The solution of convection–diffusion equations for solute transport to plant roots
The solution of convection–diffusion equations for solute transport to plant roots
To help develop models of solute uptake that are computationally efficient and suitable for up-scaling to whole root systems, we provide three alternative analytical solutions of equations for transport to absorbing roots by convection and diffusion, and we compare their performance with a numerical solution over the range of plant and soil conditions found in practice. We point out an important pitfall in commonly used methods to solve convection–diffusion equations numerically and show how it can be avoided. We identify a simple analytical solution that is valid for all realistic combinations of parameter values, and show that for most purposes it performs as well as a complete, but more complex, analytical solution allowing fully for both convection and diffusion. We conclude that this solution is suitable for use in general solute uptake models.
nutrient uptake, mathematical modelling, convection, water movement
257-264
Roose, T.
3581ab5b-71e1-4897-8d88-59f13f3bccfe
Kirk, G.J.D.
f7f5cb71-77f7-44f3-842c-ca6a6090b98c
March 2009
Roose, T.
3581ab5b-71e1-4897-8d88-59f13f3bccfe
Kirk, G.J.D.
f7f5cb71-77f7-44f3-842c-ca6a6090b98c
Roose, T. and Kirk, G.J.D.
(2009)
The solution of convection–diffusion equations for solute transport to plant roots.
Plant and Soil, 316 (1-2), .
(doi:10.1007/s11104-008-9777-z).
Abstract
To help develop models of solute uptake that are computationally efficient and suitable for up-scaling to whole root systems, we provide three alternative analytical solutions of equations for transport to absorbing roots by convection and diffusion, and we compare their performance with a numerical solution over the range of plant and soil conditions found in practice. We point out an important pitfall in commonly used methods to solve convection–diffusion equations numerically and show how it can be avoided. We identify a simple analytical solution that is valid for all realistic combinations of parameter values, and show that for most purposes it performs as well as a complete, but more complex, analytical solution allowing fully for both convection and diffusion. We conclude that this solution is suitable for use in general solute uptake models.
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Published date: March 2009
Keywords:
nutrient uptake, mathematical modelling, convection, water movement
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Local EPrints ID: 145129
URI: http://eprints.soton.ac.uk/id/eprint/145129
PURE UUID: 63a27e59-c797-4f27-a9a6-869ce40b05e7
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Date deposited: 22 Apr 2010 15:34
Last modified: 14 Mar 2024 02:54
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Author:
G.J.D. Kirk
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