An expression for the angle of repose of dry cohesive granular materials on Earth and in planetary environments

The angle of repose-i.e., the angle theta r between the sloping side of a heap of particles and the horizontal-provides one of the most important observables characterizing the packing and flowability of a granular material. However, this angle is determined by still poorly understood particle-scale processes, as the interactions between particles in the heap cause resistance to roll and slide under the action of gravity. A theoretical expression that predicts theta(r) as a function of particle size and gravity would have impact in the engineering, environmental, and planetary sciences. Here we present such an expression, which we have derived from particle-based numerical simulations that account for both sliding and rolling resistance, as well as for nonbonded attractive particle-particle interactions (van der Waals). Our expression is simple and reproduces the angle of repose of experimental conical heaps as a function of particle size, as well as theta(r) obtained from our simulations with gravity from 0.06 to 100 times that of Earth. Furthermore, we find that heaps undergo a transition from conical to irregular shape when the cohesive to gravitational force ratio exceeds a critical value, thus providing a proxy for particle-scale interactions from heap morphology