The diffusion model of nutrient release from membrane pore of controlled release fertilizer

The pores on the membrane of controlled release fertilizer (CRF) are the channel of nutrient release. On the basis of Fick's first law of diffusion, a new diffusion model of nutrient release with considering the mathematical relationship between the rate of nutrient release and the pore size, was established in this study. The model shows that the cumulative percentage of urea release has positive correlation with the membrane pore area (A, or the square of the pore radius r) and the release time (t), however, was negatively correlated with the membrane thickness (1) and particle mass (M). The experimental verification results by using the simulative diffusion release device and the single-pore CRF both show that the theoretical diameter calculated from the model is better matched with the measured diameter. This model gives excellent reproduction of the urea diffusion through membrane pores within the whole release period. That is to say, controlling the pore size of CRF membrane accurately according to this model can of great understanding the nutrient release of CRF. This model can be applied into the selection of coating material and preparation of CRF in the future. (C) 2021 The Author(s). Published by Elsevier B.V.

Automated summary

This study established a new diffusion model of nutrient release, considering the mathematical relationship between the rate of nutrient release and the pore size. The model showed that the cumulative percentage of urea release was positively correlated with the membrane pore area and release time, while negatively correlated with the membrane thickness and particle mass. Experimental verification demonstrated that the model accurately reproduced the urea diffusion through membrane pores. Therefore, accurately controlling the pore size of CRF membrane based on this model is crucial for understanding the nutrient release of CRF.