once the velocity variance o f the particles is determined. The analysis is then extended to moderately large Stokes numbers for which the anisotropy of the velocity distribution is considerable by using a kinetic theory which combines the theoretical an alysis of Koch (1990) for dilute suspensions (phi much less than 1) with nu merical simulation results for non-dilute suspensions at large Stokes numbe rs. A linear stability analysis of the resulting equations of motion provid es the first a priori predictions of the marginal stability limits for the homogeneous state of a gas-fluidized bed. Dynamical simulations following t he detailed motions of the particles in small periodic unit cells confirm t he theoretical predictions for the particle velocity variance. Simulations using larger unit cells exhibit an inhomogeneous structure consistent with the predicted instability of the homogeneous gas-solid suspension.