The Measurement of Soil Moisture Diffusivity

TLDR

The flow of moisture in unsaturated porous media is governed by a nonlinear diffusion equation whose diffusivity depends on moisture content, making analytical solutions challenging. Using Boltzmann’s method, the authors measured moisture profiles in sand columns after applying water at one end, then derived the diffusivity–moisture relationship from the resulting distribution curves. The derived diffusivity–moisture function spanned the full moisture range and revealed a peak at a moisture content below saturation.

Abstract

Abstract The solution of the differential equation describing the flow of moisture in unsaturated porous media is difficult because of the dependence of the permeability on moisture content. In the case of horizontal flow this equation can be written in a form similar to the non‐linear diffusion equation. The diffusivity in this equation is dependent upon the moisture content of the medium. Boltzmann has developed a treatment of the non‐linear diffusion equation which allows one to calculate the diffusivity‐moisture content function from a moisture content distribution curve. This treatment assumes that the moisture content is a function of a variable dependent on distance and the square root of the time. Columns of sand at a constant moisture content throughout their length were prepared. Water was applied at one end of the columns and allowed to move into them for a measured period of time. The distribution of moisture content in the columns was then determined and calculations of the diffusivity‐moisture content function were made. Data from one column gave moisture diffusivity values representing the entire moisture range of that column. The results indicate that there may be a maximum in the diffusivity‐moisture content function at a moisture content less than saturation.