Summary
The change in concentration of a solute in soil, moving near the surface of a root by both mass flow and diffusion, has been calculated by a numerical method with a computer. The effect of change in the plant controlled variables v0 (the solvent flux at the root surface) and k (the root absorbing power), and the soil variables b (the buffer power) and D (the diffusion coefficient) are described in turn.
The concentration at the root surface, relative to the undisturbed soil solution, approaches a limiting value v0/k. As v0 is increased, the limiting value is approached more rapidly, and the zone of disturbance is more compressed. A steady state is reached if r0v0/bD>2, but if r0v0/bD<2 the disturbance continues to spread outwards even though the concentration at the root surface has nearly attained its limiting value.
As k is increased, other factors being constant, the limiting relative concentration at the root surface is approached more rapidly, but the spread of the disturbance away from the root is little affected.
As Db is decreased, corresponding to a decrease in soil moisture, the concentration at the root surface reaches its limit more rapidly and the zone of disturbance is compressed.
If, because of increase in the concentration at the root surface, the efficiency of root absorption declines, the relative concentration will exceed v0/k, and may reach no limit — at least until the assumptions of the model used break down.
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Nye, P.H., Marriott, F.H.C. A theoretical study of the distribution of substances around roots resulting from simultaneous diffusion and mass flow. Plant Soil 30, 459–472 (1969). https://doi.org/10.1007/BF01881971
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DOI: https://doi.org/10.1007/BF01881971