A model for the angle of repose of granular materials on planetary surfaces

One of the most important observables characterizing the packing and flowability of particulate systems is the angle of repose, i.e., the angle between the horizontal and the sloping side of a heap of particles. Indeed, this angle provides an excellent proxy for particle size on planetary surfaces, because the smaller the particle is, the larger the impact of attractive van der Waals forces relative to particle weight. A mathematical expression for the angle of repose would thus provide a useful tool for bridging between the geomorphologic and particle scales, and would have implications in various industrial sectors as well. We have recently obtained such an expression from direct numerical simulations of particle-scale processes using Molecular Dynamics applied to granular physics [1]. Our simple expression reproduces the angle of repose observed in a very broad range of experiments, including particle sizes consistent with aerosols, sand and pebbles, and gravity values from 6% to 100 times the Earth's gravity. The future application of our equation might help to infer, for instance, on the size, surface energy and grain density of particles constituting granular surfaces on various celestial bodies of our solar system.

[1] Elekes, F.; Parteli, E. J. R. An expression for the angle of repose of dry cohesive granular materials on Earth and in planetary environments. Proc. Natl. Acad. Sci. USA 118 (38), e2107965118 (2021). doi:https://doi.org/10.1073/pnas.210796511