Mass flow and diffusion of nutrients to a root with constant or zero-sink uptake. 1. Constant uptake.

This paper deals with transport of nutrients in soil by mass flow and diffusion towards plant roots. The root system is assumed to consist of uniformly distributed cylindrical vertical parallel roots, all taking up nutrients at the same constant rate. Each root thus can be thought to be surrounded by a separate soil cylinder. Steady-state conditions with respect to flow of water to the root are assumed. Two situations with respect to the steady-state water flow are distinguished: one where replenishment of the water taken up by the root takes place at the outer boundary of the soil cylinder, and one where replenishment takes place uniformly over the soil cylinder. Analytical solutions to the transport problem are derived. The constant uptake condition leads to concentration distributions converging eventually to a steady-rate solution, where the decrease in concentration is independent of time. With these, the period of unconstrained uptake Tu, i.e., the period during which transport in the soil allows the required uptake, is calculated. It is shown that transport by mass flow is more important the stronger the nutrients are adsorbed by the soil. The solutions for the two situations of steady-state water flow are shown to differ only slightly.

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