MODELING OF SOLID PARTICLES IN FLUIDIZED-BEDS

A theory is proposed for the modeling of solid particles in fluidized beds based on ideas in the theory of interacting continua. The theory is capable of predicting the behavior of the mixture in the two extremes. That is, in one limit, as the concentration of solid particles becomes small, the theory reduces to the classical theory of incompressible viscous fluid. In the other limit, as the effect of the interstitial fluid becomes negligible, the theory reduces to the flow of incompressible granular materials. The mixture is considered to be made up of a linearly viscous fluid and granular materials. The stress tensor for the solid particles is derived using a modified version of Enskog's dense gas theory. The normal-stress effects that are observed experimentally in granular materials are predicted in this theory due to a solids fraction gradient. The dependence of the granular stress tensor on the solids fraction gradient arises by requiring that the correlating function that links the two-particle distribution function to the two single-particle distribution functions be the contact value for the radial distribution function of a non-homogeneous, hard sphere fluid. The interaction force is assumed to have contributions from density gradients, relative velocity (drag force), and relative acceleration (virtual mass force).