A study of two-body forces in fluidization

The effect of two-body forces on the structure of dynamic waves in fluidized beds is studied, with particular emphasis on expansion waves. Averaged equations of motion are used for the study, so the media appear to be interpenetrating continua. Both inertial and viscous two-body effects are considered for incompressible materials fluidized by an incompressible fluid. Inertial effects are included in the averaged momentum exchange force, using exact (classical) results for the potential flow generated by the motion of one submerged body relative to another body. Viscous effects are represented, in the limit of zero relative Reynolds number, by solutions to Stokes equations for the two-body problem. For simple one-dimensional motion the inertial force is repulsive always, giving a positive compressibility to the dispersed field total density; the force is of such a magnitude that the single-pressure continuum equations are unconditionally hyperbolic. The corresponding 1-D viscous force is attractive when the bodies move apart, and therefore introduces a negative compressibility to the dispersed field. Competition between the two-body inertial and viscous forces ultimately determines the nature of dynamic waves in a given fluidization system.