Effect of shape and friction on the packing and flow of granular materials

Abstract

The packing and flow of aspherical frictional particles are studied using discrete element simulations. Particles are superballs with shape ${|x|}^{s}+{|y|}^{s}+{|z|}^{s}=1$ that varies from sphere ($s=2$) to cube ($s=\ensuremath{\infty}$), constructed with an overlapping-sphere model. Both packing fraction, $\ensuremath{\phi}$, and coordination number, $z$, decrease monotonically with microscopic friction $\ensuremath{\mu}$, for all shapes. However, this decrease is more dramatic for larger $s$ due to a reduction in the fraction of face-face contacts with increasing friction. For flowing grains, the dynamic friction $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\mu}}$---the ratio of shear to normal stresses---depends on shape, microscopic friction, and inertial number $I.$ For all shapes, $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\mu}}$ grows from its quasistatic value ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\mu}}}_{0}$ as $(\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\mu}}\ensuremath{-}{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\mu}}}_{0})=d{I}^{\ensuremath{\alpha}}$, with different universal behavior for frictional and frictionless shapes. For frictionless shapes the exponent $\ensuremath{\alpha}\ensuremath{\approx}0.5$ and prefactor $d\ensuremath{\approx}5{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\mu}}}_{0}$ while for frictional shapes $\ensuremath{\alpha}\ensuremath{\approx}1$ and $d$ varies only slightly. The results highlight that the flow exponents are universal and are consistent for all the shapes simulated here.