Ultraslow settling kinetics of frictional cohesive powders

Abstract

Using discrete element method simulations, we show that the settling of frictional cohesive grains under ramped-pressure compression exhibits strong history dependence and slow dynamics that are not present for grains that lack either cohesion or friction. Systems prepared by beginning with a dilute state and then ramping the pressure to a small positive value $P_{\mathrm{final}}$ over a time ${\tau }_{\mathrm{ramp}}$ settle at packing fractions given by an inverse-logarithmic rate law, ${\varphi }_{\mathrm{settled}}({\tau }_{\mathrm{ramp}})={\varphi }_{\mathrm{settled}}(\infty )+A/[1+B\ln (1+{\tau }_{\mathrm{ramp}}/{\tau }_{\mathrm{slow}})]$. This law is analogous to the one obtained from classical tapping experiments on noncohesive grains, but crucially different in that ${\tau }_{\mathrm{slow}}$ is set by the slow dynamics of structural void stabilization rather than the faster dynamics of bulk densification. We formulate a kinetic free-void-volume theory that predicts this ${\varphi }_{\mathrm{settled}}({\tau }_{\mathrm{ramp}})$, with ${\varphi }_{\mathrm{settled}}(\infty )={\varphi }_{\mathrm{ALP}}$ and $A={\varphi }_{\mathrm{settled}}(0)-{\varphi }_{\mathrm{ALP}}$, where ${\varphi }_{\mathrm{ALP}}\equiv .135$ is the ``adhesive loose packing'' fraction found by Liu \textit{et al.} [W.\ Liu, Y.\ Jin, S. Chen, H.\ A.\ Makse and S.\ Li, \textit{Soft Matt.} \textbf{13}, 421 (2017)].

Supplemental Material available upon request

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