Modeling and mathematical analysis of root water uptake in the rhizosphere

Abstract

This research focuses on elucidating a system of partial differential equations designed to model the process of water uptake by a single root within an unsaturated soil. This model extends a unidimensional root scenario by incorporating radial and axial hydraulic conductance in the root structure. The flow dynamics in the rhizosphere are represented by the Richards equation, while a diffusion equation is employed to characterize water movement within the root. The resulting system forms a strongly coupled, nonlinear parabolic-elliptic system. To establish the existence and uniqueness of a solution, we utilize the technique of semi-discretization and the Schauder-Tychonoff fixed point theorem. Additionally, we approximate the system using a mixed finite element method, and the subsequent numerical tests presented align well with the model predictions. This comprehensive approach contributes to our understanding of the intricate dynamics involved in root water uptake and provides a robust framework for further exploration in this field.