A Mathematical Model of Water and Nutrient Transport in Xylem Vessels of a Wheat Plant

At a time of increasing global demand for food, dwindling land and resources, and escalating pressures from climate change, the farming industry is undergoing financial strain, with a need to improve efficiency and crop yields. In order to improve efficiencies in farming, and in fertiliser usage in particular, understanding must be gained of the fertiliser-to-crop-yield pathway. We model one aspect of this pathway; the transport of nutrients within the vascular tissues of a crop plant from roots to leaves. We present a mathematical model of the transport of nutrients within the xylem vessels in response to the evapotranspiration of water. We determine seven different classes of flow, including positive unidirectional flow, which is optimal for nutrient transport from the roots to the leaves; and root multidirectional flow, which is similar to the hydraulic lift process observed in plants. We also investigate the effect of diffusion on nutrient transport and find that diffusion can be significant at the vessel termini especially if there is an axial efflux of nutrient, and at night when transpiration is minimal. Models such as these can then be coupled to whole-plant models to be used for optimisation of nutrient delivery scenarios.