Instability of sedimenting bidisperse particle gas suspensions

A linear stability analysis for a sedimenting bidisperse gas-solid suspension (or gas fluidized bed) is performed. Mass, momentum and energy conservation equations for each of the two species are derived using constitutive equations that are valid at high Stokes numbers, (St(1) >> 1) The homogeneous suspension becomes unstable at sufficiently large St(1) to waves of particle volume fraction with the wave number in the vertical direction. Numerical calculations of the growth rate in an unbounded suspension indicate that the marginal stability limits are controlled by the small wave number (k << 1) behavior Depending on the Stokes number and the volume fractions phi(1) and phi(2) of the two species, the suspension becomes unstable due to O(k) or O (k(2)) contributions to the growth rate. The O(k) term corresponds to an instability due to kinematic waves similar to that predicted for bidisperse suspensions of particles in viscous liquids [22]. The O(k(2)) contribution represents an instability to dynamic waves similar to that obtained from an analysis of averaged equations for monodisperse fluidized beds [4].