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The purpose of modification of magnetic iron oxide nanoparticles is an eco-friendly, emerging and economical method for removing deltamethrin in the aqueous solution and wastewater effluents when compared with other adsorbent methods. Modified magnetic iron oxide nanoparticles were synthesized by co-precipitation and then coupled with 3-hydroxytyraminium chloride. The nano-sorbent was characterized by thermogravimetric analysis, elemental analysis, transmission electron microscopy, scanning electron microscope, Fourier transform infrared spectroscopy, zero point charge and surface area determination. Batch studies were conducted and adsorption equilibrium, kinetic and thermodynamic non-linear models were carried out. The resulting equilibrium data were tested with Langmuir and Freundlich non-linear isotherm models, and the results showed that the Langmuir isotherm fitted the data well. Kinetic studies were done with different initial deltamethrin concentrations, adsorbent dosage and temperature, and the data were assimilated with pseudo-first order, pseudo-second order and intra-particle diffusion kinetic equations, and it was found that the studied nano-sorbent processes followed the pseudo-second order kinetic equation. Thermodynamic analysis was also carried out to estimate the changes in free energy (ΔG), enthalpy (ΔH), and entropy (ΔS). The thermodynamic parameters revealed that the adsorption of deltamethrin into the nano-sorbent was spontaneous, feasible and showed an endothermic process.

In this research, the mathematical models, indicating the capability of various units, such as rapid mixing, coagulation and flocculation, sedimentation, and the rapid sand filtration are used. Moreover, cost functions were used for the formulation of conventional water and wastewater treatment plant by applying Clark's formula (Clark, 1982). Also, by applying dynamic programming algorithm, it is easy to design a conventional treatment system with minimal cost. The application of the model for a case reduced the annual cost. This reduction was approximately in the range of 4.5-9.5% considering variable limitations. Sensitivity analysis and prediction of system's feedbacks were performed for different alterations in proportion from parameters optimized amounts. The results indicated (1) that the objective function is more sensitive to design flow rate (Q), (2) the variations in the alum dosage (A), and (3) the sand filter head loss (H). Increasing the inflow by 20%, the total annual cost would increase to about 12.6%, while 20% reduction in inflow leads to 15.2% decrease in the total annual cost. Similarly, 20% increase in alum dosage causes 7.1% increase in the total annual cost, while 20% decrease results in 7.9% decrease in the total annual cost. Furthermore, the pressure decrease causes 2.95 and 3.39% increase and decrease in total annual cost of treatment plants.

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