Monodisperse behavior of polydisperse flows

Granular flows can occur under low inertia conditions, called the quasi-static regime, and extend to highly inertial systems, called the inertial regime. In the latter, granular flows, particularly those having a variety of grain sizes-property known as polydispersity-have not been extensively studied. Existing rheological laws for monodisperse flows effectively capture volume and friction variations across inertial ranges, assuming the grains diameter as the flow characteristic length. For polydisperse materials, this assumption is less intuitive, and rheological laws cannot be extended straightforwardly. In this work, we employed the Discrete Element Method to study granular flows across varying inertial levels, aiming to identify a physically based length scale that represents the grain scale for polydisperse flows. We show that the average branch length (i.e., distance between the centers of contacting grains) is a representative value of the material's grain size distribution, remaining nearly constant across the explored range of inertia. Moreover, we show that monodisperse and polydisperse flows follow common inertial volume and friction laws when the average branch length is considered as the characteristic length. The findings of this work propose a new perspective for understanding the characteristic length of granular flows, providing a comprehensive interpretation based on the grains contacts. They also permit to extend rheological laws, initially proposed for monodisperse flows, to polydisperse flows by considering the characteristic length scale as the average branch length. Finally, Our results are useful for choosing the characteristic length that controls large-scale flows where polydispersity plays an important role.