A mathematical model of plant nutrient uptake

The classical model of plant root nutrient uptake due to Nye, Tinker and Ba rber is developed and extended. We provide an explicit closed formula for t he uptake by a single cylindrical root for all cases of practical interest by solving the absorption-diffusion equation for the soil nutrient concentr ation asymptotically in the limit of large time. We then use this single ro ot model as a building block to construct a model which allows for root siz e distribution in a more realistic plant root system. and we include the ef fects or root branching and growth. The results are compared with previous theoretical and experimental studies.