LINEAR, NONLINEAR SMALL-AMPLITUDE, STEADY AND SHOCK-WAVES IN MAGNETICALLY STABILIZED LIQUID-SOLID AND GAS-SOLID FLUIDIZED-BEDS

The propagation of solid concentration disturbances in fluidized beds in an external magnetic field is considered. Both solid particles and the liquid phase are assumed to be simultaneously magnetizable. The to tal fluid-particle interaction force is supposed to include the inerti al component proportional to the relative acceleration of fluid and pa rticles. The effect of simultaneous magnetization of particles and flu id as well as the influence of the inertial component of interphase in teraction force on the resulting criterion of stability of the uniform fluidization are analysed. Consideration is given to the dispersion p henomena in the wave propagation process. The model of propagation of nonlinear waves is developed in approximation of small finite-amplitud e waves. The basic equations are reduced to the Korteweg-de Vries-Burg ers equation for the departure of solid concentration from the uniform state. Possible configurations of the concentration wavefront are stu died, including the oscillating wavefronts and small-amplitude shocks. The conditions of realization of each possible configuration are obta ined. The propagation of a long finite-amplitude nonlinear steady wave is considered. The conditions for the existence of the steady concent ration wave are derived. The The structure of the wavefront is studied and the thickness of the front is calculated as a function of magneti c and other physical parameters and the concentrations ahead of and be hind the front. The conditions across the concentration shock in the f luidized bed of magnetic particles are obtained. The shock speed is ca lculated. The obtained results can be used to analyse structures of bo undaries of bubbles, slugs and solid clusters formed in magnetically s tabilized fluidized beds. In conclusion the analogy between the basic equations of magnetic fluidized beds and equations of the ''particle b ed'' model by Foscolo & Gibilaro is briefly discussed in order to anal yse the possibility to apply the developed approach to the study of th e considered classes of nonlinear waves in conventional fluidized beds .