Mathematical modelling of controlled release fertilizer

Sayed Ameenuddin Irfan, Radzuan Razali


Controlled release fertilizers (CRFs) are essential for sustainable agriculture system. CRFs are designed to maintain the constant optimum release rate of nutrients from the coated granule. This increase the plant uptake of nutrients hence reduces the soil pollution and decreases the crop expenditure. In the literature, the maximum studies have been done by considering the molecular diffusion as the only phenomenon responsible for nutrient release from CRFs. The molecular diffusion model is solved mostly by using the variable separable methods and Laplace transform as well as finite difference methods by different researchers. The release of NPK (nutrient) depends on both molecular diffusions which are expressed by Fick’s second law of diffusion and ionic diffusion, due to the electrolytic behavior of NPK in the soil. In this work, an analytical solution is presented. The obtained solution helps to find the effect of granule coating thickness, nutrient release rate, pH of the soil and temperature of the soil on the nutrient release profiles.




Adomian decomposition method; nutrient release; NPK; ionic diffusion; molecular diffusion

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