## 3 Results and Discussion
### CCC Value Determined Based on DLVO Theory  
According to the results of the SEM analysis above and the EFLPs' diameter size, the EFLPs could be considered spherical in geometric structure, and their interactions were mainly dominated by face-to-face association. The total interaction energy between two  
Figure 6: Three-dimensional surface plots and contour maps for the interaction of hydro-chemical component and concentration (**II-a,II-A**), hydro-chemical component and particle size (**II-b,II-B**), and component concentration and particle size (**II-c,II-C**) on the AS and suspension of 1.1 \(\upmu\)m EFLPs in a 36-h reaction, respectively. surfaces is usually calculated by the sum of the van der Waals force (V\({}_{\rm R}\)) and electrostatic repulsion (V\({}_{\rm A}\)) [62]:  
\[\rm V_{T}=V_{R}+V_{A} \tag{4}\]  
\(\rm V_{R}\) and \(\rm V_{A}\) can be determined by Equations (5) and (6), respectively:  
\[\rm V_{A}=-\frac{Ar}{12} \tag{5}\]  
\[\rm V_{R}=\frac{64\pi r\rm n_{0}k_{B}T}{\kappa^{2}}\gamma^{2}exp(-\rm{\kappa h}) \tag{6}\]  
where r is the ionic radius, \(\rm n_{0}\) is the number of background anions and cations determined from the molar concentration of background electrolyte, \(\rm k_{B}\) is the Boltzmann constant (1.4 \(\times\) 10\({}^{-23}\) J/K), T is the absolute temperature (K), A is the Hamaker constant (2.3 \(\times\) 10\({}^{-20}\) J), h denotes the distance between particle surfaces and \(\rm\kappa\) is the reciprocal of the Debye length, which can be calculated by Equation (7):  
\[\rm\kappa=(\frac{1000e^{2}N_{A}\sum_{i}^{2}C_{i}}{\varepsilon_{0}\varepsilon_{ r}k_{B}T})^{1/2} \tag{7}\]  
where N\({}_{A}\) is the Avogadro constant (6.0 \(\times\) 10\({}^{23}\)), C\({}_{i}\) is the electrolyte concentration, \(\varepsilon_{0}\) is the vacuum permittivity (8.85 \(\times\) 10\({}^{-12}\) C\({}^{2}\)/J/m) and \(\varepsilon_{r}\) is the dielectric constant of water (78.36 F/m). \(\gamma\) as a parameter depended on the surface potential (\(\rm\psi_{0}\)) of the particles and could be calculated via Equation (8):  
\[\rm\gamma=\frac{exp(\frac{2e\rm\psi_{0}}{2k_{B}T  
The electric potential energy is dependent upon the amount of charge on the object experiencing the field and its location within the field. The influence of ions on the diffusion layer and their electrical properties of fine particles can be comprehensively manifested as the surface site accumulation on the particles and their effects, namely, the moving sites, which are generally represented as \(\zeta\)[64]. Thus, in the present study, for EFLPs with 1.1 \(\upmu\)m D\({}_{50}\), the surface potential could be considered equal to the \(\zeta\) value and employed in the calculation process. So, \(\gamma^{2}\) and \(\kappa\) were determined as 0.98 and 1 \(\times\) 10\({}^{8}\)/m, respectively. Then, according to Equation (14), CCC values were obtained for Cu(NO\({}_{3}\))\({}_{2}\) and NaF as 0.12 mmol/L and 54.04 mmol/L, respectively. Comparing their values (0.1 mmol/L and 50 mmol/L) determined by the tests above (Figures 2 and 3) showed that their errors were rather small, and even the results obtained by the two methods were approximately consistent. So, the CCC values that were determined based on the DLVO equation with electrostatic repulsion replaced by the \(\zeta\) value were acceptable. Indeed, there was an error between the results of the test and the theoretical methods. This phenomenon was also reported in other studies [60; 61; 62; 63; 64; 65; 66; 67]. For example, the CCC value for NaCl was reported by [PERSON] et al. (2017) as 91.6 mmol/L [50], by [PERSON] et al. (2020) as 62.47 mmol/L [36] and by [PERSON] and [PERSON] (2004) as 100 mmol/L [68], respectively, showing that there is error among them. Even in the present study, the errors for Cu(NO\({}_{3}\))\({}_{2}\) and NaF were not the same, and the former was obviously smaller than the latter.