Hydrodynamic Dispersion in an Unsaturated Dune Sand

Abstract

Solutes spread relative to the mean displacement position during water flow in soils as a result of meandering through the (partially) saturated pore complex. Spreading is characterized by the hydrodynamic dispersion coefficient in the convection-dispersion equation (CDE). This coefficient has been extensively studied for saturated soils. In this study hydrodynamic dispersion coefficients for nonaggregated dune sand were determined as a function of volumetric water contents, θ, ranging from saturation to 0.08 cm3cm−3 in columns of 5-cm diam. and 25- to 40-cm length. Unit-gradient flow experiments were conducted to measure solute breakthrough curves (BTCs) using four-electrode salinity probes at several column depths. Transport parameters for the CDE and the mobile-immobile model (MIM) were determined by optimizing analytical solutions to observed BTCs. A maximum dispersivity, λ, of 0.97 cm was found at θ = 0.13, whereas for saturated flow λ ≈ 0.1 cm irrespective of pore-water velocity ranging from 208 to 5878 cm d−1 For the MIM, the mobile water fraction, θm/θ, gradually deceased from almost unity at saturation to a minimum of 0.85 at θ = 0.15 followed by a slight increase with further desaturation. The exchange time between the mobile and immobile phases, 1/α, was 0.1 to 0.2 d for θ > 0.15 presumably because of the relatively homogeneous flow with convective solute mixing. For lower θ, the exchange became much slower since flow predominantly occurs in water films enveloping sand particles. The Peclet number for molecular diffusion, Pe, decreases as the role of transverse diffusion increases at lower θ because of smaller v and thinner water films while the resistance increases for solute exchange between mobile and immobile phases. These combined effects lead to a maximum dispersivity value at intermediate water contents in the case of the nonaggregated dune sand.