Transit time during the interparticle percolation process

A numerical investigation of jamming effect during the spontaneous interparticle percolation process of small beads through an unconsolidated porous media has been performed. The size ratio between the moving beads and the ones building up the porous medium was chosen larger than the geometrical trapping threshold: ${\xi }_c={\left(\frac{2}{\sqrt{3}}-1\right)}^{-1}=6.464\dots$. In this paper, we used the discrete element method algorithm to study the rebounds of particles on the top of the porous medium and the transit times of an assembly of particles through it. Several parameters such as the number of injected particles, the size ratio between beads, and the energy restitution coefficient are investigated. This study leads to give some important results of the evolution of the transit time versus the contiguous volume occupied by the percolating particles.

Figure 1

(Color online) Snapshot of flow of $20000$ small particles through a porous medium. Note that, for convenience, only half system is represented.

Figure 2

Packing fraction profile of the packing of spheres of diameter $D$. The height $h_{init}$, which permits to define $t_{init}$ is also represented.

Figure 3

Distributions of times $t_{init}$ for launches of different numbers of particles with $N=500$, $N=5000$ and $N=8000$ for $D/d=16$.

Figure 4

Evolution of mean time $⟨t_{init}⟩$ for different number of particles. This evolution is given in terms of number of filled pores via the parameter $N_p^N$. A linear adjustment is also represented.

Figure 5

Dependency of mean $t_{init}$ with $N_p^{d/D}$ for $N=1000$, $N=2000$ and $N=5000$.

Figure 6

Evolution of mean time $t_{init}$ with $e_1$ (a) and $e_2$ (b).

Figure 7

Evolution of dimensionless times: $⟨t⟩$ (global) and $⟨t^{\star }⟩$ (corrected) with $N_p^N$ with fixed value of $D/d=10$.

Figure 8

Evolutions of mean times $⟨t⟩$ (a) and $⟨t^{\star }⟩$ (b) with $N_p^{d/D}$ for $N=1000$, $N=2000$ and $N=5000$. Linear adjustments in dashed line are also represented.

Figure 9

Dimensionless velocities of a blob of particles with the restitution coefficient $e_1$ for $D/d=10$ and for $N=1000\left(N_p^N\approx 31\right)$, $N=2000\left(N_p^N\approx 60\right)$ and $N=5000\left(N_p^N\approx 146\right)$. Linear adjustments are also represented.