A mathematical model for the reaction-diffusion equation is developed to describe the nutrient release profiles and degradation of poly(lactic acid) (PLA)-coated controlled-release fertilizer. A multi-diffusion model that consists of coupled partial differential equations is used to study the diffusion and chemical reaction (autocatalytic degradation) simultaneously. The model is solved using an analytical-numerical method. Firstly, the model equation is transformed using the Laplace transformation as the Laplace transform cannot be inverted analytically. Numerical inversion of the Laplace transform is used by employing the Zakian method. The solution is useful in predicting the nutrient release profiles at various diffusivity, concentration of extraction medium, and reaction rates. It also helps in explaining the transformation of autocatalytic concentration in the coating material for various reaction rates, times of reaction, and reaction-multi diffusion. The solution is also applicable to the other biodegradable polymer-coated controlled-release fertilizers.
Keywords: controlled-release fertilizers; numerical Laplace inversion method; poly(lactic acid); reaction-diffusion.