Hierarchy of concentration waves in magnetic fluidized beds

The stability of a polarized fluidized bed is examined by theory which considers an approach of hierarchic interaction of concentration waves. A linear hyperbolic partial differential equation for particle concentration disturbances is obtained and is recast as the sum of two wave operators of different orders, which represent two kinds of waves propagating with different velocities along the fluidized bed. Stability is achieved when the propagation velocity of the higher order waves is greater than that of the lower order waves. It is verified that magnetic effects arisen from the magnetization of the particles in the presence of an external magnetic field act in the sense of increasing the propagation velocity of the higher order waves. The lower order waves, which are originated from the competition between drag and gravity forces on the particles, are found to be unaffected by the magnetic effects.