Document Type

Thesis - Open Access

Award Date


Degree Name

Doctor of Philosophy (PhD)

Department / School



A mathematical model based on the diffusion theory of gases was developed to account for the oxygen status of a moist soil. The theoretical development has its basis in the differential equation for diffusion which has been modified in include the oxygen consumption factor or activity of the soil. Solutions of the modified equation were obtained for the case where (1) the activity factor was a constant over a given time interval, and (2) the activity factor varied with time. A means for expressing the activity factor mathematically when it occurs as a complicated function of time has been proposed. This study showed that the oxygen consumption factor could be expressed as a series of first order reactions terminated by a constant during the period following the moistening of an air-dry soil. Variations in the soil moisture content in the moisture range above field capacity had little effect on the activity. A non-steady state solution of the diffusion equation was used to evaluate diffusion-porosity relationships for the moist soil. In general, there is a good agreement between theory and the experimental model when the activity factor is constant and when it varies with time as long as the soil oxygen supply does not become seriously diminished. From this study, it can be concluded that as long as the soil oxygen supply does not become seriously diminished (1) the diffusion equation can be used to describe the oxygen status of moist soil when it is modified to take in account the oxygen consumption actor or activity of the soil, and (2) under the condition that this study was made, diffusive flow accounts for the major part of the oxygen movements in soil.

Library of Congress Subject Headings

Soil absorption and adsorption


Includes bibliographical references




South Dakota State University