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An Analytical Solution to Solute Transport Near Root Surfaces for Low Initial Concentration: I. Equations Development
Author(s) -
Cushman John H.
Publication year - 1979
Publication title -
soil science society of america journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.836
H-Index - 168
eISSN - 1435-0661
pISSN - 0361-5995
DOI - 10.2136/sssaj1979.03615995004300060005x
Subject(s) - exponential function , bessel function , differential equation , exponential decay , flux (metallurgy) , convection–diffusion equation , constant (computer programming) , mathematical analysis , exponential growth , mathematics , boundary value problem , mechanics , partial differential equation , root (linguistics) , thermodynamics , physics , chemistry , linguistics , philosophy , organic chemistry , computer science , nuclear physics , programming language
In Part I of this two part paper the governing differential equation for radial flow to a root with constant moisture properties, is transformed into a nondimensional and more useful form. An analytical solution to the differential equation with two appropriate sets of boundary conditions is developed. The solution can be expressed as an infinite series of Bessel functions, powers of nondimensional distance and an exponential. Equations for total and diffusive nutrient uptake are developed for both growing and nongrowing roots. Nondimensional equations are also presented for the various components of the nutrient flux (diffusive, convective, and total). The equation for total nutrient uptake for a root growing at a rate f( t ) such that f( o ) = L o (initial length), is examined in detail when f( t ) is an exponential.