Different physical phenomena are involved in fluidization, especially at high particle Reynolds numbers. Anderson and Jackson [1] performed a linear stability analysis and found that, in the absence of the particle pressure, fluidized beds are unstable with respect to any harmonic disturbance imposed on them. In real beds, disturbances can be found in the distributor and lead to the formation of bubbles of fluid. Garg and Pritchett [10] and Hernandez and Jimenez [13] introduced a particle pressure term and found that fluidized beds can be stable under some conditions. However, the effects of particle pressure and particle viscosity in fluidized beds are still not well understood. In particular, an investigation of the propagation characteristics of the amplification factor from linear stability analysis is essential to determine correctly how fluidized beds behave.

In this study, previous results are extended to gas- and liquid-fluidized beds with different physical properties. The effects of the physical parameters on the stability of the fluidized beds are investigated through a linear stability analysis. The averaged equations governing the dynamics of the fluidized beds are developed from the basic principles of conservation of mass and momentum. They consist of a set of coupled partial differential equations with coupling and interaction between the fluid and particle phases. The linearized eigenvalue stability equations are derived and then solved for the eigenvalues for both gas- and liquid-fluidized beds.

In the long-wave limit, we find that gas-fluidized beds exhibit primary instabilities in disturbances from a uniform fluidized bed whereas liquid-fluidized beds do not.

The propagation characteristics of the amplification factor and the phase velocity for gas- and liquid-fluidized beds are discussed in detail to illustrate the effect of changing physical parameters; in particular the effects of particle pressure, particle viscosity, and inertia are investigated. The results show that for finite non-zero wavenumbers both gas- and liquid-fluidized beds suffer the primary instabilities of a uniform fluidized bed. These instabilities take the form of rising and growing fluctuations whose propagation characteristics are related to the physical properties of the fluidized system.

The analysis also shows that particle pressure has a stabilizing effect and that the particle viscosity acts as a short-wave filter. It also shows that liquid-fluidized beds are more stable than gas-fluidized beds. In particular, the growth rates of disturbances are much smaller for the case of liquid beds and much lower values of particle pressure are required to reach stability, in agreement with experimental data.

The effects of the Reynolds and the Froude numbers on the stability of the bed are also investigated. For a certain range of the wavenumber, increasing the Reynolds numbers decreases the growth rate in both gas- and liquid-fluidized beds. However, the increase of the Reynolds number leads to an increase of the phase velocity in the gas-fluidized bed and to a decrease followed by an increase of the phase velocity in liquid-fluidized bed. Although the increase of the Froude number is ultimately stabilizing, this effect is not monotone; there are instances whereasmallchangeofthis number destabilizes the bed. Furthermore, increasing this number leads to amplification of the phase velocity in the gas-fluidized bed and to reduction in the liquid-fluidized bed.

instability, gas-liquid fluidized beds, linear stability analysis.