期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2021
卷号：118
期号：38
DOI：10.1073/pnas.2107965118
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：Significance
The angle between the sloping side of a heap of particles and the horizontal, called angle of repose, is often used to characterize the flowability of granular materials on Earth and planetary environments, such as sand, dust aerosols, and powders. In planetary research, this angle provides an excellent proxy for particle size. The smaller the particle is, the larger the effect of attractive forces between atoms and molecules on the surface of the particles relative to particle weight, the less flowable the material, and the steeper, thus, the angle of repose. We present a model that accurately predicts the angle of repose as a function of particle size, both on Earth and under extraterrestrial gravity.
The angle of repose—i.e., the angle
θ
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
θ
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
θ
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.
关键词：engranular materials;angle of repose;dry cohesive powders;planetary geomorphology;discrete-element method
