Modeling water uptake by a root system growing in a fixed soil volume

The water uptake by roots of plants is examined for an ideal situation, with an approximation that resembles plants growing in pots, meaning that the total soil volume is fixed. We propose a coupled water uptake-root growth model. A one-dimensional model for water flux and water uptake by a root system growing uniformly distributed in the soil is presented, and the Van Genuchten model for the transport of water in soil is used. The governing equations are represented by a moving boundary model for which the root length, as a function of time, is prescribed. The solution of the model is obtained by front-fixing and finite element methods. Model predictions for water uptake by a same plant growing in loam, silt and clay soils are obtained and compared. A sensitivity analysis to determine relative effects on water uptake when system parameters are changed is also presented and shows that the model and numerical method proposed are more sensitive to the root growth rate than to the rest of the parameters. This sensitivity decreases along time, reaching its maximum at thirty days. A comparison of this model with a fixed boundary model with and without root growth is also made. The results show qualitative differences from the beginning of the simulations, and quantitative differences after ten days of simulations.