A simple mathematical model for investigating the effect of cluster roots on plant nutrient uptake

Cluster roots are thought to play an important role in mediating nutrient uptake by plants. In this paper we develop a mathematical model for the transport and uptake of phosphate by a single root. Phosphate is assumed to diffuse in the soil fluid phase and can also solubilised due to citrate exudation. Using multiple scale homogenisation techniques we derive an effective model that accounts for the cumulative effect of citrate exudation and phosphate uptake by cluster roots whilst still retaining all the necessary information about the microscale geometry and effects.