Stokesian relationships for the rheology of granular flows and particle-size segregation

Shear-induced segregation plays a critical role in various industrial and natural processes. The necessity to understand and predict particle segregation prompts our study of the basic principles underlying this phenomenon. This study aims to establish a relationship between segregation velocity and the properties of granular materials through various expressions connecting to a Stokes' settling velocity. We use the Discrete Element Method to simulate an intruder particle of varying sizes embedded in a sheared granular flow. From a comparison between theoretical trajectories and simulation results, we derive a new scaling law that offers a detailed characterization of the variables involved in segregation. Deviations between simulated and theoretical trajectories are also discussed. This study suggests an intrinsic connection between the segregation process and particle settling in fluids, leading to a Stokes-like expression for particle segregation velocity.