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Analysis of Radial, Steady-State Solution, and Solute Flow¹

ABSTRACT

Radial, steady-state solution and solute flow to a root can be described as flow in a hollow cylinder. The analysis was broken into two parts: the solution flow and solute flow. The equation for the solution flow was solved analytically to obtain the soil solution tension distribution subject to fixed tensions at the inner and outer boundaries. From the tension distribution, the solution content distribution and solution flux were derived. The solution flux approaches a finite limit as the tension across the cylinder increases. The equation of flow for the solute was solved seminumerically, subject to fixed inner and outer concentration boundary conditions. The solute diffusion coefficient was assumed to be dependent upon the solution content. The convective part of the solute flow equation was dependent upon the solution flux. For most cases a good approximation would be the use of a constant solute diffusion coefficient, only dependent upon a mean solution content. As the solution flux increased, the solute concentration gradient increased at the root for both plant uptake or salt sieving of the solute.

¹ Contribution from the Soil & Water Conservation Research Division, ARS, USDA, and the Illinois Agr. Exp. Sta. Presented before Div. S-1, Soil Science Society of America, Nov. 14, 1968, at New Orleans, La.

² Research Soil Scientist (Physics), U. S. Water Conservation Lab., USDA, Phoenix, Ariz.; formerly Professor of Soil Physics, University of Illinois, presently Research Soil Scientist (Physics) USDA, Ft. Collins, Colo.; and Research Soil Scientist (Physics), USDA and Associate Professor of Soil Physics, University of Illinois; respectively.

Received for publication December 8, 1969. Accepted for publication February 12, 1970.