Continuum model of mixing and size segregation in a rotating cylinder: concentration-flow coupling and streak formation

The effect of segregation and concentration-flow coupling on structure deve lopment in binary mixtures of different sized particles (S-systems) in a ro tating cylinder is studied. The system is a prototype of tumbling mixers wi dely used in industry for mixing, coating and reaction. Experiments with S- systems have shown the formation of radial streaks of the small particles w hen the size ratio is large; however, an explanation of this phenomenon is not available. A continuum model is presented here for the flow in the laye r using mass, momentum and species balance equations averaged across the la yer. The stress is assumed to be a sum of the Bagnold stress and the Coulom b frictional stress; the temperature and total solids volume fraction are a ssumed to be uniform across the layer. We consider the case of a large diff erence in particle sizes so that segregation upon flow is instantaneous and a step concentration profile exists at all points in the flowing layer wit h the smaller particles forming the lower layer. The velocity profile is as sumed to be piecewise linear with continuity of stress at the interface bet ween the small and large particles. The model predicts the time varying vel ocity, layer thickness and concentration fields in the system. The predicti ons are compared to experimental flow visualization studies. Conditions for the formation of streaks are investigated. (C) 2001 Elsevier Science BN. A ll rights reserved.