### Abstract

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.

Original language | English |
---|---|

Article number | 0149 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 474 |

Issue number | 2217 |

Early online date | 5 Sep 2018 |

DOIs | |

Publication status | Published - Sep 2018 |

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### Keywords

- Homogenization
- Porous media
- Richards’ equation

### ASJC Scopus subject areas

- Mathematics(all)
- Engineering(all)
- Physics and Astronomy(all)

### Cite this

*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*,

*474*(2217), [0149]. https://doi.org/10.1098/rspa.2018.0149

**The effect of root exudates on rhizosphere water dynamics.** / Cooper, L. J.; Daly, K. R.; Hallett, P. D.; Koebernick, N.; George, T. S.; Roose, T. (Corresponding Author).

Research output: Contribution to journal › Article

*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*, vol. 474, no. 2217, 0149. https://doi.org/10.1098/rspa.2018.0149

}

TY - JOUR

T1 - The effect of root exudates on rhizosphere water dynamics

AU - Cooper, L. J.

AU - Daly, K. R.

AU - Hallett, P. D.

AU - Koebernick, N.

AU - George, T. S.

AU - Roose, T.

N1 - L.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 [35].

PY - 2018/9

Y1 - 2018/9

N2 - 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.

AB - 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.

KW - Homogenization

KW - Porous media

KW - Richards’ equation

UR - http://www.scopus.com/inward/record.url?scp=85054500987&partnerID=8YFLogxK

U2 - 10.1098/rspa.2018.0149

DO - 10.1098/rspa.2018.0149

M3 - Article

C2 - 30333700

AN - SCOPUS:85054500987

VL - 474

JO - Proceedings of the Royal Society A: Mathematical, Physical, and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical, and Engineering Sciences

SN - 1364-5021

IS - 2217

M1 - 0149

ER -