Percolation of a rod-like particle in a static bed of spheres: trapping and passing
We numerically investigate percolation of independent frictionless glued-sphere rod-like particles under gravity through a disordered static bed of larger spheres. We identify two distinct regimes: a \emph{trapping} regime, where rods stop after percolating a limited distance in the bed and a \emph{passing} regime, where rods percolate continuously with constant mean velocity. The transition between these regimes is governed by the length of the rod and the geometrical trapping threshold for spherical particles based on the rod diameter and the minimum pore throat diameter defined by three touching large spheres. The percolation velocity for all rod geometries, including the single sphere limit, collapses onto a single curve when scaled with the gravitational acceleration and the bed sphere diameter. The results also demonstrate that short rods percolate nearly twice as fast as long rods due to the geometric constraints associated with the disordered pore structure of the static bed. Consequently, long rods are more susceptible to trapping via specific contact configurations with the bed spheres, which differ from those for short rods. These results reveal how shape anisotropy introduces dynamical constraints and thresholds in granular percolation, with implications for predicting segregation in mixtures of non-spherical particles.