Modeling NPK nutrients release via nanoparticle/hydrogel system

In this work, we present a detailed mathematical modeling of the controlled release of nutrients encapsulated in a nanoparticle/hydrogel system. The main objective was to investigate how hydrogels can be used to sustainably release water and nutrients, keeping the soil moist and improving nutrient availability for plants. Experimental reference data were used, which underwent rigorous numerical and statistical treatment. The mass transfer equation in spherical coordinates was employed to obtain concentration profiles and released fraction of each nutrient. Additionally, the effective diffusion coefficients of the nutrients were determined through an optimization process controlled by the mean squared error (MSE) statistic. The results revealed that the nanoparticle/hydrogel system demonstrated efficient controlled release of the studied nutrients. The obtained effective diffusion coefficients were 1.3 x 10^-11 m²/s for nitrogen in the form of ammonium (MSE=0.0125), 7.2 x 10^-10 m²/s for potassium ion (MSE=0.0697), and 5.8 x 10^-12 m²/s for phosphorus in the form of hydrophosphate (MSE=0.2023), consistent with typical values observed in similar mass transfer processes. These findings have significant implications for sustainable agriculture as the use of nanoparticle/hydrogel systems can reduce nutrient loss, promote microbial life in the rhizosphere, and enhance nutrient uptake by plants.

Keywords: nanoparticle, hydrogel, modeling, release, NPK nutrients.

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