#### 3.1. Effects of Four Treated Sludges when Removing Fluoride

The compositions of WS for the experiment are shown in

Table 3. The WS contained large number of Al

_{2}O

_{3} and Fe

_{2}O

_{3} through the coagulation with the addition of polyaluminum chloride (PAC), aluminum sulfate (Al

_{2}(SO

_{4})

_{3}), and ferric chloride (FeCl

_{3}) in the process of producing water. SiO

_{2} was brought by the sludge in the settlement process

_{.} Compared to the WS, alum sludge coming from the alum plant [

17] contained almost the same content of Al

_{2}O

_{3} and Fe

_{2}O

_{3} but less SiO

_{2} and more TiO

_{2}, which was decided by the raw materials and the production process. In order to improve the adsorption ability, the original sludge sample was treated with different methods. Meanwhile, fluorine removal experiments were carried out with the treated samples. The results shown in

Figure 1 indicate that acid treatment can improve the ability of sludge to adsorb fluoride from water. Compared to other methods of treatment with original sludge, the sludge after acid treatment has the best efficiency, and HCl-acidified sludge is better than H

_{2}SO

_{4}. The fuel oxidation treatment can slightly improve the removal efficiency, while the pyrolysis displays a little suppression (

Figure 1).

#### 3.4. Effects of Variable Conditions on the Adsorption of Fluoride

The effects of variable conditions on fluoride removal were studied using RSM. As mentioned earlier, RSM based on BBD was employed to investigate the effects of three independent variables, HWS dose, pH, and initial concentration on the adsorption of fluoride by HWS. The BBD factorial design along with five replicates at central points is presented in

Table 1. Design Expert 8.0.6 software (Stat-Ease Corporation, Minneapolis, MN, USA) was used for experimental design and analysis. Experimental data were fitted to a second-order polynomial model [

31]:

in which Y is the predicted response (Removal efficiency in %) used as dependent variable, x

_{i} and x

_{j} are the in dependent variables, b

_{0} is the constant coefficient, b

_{i} is the coefficient that determines the influence of variable i in the response, b

_{ij} is the coefficient that determines the effect of interaction between variables i and j, b

_{ii} is the parameter that determines the shape of the curve, and k is the number of variables studied [

25,

32].

RSM model and its validation based on the experimental results are presented in

Table 2. Based on the experimental data, regression models using a second-order polynomial were represented by Equation (4), which was developed, after which statistically insignificant coefficients (

p-value greater than 0.1) were excluded from the analysis.

The analysis of variance (ANOVA) for the proposed model and corresponding

p-values and F-values for assessing the significance of the regression coefficients are presented in

Table 7. A

p-value of model less than 0.05 implies that the proposed model well predicts the experimental results at 5% confidence interval [

21]. A large

p-value for lack of fit (>0.05) is preferred, as it measures the model failure in representing data points in the experimental domain [

33]. In this case, the

p-value of lack of fit is 0.1792, implying that lack of fit of the model is insignificant. Adequate precision (AP) is the ratio of the predicted responses from the design points to their average standard deviation, which, for a good model fit, its desired value is 4 or more [

21]. The ratio of 48.388 implies that the model is acceptable. The overall prediction performance of the model is described by coefficient of determination (R

^{2}). A high R

^{2} value, close to 1, is desirable to ensure a satisfactory adjustment of the model to the experimental data [

26]. The value of R

^{2} = 0.9957 and a reasonable agreement with R

^{2}_{adjusted} is necessary [

25,

34]. In the present models, the values of R

^{2}_{adjusted} = 0.9901 was close to R

^{2}, indicating high significance of the model.

A plot of the residuals was also used to assess the adequacy of the model. The residual plots of the models are presented in

Figure 6a. The residuals are normally distributed if the points on the plot follow a straight line [

31]. As

Figure 6a illustrates, the assumption of normality is satisfied for the models [

26].

Figure 6b presents the observed and predicted values. The statistical significances of the models are evident from

Figure 6a, as observed and predicted values fit each other well. The statistical model can be used to predict the removal efficiency in this experiment in the range above.

Response surface graphs presented in

Figure 7 demonstrate the effects of variables and their interactive effects on the removal of fluoride. These plots are generated as a function of two variables at the same time, keeping the third variable at a centre level. As shown in (a) and (b), the increase of initial fluoride concentration leads to the decrease of final efficiency. As shown in (c), the removal efficiency increased as the HWS dose increased under the same pH. The increase in fluoride adsorption was possibly attributed to the increase in availability of F

^{−}due to the presence of a greater number of active sites [

35,

36]. Considering initial concentration = 3 mg·L

^{−1}, the WHO standard for permissible limit of fluoride in water (≤1.5 mg·L

^{−1}), which would be fulfilled with HWS (≥6.17 g·L

^{−1}) in the neutral condition of the present work，can be less at pH = 6. However, the effect of removal efficiency of fluoride was more prominent by initial concentration compared to HWS dose and pH from (a) and (b), meaning initial concentration of fluoride has an adverse effect on its removal. Samarghandi reported a similar result in adsorption of fluoride [

31]. At low initial concentration, most of fluoride will interact with the binding sites of the adsorbent, resulting in higher removal percentage. On the other hand, at high initial concentration, only some of the ions will combine with the finite available sites for binding [

37].

Usually, pH has been seen as an important factor influencing adsorption of the crystalline form to the adsorbent. It has been reported that, in case of zeolite and activated alumina, the pH of zero charge (pHpzc) may vary from 5.5 to about 8.3 [

24], and the optimum pH for maximum adsorption is between 5 and 7 [

31,

38]. The influence of the initial pH on the removal efficiency of this study is shown in

Figure 7b,c. The percentage of fluoride removal remains nearly constant within the pH range of 4–7. Further increase in the pH of the solution slightly decreases the removal efficiency. The fluoride uptake capacity of this media is not affected in the pH range less than or equal to 7, possibly due to the presence of positively charged and neutral sites at the surface of the adsorbent [

24]. The decline at pH > 7 may be due to the competition between OH

^{−} and F

^{−} [

39]. This is in agreement with fluoride removal studies on activated alumina by other researchers.

The numerical simulation optimum conditions for removal efficiency of fluoride using HWS were carried by RSM with the help of the desirability function. In this study, the desirability function approach was employed for optimization using Design Expert, which provides several possible options including minimum, maximum, target, within the range, none (only for response), and equal to (factors only) for choosing a desired goal for each variable and response [

39]. The average values of confirmation tests in triplicates and predicted by the model under optimum conditions are presented in

Table 7. As shown in

Table 8, the removal efficiency of confirmation tests was closed to the prediction. The optimum removal efficiency of fluoride can reach 81.153% under the optimum condition: HWS dose of 14.10 g/L and pH value at 6.12. Meanwhile, the lower initial fluoride concentration is better.