op is the soil diffusion coefficient o0 is Diffusion coefficient in a free water system

œ is the volumetric water content and a and b are empirical constants characterising the soil

Solutes are transported at average velocity of the solution by convection, and in addition they are dispersed around the mean position of the front. Mathematically the mechanical dispersion may be treated as a diffusion process if one replaces the diffusion coefficient with the mechanical dispersion coefficient. The latter can be taken to be proportional to the first power of the average flow velocity. Under saturated and steady conditions we have:

oh is the mechanical dispersion coefficient

V is the average interstitial flow velocity

X is an experimental constant depending on the characteristics of the porous medium

The convection flux generally causes hydrodynamic dispersion, an effect that stems from the microscopic non-uniformity of flow velocity in the various pores. Thus a sharp boundary between two miscible solutions becomes increasingly diffuse about the mean position of the front. The change of solute content within a soil is related to the difference in the mass flux of solute applied to, and leaving the soil profile. As many authors ( Brandt, A. et al, 1971; Bresler E. et al, 1971; Thorburn et al., 1990), we can describe this by the following equation:

Csoii,z is the solute concentration of soil water, at depth z t is the time

œt is the moisture content at which leaching occurs I is the average infiltration rate L is the leaching flux, past some soil depth z Cj is the solute concentration of infiltrating water

We can then express the solute concentration of soil water at any time as follow:

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