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A boundary-layer solution for flow at the soil-root interface
Gerardo Severino1, Daniel M Tartakovsky
1Division of Water Resources Management and Bio-System Engineering, University of Naples, Federico II via Universitá 100, 80055 , Portici, Naples, Italy, severino@unina.it.
Journal of Mathematical Biology
|July 11, 2014
Summary
This study models plant water uptake, explaining transpiration by analyzing root water absorption from soil. The findings provide a theoretical basis for understanding how plants absorb water and influence the hydrological cycle.
Area of Science:
- Hydrology
- Plant Physiology
- Soil Science
Background:
- Transpiration is a critical yet under-quantified process in the hydrological cycle.
- Understanding plant water uptake at the root scale is essential for accurate hydrological modeling.
Purpose of the Study:
- To develop a first-principles, root-scale model for plant water uptake and transpiration.
- To theoretically justify existing root-scale cylindrical flow models.
Main Methods:
- Utilized the Richards equation for water flow in unsaturated porous media.
- Employed Gardner's exponential constitutive relation for hydraulic conductivities.
- Applied matched asymptotic expansion techniques to derive approximate solutions.
Main Results:
- Derived approximate solutions for transpiration rate and plant capture zone size.
- Identified a perturbation parameter relating root size to soil capillary length.
- Defined a boundary layer at the soil-root interface with horizontal flow.
Conclusions:
- The model provides a theoretical foundation for the standard root-scale cylindrical flow model.
- The derived solutions are valid for roots larger than the soil's macroscopic capillary length.
- The analysis clarifies kinematic constraints on water flow in the soil-root continuum.
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