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