A generalized segregation and dispersion model for liquid-fluidized beds

This work builds upon our previous two studies [Ramirez, W.F., Galvin, K.P., 2005. Dynamic model of multispecies segregation and dispersion in liquid fluidized beds. A.I.Ch.E. Journal 51, 2103-2108; Galvin, K.P., Swann, R., Ramirez, W.F., 2006. Segregation and dispersion of a binary system of particles in a fluidized bed. A.I.Ch.E. Journal 52, 3401-3410] in establishing a dynamic continuum description of the segregation and dispersion of multiple particle species in a liquid-fluidized bed. A correlation for the particle dispersion coefficient, based on the kinetic theory of gases, is investigated in this present paper. Our adjustable model parameter was found to vary inversely with a particle Froude number, in a manner similar to the variation of the particle drag coefficient with the particle Reynolds number. Hence a new relationship for the dispersion coefficient, based around the kinetic theory of gases, was proposed and validated. The validation applies to a nominal particle Reynolds number in the range of 20-1000. A new solution strategy to the dynamic segregation and dispersion model, a shell balance approach, was developed to overcome the potential for a singularity above the bed where exceedingly low particle concentrations arise. This approach guarantees mass conservation of the particles. The model was validated against steady-state experimental data of binary particle systems consisting notionally of one particle size and two different particle densities. When the particle densities of the two species are very similar, it becomes necessary to treat each particle species as having a range of particle sizes, given that the small size range was equally significant to the difference in particle density. In this case the model was applied to 10 particle species. Moreover, the model is capable of capturing the dynamics of the layer inversion problem, illustrating the power of the model to describe complex fluidization behaviour.