Abstract
An approximation to the analytical solution of the one-dimensional diffusion equation in cylindrical coordinates is derived. The solution applies to a semi-infinite system with a prescribed concentration at the root surface. From this approximate solution, simple formulas for calculating the radius of the depletion zone and the nutrient flux at the root surface as a function of time are obtained.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Carslaw H S and Jaeger J C 1959 Conduction of Heat in Solids. 2nd ed. Clarendon Press, Oxford.
Claassen N, Syring K M and Jungk A 1986 Verification of a mathematical model by simulating potassium uptake from soil. Plant and Soil 95, 209–220.
Claassen N 1990 Nährstoffaufnahme höherer Pflanzenaus dem Boden. Severin Verlag, Göttingen.
Crank J 1975 The Mathematics of Diffusion. Clarendon Press, Oxford.
Cushman J H 1979 An analytical solution to solute transport near root surfaces for low initial concentration: I. Equations development. Soil Sci. Soc. Am. J. 43, 1087–1090.
Nye P H and Marriot F H C 1969 Theoretical study of the distribution of substances around roots resulting from simultaneous and mass flow. Plant and Soil 3, 459–472.
Rengel J 1993 Mechanistic simulation models of nutrient uptake. Plant and Soil 152, 161–173.
Ritchie R H and Sakakura A Y 1956 Asympotic expansions of solutions of the heat conduction equation in internally bounded cylindrical geometry. J. Appl. Physiol 27, 1453–1459.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Syring, K.M., Claassen, N. Estimation of the influx and the radius of the depletion zone developing around a root during nutrient uptake. Plant Soil 175, 115–123 (1995). https://doi.org/10.1007/BF02413016
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02413016