The motion of particles near a bubble in a gas-fluidized bed

Most models of gas bubbles in fluidized beds are based on the assumption of an empty central region, the void, surrounded by a 'cloud' or 'shell' of particles whose voidage is larger than that of the remote emulsion phase. Batchelor & Nitsche (1994) investigated the formation of a void by tracking the paths of particles initially within a buoyant 'blob' of gas that has the form of a toroidal vortex. They showed that the particles dropped through the floor of the blob under the influence of gravity, leaving it empty. This paper extends their method to particles initially outside the blob. It is shown that inertia allows these particles to penetrate the blob and it is the extent of this penetration that determines the size of the void. The void is nearly as large as the blob for small, light particles, but becomes smaller relative to the blob with increasing particle size and weight until it disappears altogether. This provides an explanation for experimental observations of voids smaller than the blob (or 'cloud' as it is sometimes known), and suggests that when examining bubbles in a gas-fluidized bed the most significant dimension is the diameter of the blob and not that of the void.