Roots Partially in Contact with Soil: Analytical Solutions and Approximation in Models of Nutrient and Water Uptake

Root-soil contact entails a trade-off between uptake opportunities and aeration requirements. A single root in the center of a cylinder of soil has been the standard geometry for which most root-level water and nutrient uptake models have been derived. However, this implies assumptions about complete root-soil contact and regularly spaced, parallel roots that do not conform to the situation in the field. In reality, the frequency distribution of transport distances will differ from what the cylinder model assumes, both by partial root-soil contact and irregular three-dimensional (3-D) distribution. We derived analytical equations describing the transport of water and nutrients to and uptake by roots in partial contact with soil for two extremes: (i) part of each root in contact or (ii) part of all roots in full contact and the rest without. Solutions range from negligible impacts to proportionality of uptake to the part of roots in contact with soil.