A comprehensive model describing the complex and "non-Fickian" (mathematically nonlinear) nature of the release from single granules of membrane coated, controlled release fertilizers (CRFs) is proposed consisting of three stages: i. a lag period during which water penetrates the coating of the granule dissolving part of the solid fertilizer in it ii. a period of linear release during which water penetration into and release out occur concomitantly while the total volume of the granules remains practically constant; and iii. a period of "decaying release", starting as the concentration inside the granule starts to decrease. A mathematical model was developed based on vapor and nutrient diffusion equations. The model predicts the release stages in terms of measurable geometrical and chemophysical parameters such as the following: the product of granule radius and coating thickness, water and solute permeability, saturation concentration of the fertilizer, and its density. The model successfully predicts the complex and "sigmoidal" pattern of release that is essential for matching plant temporal demand to ensure high agronomic and environmental effectiveness. It also lends itself to more complex statistical formulations which account for the large variability within large populations of coated CRFs and can serve for further improving CRF production and performance.

A statistically based model for describing the release from a population of polymer coated controlled release fertilizer (CRF) granules by the diffusion mechanism was constructed. The model is based on a mathematical-mechanistic description of the release from a single granule of a coated CRF accounting for its complex and nonlinear nature. The large variation within populations of coated CRFs poses the need for a statistically based approach to integrate over the release from the individual granules within a given population for which the distribution and range of granule radii and coating thickness are known. The model was constructed and verified using experimentally determined parameters and release curves of polymer-coated CRFs. A sensitivity analysis indicated the importance of water permeability in controlling the lag period and that of solute permeability in governing the rate of linear release and the total duration of the release. Increasing the mean values of normally distributed granule radii or coating thickness, increases the lag period and the period of linear release. The variation of radii and coating thickness, within realistic ranges, affects the release only when the standard deviation is very large or when water permeability is reduced without affecting solute permeability. The model provides an effective tool for designing and improving agronomic and environmental effectiveness of polymer-coated CRFs.