Cluster Kinetics of Granular Mixing

Granular mixing of identical particles that cluster together is a challenging and important engineering problem. Mixing requires the breakup of clusters, both by individual particle detachment and cluster fragmentation. We apply a population balance (distribution kinetics) approach to describe such size-distributed cluster processes. Expressions for mixing effectiveness and segregation measures are derived and expressed in terms of the rate coefficients for reversible cluster distribution kinetics. Analytical and numerical moment solutions illustrate how the novel method is implemented and also provide some realistic results. The method allows straightforward derivation of experimentally observed long-time power law or exponential asymptotic behavior of segregation metrics for various rate coefficient expressions. © 2005 American Institute of Chemical Engineers AIChE J, 51: 406–414, 2005