Plant and Soil

, Volume 77, Issue 2–3, pp 215–231 | Cite as

Mathematical models on diffusion of oxygen to and within plant roots, with special emphasis on effects of soil-root contact

I. Derivation of the models
  • P. De Willigen
  • M. Van Noordwijk


A mathematical model is presented for diffusive transport of oxygen inside the root, for the case that oxygen can enter only through part of the root's perimeter because the remainder is blocked by soil-root contact. Without soil-root contact, concentration profiles inside the root can be shown to converge rapidly to a steady-state solution. For the case of soil-root contact a steady-state solution is presented. Steady-state solutions have also been obtained for the presence of a water film, with and without rhizosphere respiration inside the water film. Results are presented in the form of isoconcentration lines.

Key words

Conformal mapping Diffusion Oxygen Soil-root contact 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Brouwer R and Wiersum L K 1977 Root aeration and crop growth.In Crop Physiology Vol. II. Ed. U S Gupta. Oxford Univ. Press and IBN Publ. Co., New Delhi. pp 157–201.Google Scholar
  2. 2.
    Cannel R Q 1977 Soil aeration and compaction in relation to root growth and soil management. Appl. Biol. 2, 1–86.Google Scholar
  3. 3.
    Cannel R Q and Jackson M B 1981 Alleviating aeration stresses.In Modifying the Root Environment to reduce Crop Stresses. Eds. G F Arkin and H M Taylor. ASAE monograph no 4, 141–194.Google Scholar
  4. 4.
    Carslaw H S and Jaeger J C 1959 Conduction of heat in solids. Second edition. Oxford, Clarendon, 510 p.Google Scholar
  5. 5.
    Churchill R V 1971 Complex variables and applications. McGraw-Hill-Kogakusha, Tokyo, 332 p.Google Scholar
  6. 6.
    Drew M C and Lynch J M 1980 Soil anaerobiosis, microorganisms and root function. Annu. Rev. Phytopathol. 18, 37–66.Google Scholar
  7. 7.
    Fluehler M, Ardakani M S, Szukiewicz T E and Stolzy H 1976 Field measurements of nitrous oxide concentration, redox potentials, oxygen diffusion rates and oxygen partial pressures in relation to denitrification. Soil Sci. 122, 107–114.Google Scholar
  8. 8.
    Lawrentjew M A and Schabat B W 1967 Methoden der komplexen Funktionentheorie. VEB Deutscher Verlag der Wissenschaften, Berlin, 846 p.Google Scholar
  9. 9.
    Lemon E R and Wiegand C L 1962 Soil aeration and plant root relations. II. Root respiration. Agron. J. 54, 171–175.Google Scholar
  10. 10.
    Stolzy L H and Fluehler H 1978 Measurement and prediction of anaerobiosis in soils.In Nitrogen in the Environment. Eds. D R Nielsen and J G MacDonald Academic Press, New York, Vol. 1, pp 363–426.Google Scholar
  11. 11.
    Wiligen P de 1984 Mathematical analysis of the significance of partial blocking of the root perimeter for oxygen and nutrient supply (In preparation).Google Scholar

Copyright information

© Martinus Nijhoff/Dr W. Junk Publishers 1984

Authors and Affiliations

  • P. De Willigen
    • 1
  • M. Van Noordwijk
    • 1
  1. 1.Institute for Soil FertilityHaren (Gr.)The Netherlands

Personalised recommendations