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 development in binary mixtures of different sized particles (S-systems) in a rotating cylinder is studied. The system is a prototype of tumbling mixers widely used in industry for mixing, coating and reaction. Experiments with S-systems have shown the formation of radial streaks of the small particles when 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 layer using mass, momentum and species balance equations averaged across the layer. The stress is assumed to be a sum of the Bagnold stress and the Coulomb frictional stress; the temperature and total solids volume fraction are assumed to be uniform across the layer. We consider the case of a large difference in particle sizes so that segregation upon flow is instantaneous and a step concentration profile exists at all points in the flowing layer with the smaller particles forming the lower layer. The velocity profile is assumed to be piecewise linear with continuity of stress at the interface between the small and large particles. The model predicts the time varying velocity, layer thickness and concentration fields in the system. The predictions are compared to experimental flow visualization studies. Conditions for the formation of streaks are investigated.