A model for water uptake in plants

摘要

A model is developed to describe water flow through soil containing roots. The governing equation is Richard's equation with a sink term representing extraction of water by the root system. Radial and axial flow in the root system is modeled as a resistance network, with radial resistances obtained approximately from a single root radial model and axial resistances obtained using the Hagen-Poisuille law. The analysis leads to a nonlinear parabolic partial differential equation coupled with a second order two-point boundary value problem. A maximum principle is proved for the system, giving uniqueness and continuous dependence on the data. Results of simulations are presented.