On the mathematics of fluidization Part 1. Fundamental equations and wave propagation

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Abstract
When the upward flow of a fluid through a bed of particles of appropriate and almost uniform size is rapid enough so that the drag on each particle is as great as the particles buoyant weight, the particles do not remain close packed and the bed is said to be fluidized. Industrial uses of fluidized beds in the chemical and petroleum industries in particular are already extensive. Uses in the atomicenergy industry are being developed.In this paper a mathematical model which describes the phenomena on a continuum basis is deduced. With this model we find that the system is unstable to small internal disturbances. Alternatively, we find that surface waves can be propagated (with attenuation) in the composite fluid and these waves for fluidized beds with a high ratio of solids density to fluid density are stable. These results are in agreement with experiment. Hot beds, where strongly exothermic reactions may be taking place, centrifugal beds (beds fluidized within a rotating system), and electromagnetic beds (those in which the particulate phase is electrically conducting) are all shown to be unstable to small internal disturbances.The equations derived here may also be used as approximate equations for dispersed particle two-phase flow.