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An Analytical Solution to Solute Transport Near Root Surfaces for Low Initial Concentration: I. Equations Development¹

ABSTRACT

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.

¹ Contribution from the Purdue Agric. Exp. Stn., West Lafayette, IN 47907, Journal Paper no. 7455.

² Assistant Professor of Soil Physics, Purdue University.

Received for publication December 20, 1978. Accepted for publication August 14, 1979.

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