Clogging-flowing transition of granular media in a two-dimensional vertical pipe

TL;DR

This study reveals a nonmonotonic clogging probability $J$ for granular flow in a 2D vertical pipe, extending prior 3D findings to a planar geometry. By combining experiments with DEM simulations, it shows that both the geometric constraint $D/d$ and the interparticle friction coefficient $μ$ jointly govern the transition between clogging and flowing, enabling a $D/d$-$μ$ phase diagram with a friction-influenced flowing regime. The mechanism is anchored in arch formation: three-particle arches mediate clogging, and a simple force-torque balance criterion explains the observed nonmonotonicities, including a sharp drop near $D/d o 2.73$ due to contact-direction changes and a secondary drop near $D/d o 2.9$ due to arch geometry. The results advance predictive understanding of clogging in narrow vertical channels and highlight the critical role of non-equilibrium force states and arch geometry in 2D granular flows, with planned extensions to 3D and polydisperse systems.

Abstract

We experimentally and numerically investigate the clogging behavior of granular materials in a two-dimensional vertical pipe. The nonmonotonicity of clogging probability found in a cylindrical vertical pipe [López et al., Phys. Rev. E 102, 010902 (2020)] is also observed in the two-dimensional case. We numerically demonstrate that the clogging probability strongly correlates with the friction coefficient $μ$ in addition to the pipe-to-particle diameter ratio $D/d$. We thus construct a clogging-flowing $D/d$-$μ$ phase diagram within the $2<D/d<3$ range. Finally, by analyzing the geometrical arrangements of particles and using a simple analysis of forces and torques, we are able to predict the clogging-flowing transition in the $D/d$-$μ$ phase diagram and explain the mechanism of the observed counterintuitive nonmonotonicity in more detail. We demonstrate that for pipe clogging, friction-mediated force and torque equilibrium are essential for arch formation.

Figures (11)

• Figure 1: (a) Sketch of experimental setup. (b) Photo of experimental setup. (c) Sketch of discrete simulation before the discharge process is initiated. (d) Diagram of a typical arch composed of three particles. Forces on one particle near the wall are represented with blue vectors, from left to right: the frictional force exerted by the wall $f_1$, normal force exerted by the central particle $F_2$ of weight $G$, normal force exerted by the wall $F_1$ and the frictional force exerted by the central particle $f_2$. Also shown is a comparison of the experimental and discrete simulation results: (e) clogging probability $J_N(D/d)$ and (f) initial bulk particle volume fraction $\phi_b$ versus $D/d$ for $N=40$ and $\mu=0.4$. The total number of trials for the data in (e) is reported in supplementary. The results and error bars for $\phi_b$ in (f) are obtained from fewer trials ($N_t = 10$).
• Figure 1: Discrete simulation results: (a) initial height of the particle bed ${h_p}_i$, (b) final height of the particle bed ${h_p}_f$, and (c) the free-flowing fraction of clogging events $P_{t_f>2\sqrt{2d/g}}$ versus diameter aspect ratio $D/d$ for various $\mu$ with $N = 50$. The dashed black lines in (b) and (c) represent $x=2.73$.
• Figure 2: Discrete simulation results. Clogging probability $J_N(D/d)$ is plotted versus diameter aspect ratio $D/d$ (a) for various $N$ with $\mu=0.4$ and (b) for various $\mu$ with $N=50$. The vertical black dashed line represents $x=2.73$. (c) Clogging phase diagram of $D/d$ versus $\mu$. The black dashed line represents Eq. \ref{['equation8']}, shown for $2 < y < 3$. Clogging probability follows the color scale.
• Figure 2: A free-flowing fraction phase diagram $D/d-\mu$. The dashed black line represents Eq. 8 in the main manuscript. The dashed blue and red horizontal lines represent $y = 2.73$ and $y = 3$, respectively. $P_{t_f>2\sqrt{2d/g}}$ follows the color scale.
• Figure 3: (a) Typical particle arrangement at initial time and after clogging for various $D/d$ obtained by experiments. (b)Normal forces and particle arrangements for different $D/d$, obtained from simulations. Each panel shows the time sequence (from left to right) of the initial arrangement ($t = 0$) and subsequent states: for non-clogging cases at $t = 0.1875$ s ($D/d = 2.0, 2.4$); the clogged final state ($D/d = 2.6$); and the clogging evolution towards final arrest for $D/d = 2.8$, captured at $t = 0.025$, $0.055$, and $0.058$ s. The line thickness is proportional to the normal force. (c) Representative localized arch structure from a clogged state in the simulations.