Fine Particle Percolation Dynamics in Porous Media

The influences of restitution coefficient, eₙ, inter-particle friction, $μ$, and size ratio, R, on gravity-driven percolation of fine particles through static beds of larger particles in the free-sifting regime (R 6.5) remain largely unexplored. Here we use discrete element method simulations to study the fine particle percolation velocity, vₚ, and velocity fluctuations, vᵣₘₛ, for 7 ≤ R ≤ 50 and a range of eₙ and $μ$. Increasing eₙ increases velocity fluctuations and reduces percolation velocity. Increasing $μ$ decreases vᵣₘₛ but its influence on vₚ varies with vᵣₘₛ, decreasing vₚ for low vᵣₘₛ and increasing vₚ for high vᵣₘₛ. Although the influence of size ratio is weaker, larger values of R increase both vₚ and vᵣₘₛ. We also assess the influence of different excitation mechanisms, specifically using static, randomly excited, and sheared beds, finding that an inverse correlation between vₚ and vᵣₘₛ persists across all cases and is well-described by the Drude model, where increased scattering reduces mobility, when vᵣₘₛ is large. However, for weakly excited particles with low vᵣₘₛ, the Drude analogy breaks down. In this regime, we introduce a staircase-inspired model that accounts for the gravitationally dominated percolation behavior. These findings provide fundamental insight into the mechanisms governing percolation dynamics in porous media and granular systems.