Transport analogy for segregation and granular rheology

Here, we show a direct connection between density-based segregation and granular rheology that can lead to insight into both problems. Our results exhibit a transition in the rate of segregation during simple shear that occurs at $I\sim 0.5$ and mimics a coincident regime change in flow rheology. We propose scaling arguments that support a packing fraction criterion for this transition that can both explain our segregation results as well as unify existing literature studies of granular rheology. By recasting a segregation model in terms of rheological parameters, we establish an approach that not only collapses results for a wide range of conditions, but also yields a direct relationship between the coordination number $z$ and the segregation velocity. Moreover, our approach predicts the precise location of the observed regime change or saturation. This suggests that it is possible to rationally design process operating conditions that lead to significantly lower segregation extents. These observations can have a profound impact on both the study of granular flow or mixing as well as industrial practice.