7 - The first equations of change for fluidization

Abstract

This chapter discusses the first equations of change for fluidization. The first published formulations of the governing equations for fluidization appeared in the scientific literature in the mid-1960s. This was a period of crucial importance for chemical engineering development, marking a change in emphasis away from applied, process-specific rules-of-thumb to the basic concepts embodied in the conservation laws for mass, momentum, and energy transport. The analysis presented in this chapter represents simplified generalization of formulations appearing around that time, which all arrived at the same conclusion regarding the stability of the state of homogeneous fluidization—a convergence that led to its almost universal acceptance. The main differences in the separate treatments concerned the manner in which the interaction force between the particle and fluid phases was formulated; one shall see that stability predictions are largely independent of such details. In the analysis that follows, the particle phase of a fluidized bed is treated in some respects as though it were a continuum, or fluid. Thus the term two-fluid model is sometimes applied to this and related formulations. A differential control volume is defined, from which equations specifying conservation of mass and momentum for the one-dimensional vertical flow of the fluid and particle phases may be written. Both the particles and the fluid may be regarded as being incompressible.