Résumé
The flow behavior of granular matter is significantly influenced by the shape
of constituent particles. This effect is particularly pronounced for very
concave particles, which exhibit unique flow characteristics such as higher
porosity and sharper phase transitions between jamming and unjamming states.
Despite the richness and ubiquitousness of these systems, our understanding of
their intricate flow behavior and the local mechanisms driving these behaviors
remains incomplete. In this work, we investigate the effect of particle shape,
ranging from spherical to highly concave, on steady flows in a rotating drum -
a system that facilitates a continuous phase transition from a jamming state at
greater depths to an unjamming state at shallower regions. We develop an
analytical model to elucidate granular behavior within the rotating drum: (i)
Firstly, by decomposing the shear stress, we reconcile the discrepancy between
simulation data and theoretical predictions, establishing a relationship with
the angle of repose. (ii)Secondly, we extend the generalized Bagnold scaling ,
coupled with a non-local fluidity relation based on packing fraction, providing
a framework for a correlation between shear stress, shear rate, and packing
fraction. Additionally, we introduce a characteristic length to quantify the
influence of particle shape and drum speed. This analytical model offers
explicit functional forms for physical quantity profiles, which are validated
experimentally in a thin rotating drum and numerically in a two-dimensional
rotating drum. Our results demonstrate that this model accurately describes the
change of velocity due to the phase transition of granular flow within a
rotating drum. Moreover, for different shapes of particle and drum speeds, the
characteristic length captures the interplay between shear stress, shear rate,
and the variation of packing fraction.