Three approaches to the simulation of the self‐diffusion and non‐instantaneous isotopic exchange of phosphate in soil

SUMMARY Three models of the self‐diffusion of phosphate in moist soil are presented, and their predictions compared to experimental data. The latter appeared to show that isotopic exchange was limited by access to exchange sites. The apparent rate of access was first described by a series of first‐order reactions, then as the diffusion of isotope into, and within, uniformly distributed, porous spherical aggregates, where the majority of exchange sites were situated, and finally as an Nth order ( N 1) reversible reaction. All models were solved using Crank‐Nicolson finite difference methods. The first two gave similar predictions; they were not capable of giving an adequate fit to experimental results. The third, although purely an empirical model, not based on a possible mechanism, was able to simulate data well. The mechanistic implications of each model, and of its relative success in simulating phosphate diffusion are discussed.