A mathematical model is presented from which one can predict the likely dimensions of oxidised rhizospheres due to oxygen diffusing from roots into anaerobic media such as wet soil. The analysis applies Fick's law of diffusion to the diffusion of oxygen from a cylindrical object (the root) into a sink (the soil) which is absorbing oxygen at a constant rate M. Solution of the final equation gives the dimensions of the oxygenated rhizosphere, i.e. the distance from the root at which the oxygen concentration becomes zero.
The results obtained supoprt the view that oxygen diffusing from roots will produce a rhizosphere ‘sheath’ charged with oxygen. Furthermore, some of the predicted limits for this oxygen sheath correspond with those of ferric iron sheaths around roots in waterlogged soils. Calculations also show that oxygenated rhizospheres around the roots of plants very tolerant of reducing conditions. e.g. Menyanthes trifoliata, Oryza sativa and Eriophorum angustifolium, should be from two to three times as broad as for Molinia coerulea which is a species intolerant of strong reducing conditions.
Consequently if oxidation reactions are not instantaneous but occur only gradually as quantities of reduced products enter the oxygenated zone, then the plants with the larger rhizospheres will be significantly better protected from absorbing large amounts of reduced products than will those plants with smaller oxygenated zones. This may in part explain the reason for intervarietal defferences in physiological disease resistance in rice.
Finally the observation is made that small lateral roots can be expected to oxygenate a zone nearly as large as, or probably larger, than the primary root from which they have arisen.