Modelling and optimization study to improve the filtration performance of fibrous filter.

Fibrous filter made up of non-woven material was utilized in many industrial applications for increasing the collection efficiency and the quality factor. But there exists a competing effect among the fibre diameter, filtration efficiency, pressure drop, and sometime type of aerosol (liquid or solid) plays a crucial role in the performance of the fibrous filter. To avoid overdesigning of the filter along with better performance, optimum set of parameters are to be decided before the manufacturing process. In the current effort, the desirability approach and along with the "Response Surface Methodology (RSM)" were considered to optimize filtration efficiency and pressure drop simultaneously. In this perspective, the impact of Filtration velocity (v), Basis weight (φ), Particle diameter (dp), and Packing fraction (α) on filtration efficiency (η) and pressure drop (Pd) was studied. Based on the outcome, the predicted values lie within experimental data through smart agreement. The maximum percentage (%) error was only 3% and 6% filtration efficiency (η) and pressure drop (Pd), which determine the effectiveness of this useful model. The most dominant factor which affects the filtration efficiency (η) was found to be the Basis weight (φ), followed by packing fraction. However, in the case of pressure drop, the most dominant factors were filtration speed followed by the pachining fraction. Moreover, artificial neural network (ANN) models are developed for the prediction of filtration efficiency and pressure drop. The model accuracy has been estimated by calculating "Mean Square Error (MSE), Mean Absolute Error (MAE), and coefficient of determination (R2)". Both models show promising results when compared with experimental data with the R2 value of 98.50-99.86. The optimized values of the maximum filtration efficiency and minimum pressure drop simultaneously were obtained for v = 5, φ = 59.60, dp = 52.23, α = 0.24 according to desirability approach.

A review of mathematical modeling and simulation of controlled-release fertilizers.

Nutrients released into soils from uncoated fertilizer granules are lost continuously due to volatilization, leaching, denitrification, and surface run-off. These issues have caused economic loss due to low nutrient absorption efficiency and environmental pollution due to hazardous emissions and water eutrophication. Controlled-release fertilizers (CRFs) can change the release kinetics of the fertilizer nutrients through an abatement strategy to offset these issues by providing the fertilizer content in synchrony with the metabolic needs of the plants. Parametric analysis of release characteristics of CRFs is of paramount importance for the design and development of new CRFs. However, the experimental approaches are not only time consuming, but they are also cumbersome and expensive. Scientists have introduced mathematical modeling techniques to predict the release of nutrients from the CRFs to elucidate fundamental understanding of the dynamics of the release processes and to design new CRFs in a shorter time and with relatively lower cost. This paper reviews and critically analyzes the latest developments in the mathematical modeling and simulation techniques that have been reported for the characteristics and mechanisms of nutrient release from CRFs. The scope of this review includes the modeling and simulations techniques used for coated, controlled-release fertilizers.

Reaction-Multi Diffusion Model for Nutrient Release and Autocatalytic Degradation of PLA-Coated Controlled-Release Fertilizer.

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.