Diffusion of Ions in Soil

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Ion diffusion in soil plays a key role in agriculture. Use the slider to change the initial density of three common ions found in soil. Application of Fick’s second law and an initial flux are displayed for a range of distances within a soil bed. Fick’s second law can be used to show the concentration as functions of distance and time. Each ion has a different diffusion coefficient and thus a different diffusion rate. The relevant results are represented by the plots, which show the qualitative role of diffusion for the different ions in soil.

Contributed by: Sierra Cole, Dan Sweitzer and Brian Yost (May 2018)
Open content licensed under CC BY-NC-SA



Diffusion is a well-understood phenomenon that occurs when a substance moves from a region of higher concentration to a region of lower concentration across a concentration gradient. Initially, the system is not in equilibrium, but diffusion drives the transition to equilibrium, in which there is no net movement of any of the components. Fick’s second law, shown below, is used to predict concentration changes with time, the rate at which the substance moves across the gradient to approach equilibrium. The concentration of the substance is dependent on the distance from the soil surface. In this Demonstration,


To describe diffusion in a particular system, the properties of the solute and solvent in the system, as well as their interactions, must be considered. More specifically, the diffusion constants of the solute define the unique interaction between a given substance and the medium it is found in. In other words, diffusion constants control how far the particles are able to move (in random motion) before hitting another particle. This Demonstration describes the diffusion of ions in soil based on the diffusion constants reported in [1]. To model the flux of these ions in soil, the following equation was used:

= amount diffused at a given distance

= time

= diffusion constant

= concentration at starting point

= concentration at end point

= area

= number density

= starting density


[1] L. V. Vaidyanathan and P. H. Nye, "The Measurement and Mechanism of Ion Diffusion in Soils," European Journal of Soil Science, 17(2), 1966 pp. 175–183. doi:10.1111/j.1365-2389.1966.tb01464.x.

[2] J. Crank, The Mathematics of Diffusion, Oxford: Clarendon Press, 1956 pp. 30–31.

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