Characteristics of the dispersion coefficient in miscible displacement through a glass beads medium

Abstract

The importance of understanding the process of solute transport in soils is well documented in several fields of study, including water supply, environmental protection and agriculture. However, researchers still disagree on some topics, especially the nature of the unsaturated dispersion coefficient. Miscible displacement experiments, carried out using glass beads as the porous medium show that while the saturated dispersion coefficient increases linearly with pore water velocity, under unsaturated conditions, the dispersion coefficient increases linearly but more rapidly with pore water velocity up to a limiting moisture content. Beyond this moisture content, the unsaturated dispersion coefficient decreases and approaches that of the saturated condition. These phenomena are discussed in relation to variation in pore water velocity and the mixing length of flow paths inside the porous medium. Mixing length in this sense is characteristic of the porous medium within which the concentration of the solution conforms to the surrounding concentration. The dispersion coefficient is expressed as the product of mixing length and standard deviation of the pore water velocity which is estimated from the ψ-θ and K-θ relationships. The mixing lengths are found to be almost constant (about 0.23 cm) in the lower moisture content range (0.16–0.27 cm3 cm−3), but decrease at moisture contents greater than 0.27 cm3 cm−3. Mixing lengths are also smaller in saturated than in unsaturated conditions. Despite the apparent increase in pore water velocity and its variance at higher moisture content, the decrease in the dispersion coefficient can be attributed to a decrease in the mixing length.This study shows that the dispersion phenomenon, both in saturated and unsaturated conditions, can be described successfully using mixing length theory.