## 3 Results and Discussion
### Experimental Performance of NF
#### 3.1.2 Response Surface Plots  
The response surface plot for the permeate flux of NF is presented in Figure 2. The observations show an upsurge in the permeate flux simultaneously with the increase in trans-membrane pressure. It has been well established that permeate flux depends on pressure and gets amplified almost linearly with increasing pressure [32; 33; 34; 35; 36]. The maximum permeate flux of 59.34 L/m\({}^{2}\cdot\)h is obtained at the feed concentration of 25 ppm, pH 9.5, pressure 25 bar, and temperature 35 \({}^{\circ}\)C, as shown in Figure 2. It is typically theorized that an increased temperature accelerates the permeate flux due to one or more reasons such as a decline in solvent viscosity, a rise in solvent diffusion, intensification in the solvent diffusion coefficient, or a surge in polymer chain mobility [24]. Membrane-solvent interactions can be expected to differ with a change in solvent properties, like dielectric constant, molecular size, dipole movements, and Hildebrand solubility parameter. The rise in temperature also affects structural properties such as pore radius and membrane thickness, which have shown a much more noticeable impact on membrane performance in comparison to solvent and solute motilities [37; 38; 39]. Experiments have demonstrated a linear increase in the slope of flux with a rise in temperature, as reported by others [40; 41]. Figure 2a shows a direct increase of permeate flux with an increase in trans-membrane pressure. Figure 2b demonstrates a significant increase in the permeate flux with an increase in temperature. Water permeation by micropores is an activated process that is absolutely dissimilar from viscous flow. It should be taken into account that the water molecule is one of the smallest molecules, having the same range of kinetic diameter (0.29 nm), as helium (0.24 nm) and hydrogen (0.27 nm). A portion of water molecules gets adequate thermal energy to cross the energy barrier from the pore wall and passes over the pores, which is another justification based on the adsorption of water on hydrophilic pore walls. The actual pore diameter might get reduced by the water adsorbed on pore walls. In such a case, the adsorbed water layer can be thinner at higher temperatures resulting in the effective pore diameter becoming more extensive [41]. The separation of metal ions by NF is attained by size exclusion, and electrical interactions between the ions in the feed aqueous solution and the charged NF membranes. The degree of ionization of these functional groups is a function of the solution pH, which influences the membrane charge and, therefore, the rejection properties of the membrane [41]. The rejection of Cu, Ni, and Zn ions increased with the increase in the solution pH (Figure 3a-c). The feed solution pH determines the ion charge in the solution and the surface charge density of the membranes. The more the pH increases, the more the membrane charge becomes positive, leading to a stronger electrostatic repulsion between the membrane and the metal ions [35]. Copper hydroxide precipitation starts at pH 5.24, and the precipitation of the other metals (Zn and Ni) at a still higher pH. At the different pH values studied, the rejection of copper was higher than for Zn and Ni ions, as reported earlier [42]. The maximum rejection of Cu, Zn, and Ni was demonstrated as 99.99%, 99.96% and 99.63%, respectively, in the experiments where concentrations ranged between 10-25 ppm and pressure between 10-25 bar. It was observed that the rejection of metal ions decreased when the concentration of feed solution increased, a common phenomenon for NF membranes [37]. The increase in concentration in the feed solution apparently generates a screen formation of cation adjacent to the membrane on the high-pressure side, which neutralizes the negative charges of the NF membrane. Thus, the total negative charge of the membrane decreases, and the repulsion between membrane and anion decreases.