5.1.2 Diffusion
Diffusion refers to the movement of particles driven by the tendency to equalize concentration differences, based on Brownian molecular motion.
In soil, this diffusion flux (FD)—unlike in liquids—depends not only on the concentration gradient (dc/dx) and the diffusion coefficient in solution (Dₗ), but also on soil factors: buffering capacity (b), tortuosity factor (f), and water content (θ). As a result, the diffusion coefficient in soil can be as low as 1/10,000 of the diffusion coefficient in solution. Therefore, the diffusion coefficient in soil is referred to as the "effective" diffusion coefficient (Dₑ).
FD= dc/dx De
De = DL T f 1/b
b = c/cL

If the supply via mass flow does not lead to an accumulation of ions in the root zone, and the plant simultaneously has the ability to lower the concentration of the soil solution, then the equilibrium between sorbed ions and ions in the soil solution is disturbed. This causes ions to move from more distant soil regions toward the root. The extent of the "depletion zone" is a function of time and the effective diffusion coefficient (dx = √(Dₑ · t)).
graphic

The figure above schematically illustrates the process of supply via diffusion over time:
  • The plant lowers the concentration of the soil solution at its surface.
  • To maintain equilibrium, sorbed ions are desorbed from the solid phase.
  • In the soil solution, ions are transported along the concentration gradient toward the root.
  • "Depletion profiles" are formed.
The following two images are autoradiograms ("X-ray images" produced using isotopes; image height approx. 10 cm) of the root environment:
  • In agar, which has no sorption sites for phosphate.
  • In soil, which sorbs phosphate.
graphic
graphic


It becomes evident that in a sorbing substrate, the depletion zone is very narrowly confined around the root. Consequently, only a small portion of the total soil volume contributes to the phosphorus supply.
Diffusion Ceffizient
Diffusion coefficients in solution (Dₗ, water, 25°C) for selected ions, compared with common ranges of diffusion coefficients in soils (Dₑ)

Ion
DL, cm² /s
De cm²/s
K+
1.98 10exp-5
10exp-7 bis 10exp-8
H2PO4
0.89 10exp-5
10exp-8 bis 10exp-11
NO3
1.90 10exp-5
 
Buffer Capacity
The "buffering capacity" of a nutrient in soil refers to the ratio of ions adsorbed to the soil's solid phase to ions present in the soil solution (µmol/cm³ soil vs. µmol/cm³ solution). Thus, buffering capacity is a measure of a soil's ability to store nutrients in adsorbed form.

The figure below shows the potassium buffering curve for a loess soil. Increasing amounts of potassium were added to it, and the change in soil solution concentration was measured. It can be observed that the buffering capacity decreases with increasing potassium application, meaning that proportionally less K is adsorbed. Consequently, Dₑ and thus the nutrient's mobility in the soil increase.

graphic

Merke: in unseren Böden wird von den Anionen Phosphat an Bodenkolloiden sorbiert; Nitrat, Sulfat, Molybdat etc. unterliegen diesen Einflüssen in weit geringem Umfang. Kationen werden mit austeigender Wertigkeit zunehmend sorbiert, innerhalb der gleichen Wertigkeit mit zunehmendem Ionendurchmesser. Spezielle Bindungsstellen exitieren z.B. für Kalium und Ammonium in den Zwischenschichten von illitischen Tonmineralen.
Soil water Content
Difusionskoeffizienten vom Wassergehalt für einen Lössboden.

The water content (θ) is expressed in (cm³ water)/(cm³ soil), typically ranging between 0.05 and 0.45. Consequently, Dₑ, as a measure of a nutrient's mobility, depends on the soil water content (see also the effects on the tortuosity factor). The figure below shows the dependence of the effective diffusion coefficient (Dₑ) on water content for a loess soil.Difusionskoeffizienten vom Wassergehalt für einen Lössboden.

The water content (θ) is expressed in (cm³ water)/(cm³ soil), typically ranging between 0.05 and 0.45. Consequently, Dₑ, as a measure of a nutrient's mobility, depends on the soil water content (see also the effects on the tortuosity factor). The figure below shows the dependence of the effective diffusion coefficient (Dₑ) on water content for a loess soil.

The figure below shows the dependence of the effective diffusion coefficient (Dₑ) on water content for a loess soil.
graphic
Tortuosity Factor
The tortuosity factor (f) represents the ratio between the shortest (straight-line) distance for an ion to travel between two points and the actual path length it must follow. Therefore, f always ranges between 0 and 1. In a given soil, the tortuosity factor is highly dependent on soil water content. This is because as larger pores drain, the available flow pathways become more restricted and convoluted, leading to greater "detours."
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