ROOT AERATION IN UNSATURATED SOIL: A MULTI‐SHELLED MATHEMATICAL MODEL OF OXYGEN DIFFUSION AND DISTRIBUTION WITH AND WITHOUT SECTORAL WET‐SOIL BLOCKING OF THE DIFFUSION PATH

S ummary Treating the root as a homogeneous cylinder with respect to oxygen diffusivity and respiratory demand is a mathematically convenient assumption that has long been an inherent weakness and potential source of error in modelling the oxygen relations of soil‐aerated roots. The two models described here render such assumptions unnecessary: radial differences in oxygen diffusivity and respiratory demand between stele, cortex, wall layers and rhizosphere film have been accommodated by modelling the root: rhizosphere system as a multicylindrical unit. The models were designed to examine the influence of radial and circumferential cortical gas‐phase diffusion on oxygen concentrations and, also, to supplement recent theoretical studies into the effects of a sectoral blocking of the radial diffusion path for oxygen by circumferential contact between root and wet soil. Model I treats symmetrical surroundings assuming uniformity in the rhizosphere and accommodates the formation of an anoxic region within the root. Model II allows for the probability of partial blocking of the root's circumference, but only holds for fully aerobic roots. As expected the results reveal markedly contrasting oxygen profiles between those roots having significant cortical gas‐phase diffusion (porous roots) and those without such diffusion (non‐porous). A stepped oxygen profile, the result of a shallow gradient in the cortex, characterizes the porous roots; in non‐porous roots a smooth profile is predicted. It is also predicted that as a consequence of cortical gas‐phase diffusion the maximum oxygen deficit (MOD) in porous roots ought normally to be confined to the stele and, with a deterioration in the soil oxygen supply, the stele will be first to experience anoxia. More adverse conditions accompany a high level of circumferential blocking and a second anoxic zone (in a part of the wall) should arise prior to the development of more widespread anoxia. In the examples shown, extensive blocking was required to create some stelar anoxia in porous roots but the apparent resistance to diffusion in the wall layer(s) and rhizosphere film in the unblocked sector was greatly enhanced by the effects of blocking elsewhere. It is shown that in the partially blocked porous root oxygen should mostly move circumferentially in the cortex of the blocked sector; movement in the stele should be largely radial. In non‐porous roots, blocking quickly shifts the MOD to the wall layers adjoining the blockage centre and the examples chosen indicated a wedge of anoxia spreading from the wall into cortex and stele when blocking exceeded 20%. Wall thickness was however of no particular significance. Annular contours, which indicate radial transport, are quickly lost as blocking progresses around non‐porous roots and eventually transport is approximately unidirectional across most of the root.