A mathematically tractable model for controlled-release urea fertilisers

The dissolution of polymer-coated, controlled-release urea fertilisers by means of a simple, Fickian diffusion-based model is described. This is in contrast to prior contributions that invoke non-Fickian mechanisms or take a more quantitative view. Within a quasi-static approximation, simple expressions for the granule radius and release profile as a function of time are obtained in terms of experimentally accessible parameters. Predictions compare well with available experimental data, although the full model is required to capture the gradual saturation of released urea in the late stages of the process. If scaled appropriately, a wide range of experimental data for different coatings turn out to collapse onto what for all intents and purposes can be called a universal curve. This suggests that extensive experimental testing can be avoided if the properties of the coating are known beforehand.