Kinematics of monodisperse and bidisperse granular flows in quasi-two-dimensional bounded heaps

Yi Fan*, Paul B. Umbanhowar, Julio M. Ottino, Richard M. Lueptow

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

46 Scopus citations


Quasi-two-dimensional bounded heap flow is a useful model for many granular flows in industry and nature. It belongs to a family of free surface flows-inclined chute flow, rotating tumbler flow and unbounded heap flow-but differs from the others in that uniform deposition of particles onto the static bed results in the uniform rise of the heap. The kinematics, however, are only partially understood. We performed discrete element method simulations to study granular flows in quasi-twodimensional bounded heaps. The experimentally validated computational results show a universal functional form for the streamwise velocity profile for both monodisperse and bidisperse systems when velocities and coordinates are scaled by the local surface velocity and the local flowing layer thickness. This holds true regardless of streamwise location, feed rate, particle size distribution and, most surprisingly, the local particle concentration for bidisperse flows. The local surface velocity decreases linearly in the streamwise direction, while the flowing layer thickness remains nearly constant; both quantities depending only on local flow rate and local mean particle diameter. Additionally, the velocity profile normal to the overall flow, which is important in understanding segregation, can be predicted analytically from the streamwise velocity and matches the simulation results.

Original languageEnglish (US)
Article number20130235
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2157
StatePublished - Sep 8 2013


  • Granular materials
  • Heap flow
  • Kinematics

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)


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