Segregation-rheology feedback in bidisperse granular flow: a coupled Stokes' problem

The feedback between particle-size segregation and rheology in bidisperse granular flows is studied numerically using the Stokes' problem configuration. A method of lines scheme solves the coupled momentum and segregation equations for an initially-graded particle bulk that suddenly is subjected to an upper plate movement at constant velocity. We show that the velocity profiles develop quickly into a short-lived steady state, decoupled from segregation yet determined by the particles' size ratio. From this transitory state, the velocity profile morphs due to the particles' relative movement, which redistributes the bulk's frictional response, hence its rheology. Additionally, we change the particles' friction via a frictional-coefficient ratio, in analogy with the particles' size ratio and the asymmetric coefficient. While positive values of this ratio exacerbate the size-ratio-induced non-linearity, negative values neutralize this behavior. The numerical solutions adjust well to the here-developed analytical solutions for the velocity profiles, which can be obtained from the steady-state conditions of the momentum and segregation equations for the short-lived and definitive steady states, respectively.