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

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 [L\'opez 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 $\mu$ in addition to the pipe-to-particle diameter ratio $D/d$. We thus construct a clogging-flowing $D/d$-$\mu$ 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 $D/d$-$\mu$ 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.