Numerical Simulation of Diffusion in Cylindrical Pores: The Influence of Pore Radius on Particle Capture Kinetics

The diffusion and trapping of particles in complex porous media are fundamental processes in materials science and bioengineering. This study systematically investigates the influence of pore radius on particle capture kinetics within a three-dimensional cylindrical pore containing randomly distributed absorbing traps. Numerical simulations were performed for a wide range of pore radii (from 3a to 81a, a is a minimal length of the problem, arbitrary unit) and trap concentrations M (from 100 to 5090, these numbers are determined by the pore geometry) using a random walk algorithm. The particle lifetime (τ), characterizing the capture rate, was calculated and analyzed. Results reveal three distinct capture regimes dependent on trap concentration: a diffusion-limited regime at low concentration M (<1000), a transition regime at medium M (1000 < M < 2000), and a trap-density-dominated saturation regime at high M (>2000). For each regime, optimal approximating functions for τ(M) were identified. Furthermore, empirical relationships between the approximating coefficients and the pore radius were derived, which enable the prediction of particle lifetimes. The findings demonstrate that while the pore radius significantly impacts capture kinetics at low trap densities, its influence diminishes as trap concentration increases, converging towards a universal behavior dominated by trap density.