## 2 Experimental
### Modeling Methodology  
The main factors which influence the textile effluent treatment in the experimental SD setup were considered to be flowrate (\(z_{1}\)), rotational speed (\(z_{2}\)), and operating time (\(z_{3}\)). As response functions or optimization criteria, the removal degree (\(Y\), [%]) in terms of suspended solids (\(Y_{1}\)) and color (\(Y_{2}\)) were selected. The modeling was organized according with the experimental planning used in an \"\(n\)\" variable active central composite rotatable design where the mathematical model is expressed by Equation (2), with no excessive experiments in comparison with the number of coefficients to be determined (i.e., \(n=20\), consisting of \(2^{3}\) factorial experiments (each corner of cube), \(2\times 3\) axial  
Figure 1: Experimental setup for the wastewater quality measurements. 1—rotating disc; 2—electric motor; 3—housing; 4—tank; 5—centrifugal pump; 6—adjusting tap; 7—flowmeter; 8—tap.  
experiments (on axes, distance of \(\pm\alpha\) from center of rotation, \(\alpha=\pm 1.682\)), k = 6 (experiments in the center of variation field, for the independent estimation of \"pure\" experimental error variance, data reproducibility) [30; 31; 32; 33].  
\[Y=\mathrm{b}_{0}+\sum\mathrm{{}^{n}_{i=1}}\mathrm{b}_{i}X_{i}+\sum\mathrm{{}^{ n}_{ij=1}}\mathrm{b}_{ij}X_{i}X_{j}, \tag{2}\]  
where \(Y\) is the response function (removal degree, [%]); \(X_{i}\) or \(X_{j}\) is the coded selected variable in the SD treatment system (\(n=20\)); \(i,j=1\) or \(2\); \(\mathrm{b}_{0}\), \(\mathrm{b}_{i}\), \(\mathrm{b}_{j}\), \(\mathrm{b}_{ij}\) are the model coefficients. The model coefficients are estimated using statistics for the processing of the experimental results obtained in the central points of the central composite rotatable design, according to the equations presented in previous reports [30; 31].  
In the active central composite rotatable (\(2^{3}\)) design, a basic value \(\mathrm{z}_{i0}\) and a variation step \(\Delta\mathrm{z}_{i0}\) of each independent variable \(\mathrm{z}_{i}\) (flowrate, rotational speed, or operating time) were established. The coded value of \(\mathrm{z}_{i}\), denoted as \(X_{i}\), was determined with Equation (3) [30; 31; 33]:  
\[X_{i}=(\mathrm{z}_{i}-\mathrm{z}_{i0})/\Delta\mathrm{z}_{i0}. \tag{3}\]  
The upper level is coded with 1, the lower level with \(-1\), and the basic level with 0. There are other possible values of the variable level (\(\alpha_{i}=\pm 1.682\)) [27; 28; 29].  
The model validation was carried out by an appropriate analysis of variance, consisting of: (i) the calculation of the F constant and its comparison with the statistical value; (ii) the calculation of the multiple correlation coefficient in order to establish the correlation between the dependent variable (\(Y\)) and the three independent variables (\(X_{i}\)) as a whole; (iii) the determination of the coefficient's significance using the Student test, for a certain significance level (\(p=0.05\)) and degrees of freedom (\(\mathrm{v}_{1}=n-1\) and \(\mathrm{v}_{2}=\mathrm{k}-1\)) [30; 31; 33]; (iv) the application of the Fisher test to calculate the \(\mathrm{F}_{\mathrm{c}}\) value and to compare it with the statistical value; and (v) the calculation of deviation (A) between the calculated values with the proposed model and the experimental data, which must be between \(+10\%\) and \(-10\%\) for a good data agreement. The optimal values of independent variables are determined using the classical optimization by the analysis of first- and second-order derivatives systems [30].