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 $P_{\rm final}$ over a time $\tau_{\rm ramp}$ settle at packing fractions given by an inverse-logarithmic rate law, $\phi_{\rm settled}(\tau_{\rm ramp}) = \phi_{\rm settled}(\infty) + A/[1 + B\ln(1 + \tau_{\rm ramp}/\tau_{\rm slow})]$. This law is analogous to the one obtained from classical tapping experiments on noncohesive grains, but crucially different in that $\tau_{\rm slow}$ 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 $\phi_{\rm settled}(\tau_{\rm ramp})$, with $\phi_{\rm settled}(\infty) = \phi_{\rm ALP}$ and $A = \phi_{\rm settled}(0) - \phi_{\rm ALP}$, where $\phi_{\rm ALP} \equiv .135$ 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)].