A Phase Segregation Model for a inary Granular Flow Using Mixture Theory

This thesis applies the mixture theory to develop a two-dimensional segregation model for a steady binary granular flow down an inclined plane. The mixture considered here is composed a group of large and heavy granulates and another group of small and light granulates. The current model is an extension of the vertical size segregation model developed by Gray and Thornton (2005) by considering more general flow conditions. Streamwise size segregation and density segregation are included to the model by appropriate interaction force components. Further, a new force component is proposed in this thesis by considering the gradient of a hydrodynamic pressure field formed in the bulk and in the constituent phases when segregation occurs. This new force is inviscid in nature and can be interpreted as a lift force in the potential flow theory generated across two streamlines with different velocities. Such a dynamic pressure force contributes to the total interaction force between the constituents which is the key element in the mixture theory when applied to study the bulk segregation dynamics. numerical scheme has been developed to solve the generalized segregation model and employed to investigate the segregation dynamics under various flow conditions. Special efforts are made to examine how the newly introduced segregation mechanisms affect the dominating vertical size segregation, a feature that generally determines the bulk segregation behavior. In general, all these new mechanisms hinder the segregation process and thus prolong the settling time for a uniform mixture to transit to its fully-segregated state. Density segregation, however, has the most pronounced influence. The onset of segregation leads to jump in the flow concentration profile, which is described as a ‘shock boundary’ in this work. The intersection of these shock boundaries determines a ‘triple point’ in a reference frame that moves with the bulk. The position of this triple point thus characterizes the final segregation pattern. It is found that the streamwise segregation convects the triple point towards the downstream and the non-uniform hydrodynamic pressure field may blur the shock boundaries.