Péclet number and transport length dependences of dispersion and dispersivity coefficients during the transition to Fickian transport in homogeneous sands

Abstract

This experimental study systematically investigates the influence of the Peclet number (Pe) and transport length on the transition to Fickian transport in homogeneous sand packs. Through Darcy column experiments with varying lengths and two distinct sediment sizes (d₅₀), we analyzed breakthrough curves (BTCs) to quantify non-Fickian characteristics and transport parameters. The dispersion coefficient exhibited an asymptotic transition to steady-state values between transport lengths of 0.91 m and 1.83 m, coinciding with a shift from heavy-tailed residence time distributions (RTDs) towards inverse Gaussian (Fickian) behavior. Non-Fickian attributes (quantified by skewness) scale with Pe via a power-law relationship, with exponents decreasing as transport length increases. During non-Fickian transport, the dispersion coefficient exhibited nonlinear power-law relationships with Pe, with the power-law exponent converging to ∼1 as transport length increased, consistent with hydrodynamic dispersion theory in the mechanical transport regime. The dispersivity coefficient (α) showed weak Pe dependence only in the non-Fickian regime and became Pe-independent under Fickian conditions. No significant length scale dependence of α was observed between 0.18 m and 1.83 m. This study demonstrates that extrapolating dispersivity from shorter length scales can be unreliable, as convergence to Fickian behavior requires transport lengths or solute transport representative elementary volume (REV) of at least 1 m These findings emphasize the need for longer experimental setups to determine asymptotic transport coefficients consistent with Fickian solute transport theory in porous media.