Ultraslow settling kinetics of frictional cohesive powders

TL;DR

This study reveals that frictional cohesive powders exhibit ultraslow settling dynamics with a history-dependent inverse-logarithmic law, explained by a kinetic free-void-volume theory, highlighting the role of void stabilization in packing behavior.

Contribution

The paper introduces a kinetic free-void-volume theory to explain ultraslow settling kinetics of cohesive powders, emphasizing the importance of void stabilization over bulk densification.

Findings

Settling follows an inverse-logarithmic rate law.

Void stabilization governs slow dynamics.

The theory predicts the final packing fraction.

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)].