Most water and nutrients essential for plant growth travel across a thin zone of soil at the interface between roots and soil, termed the rhizosphere. Chemicals exuded by plant roots can alter the fluid properties, such as viscosity, of the water phase, potentially with impacts on plant productivity and stress tolerance. In this paper, we study the effects of plant exudates on the macroscale properties of water movement in soil. Our starting point is a microscale description of two fluid flow and exudate diffusion in a periodic geometry composed from a regular repetition of a unit cell. Using multiscale homogenization theory, we derive a coupled set of equations that describe the movement of air and water, and the diffusion of plant exudates on the macroscale. These equations are parametrized by a set of cell problems that capture the flow behaviour. The mathematical steps are validated by comparing the resulting homogenized equations to the original pore scale equations, and we show that the difference between the two models is 7% for eight cells. The resulting equations provide a computationally efficient method to study plant–soil interactions. This will increase our ability to predict how contrasting root exudation patterns may influence crop uptake of water and nutrients.
|Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
|Early online date
|5 Sept 2018
|Published - Sept 2018
Bibliographical noteL.J.C. and N.K. are funded by BBSRC SARISA BB/L025620/1, L.J.C. is also funded by EPSRC EP/P020887/1. K.R.D. is funded by ERC 646809DIMR. P.D.H. and T.S.G. are funded by BBSRC BB/J00868/1. The James Hutton Institute receives funding from the Scottish Government. T.R. is funded by BBSRC SARISA BB/L025620/1, EPSRC EP/M020355/1, ERC 646809DIMR, BBSRC SARIC BB/P004180/1 and NERC NE/L00237/1.
Data supporting this study are available on request from the University of Southampton
repository at https://doi.org/10.5258/SOTON/D0609 .
- Porous media
- Richards’ equation