• Aco Janićijević University of Belgrade, Faculty of Technology and Metallurgy, Karnegijeva 4, Belgrade, Serbia
  • Svetislav Savović University of Kragujevac, Faculty of Science, R. Domanovića 12, Kragujevac, Serbia
  • Alexandar Djordjevich City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong, China



By solving the diffusion equation using the explicit finite difference method, oxygen concentrations inside the soil are determined for various periods of time. Two different cases are investigated, with constant and daily changing air oxygen concentrations. It was concluded that the influence of the periodical change of the air oxygen concentration on the oxygen concentration in the soil was more pronounced for smaller diffusion times at smaller lengths of the soil profile.


D. Hillel, Fundamentals of Soil Physics, Academic Press, New York 1980.

J. C. Refsgaard, T. H. Christensen, H. C. Ammentrop, A model for oxygen transport and consumption in the unsaturated zone, J. Hydrol., Vol. 129 (1991) 349–369.

R. S. Kanwar, S. Mukhtar, P. Singh, Transient state oxygen diffusion through undisturbed soil columns, Trans. ASAE 32 (1989) 1644–1650.

C. H. Huang, Y. Ouyang, J. En. Zhang, Effects of a compact layer on soil O2 diffusion, Geoderma, Vol. 135 (2006) 224–232.

J. Letey, L. H. Stolzy, N. Valoras, T. E. Szuskiewicz, Influence of soil oxygen on growth and mineral concentration of barley, Agron. J., Vol. 54 (1962) 538–540.

A. E. Erickson, Tillage effects on soil aeration, In: Predicting Tillage Effects on Soil Physical Properties and Processes, ch. 6. Am. Soc. Agron., Madison, WI (1982) 91–104.

R. I. Papendick, J. R. Runkles, Transient state oxygen diffusion in soil: I. The case when rate of oxygen consumption is constant, Soil Sci., Vol. 100 (1965) 251–261.

R. S. Kanwar, Analytical solutions of the transient-state oxygen diffusion equation in soil with a production term, J. Agron. Crop. Sci., Vol. 156 (1986) 101–109.

P. K. Kalita, Transient finite element method solution of oxygen diffusion in soil, Ecol. Modell., Vol. 118 (1999) 227–236.

S. Savović, J. Caldwell, Finite difference solution of one-dimensional Stefan problem with periodic boundary conditions, Int. J. Heat Mass Transfer, Vol. 46 (2003) 29112916.

S. Savović, J. Caldwell, Numerical solution of Stefan problem with time-dependent boundary conditions by variable space grid method, Thermal Science, Vol. 13 (2009) 165174.

J. D. Anderson, Computational Fluid Dynamics, McGraw-Hill, New York 1995.