**2. Experimental**

### **2.1 Anionic-exchange membranes**

During the Donnan dialysis operation, three commercial anion-exchange membranes have been used: ACS, AMX, and AFN. These membranes have the same structural properties and are homogeneous. **Table 1** presents the characteristics and properties of these membranes.

In order to prepare the samples for use in the Donnan dialysis, they had to be conditioned before any measurement. This was done primarily to eliminate contaminants from the production process and to stabilize their physical-chemical properties. French standard NF X 45-200 [21] was followed in doing this conditioning.

## **2.2 Donnan dialysis**

All Donnan dialysis experiments were carried out using a laboratory cell. The device was used to study the nitrate and nitrite removal by Donnan dialysis. It is composed of a thermoregulated water bath (25.0 0.1°C in this study), containing a cell with feed and receiver compartments separated by an anion-exchange membrane.

The dialysis cell consists of two detachable compartments made with polymethylmetacrylate (plexiglass) as shown in **Figure 1a** and **b**, in two formats, a photo of the mounted cell ready to be connected to the peristaltic pump, and a drawing of the


### **Table 1.**

*The main characteristics of the three commercial anion-exchange membranes.*

### **Figure 1.**

*The two-compartment cell used for the Donnan dialysis experiments. (a) Photo of an assembled cell. (b) Plan with different cuts according to three sections.*

different sections of this cell. It is composed of four parts joined by three stainless steel threaded rods. The centering is assured by bolsters. The two central compartments, consisting of two tubes are symmetrical. Two threaded holes penetrate each compartment and serve as support for stuffing boxes. The membrane is sandwiched between these two compartments, making a seal at the same time [22].

Then, the solution of nitrate or/and nitrite was prepared as a feed compartment with different concentrations varying from 50 to 500 mg/L, and the solution of chloride with different concentrations varying from 10 to 100 mg/L. The solutions are placed in volumetric flasks which are essential due to their geometry because they limit the losses of solvent by evaporation. There the circulation of these solutions in the two compartments is ensured by a peristaltic pump equipped with two identified heads controlled by a speed variator acting on his engine. The circulation of fluids takes place in flexible reference pipes. The volume flow rates Qf and QR of solutions leaving the feed and receiver compartments respectively are determined using a 1000 mL flask and a stopwatch measuring their filling times. This method assumes that the transmembrane volume flux is infinitely small compared to the solution flow rate imposed in each compartment.

The residual concentration of nitrate or/and nitrite at the outlet of the receiver compartment was determined spectrophotometrically. The UV-spectrophotometry approach was used to measure the nitrite and nitrate content at the receiver compartment during the dialysis operations [23]. The sodium salicylate and nitrate reaction produce paranitrosalicylate sodium, which is yellow colored. This reaction is followed by absorbance measurements at 415 nm using a UV-visible spectrophotometer to determine the amount of nitrate present. The amino-4-benzenesulfonamide was diazotized by nitrites in an acidic medium, and when it was coupled with N-(naphthyl-1) diamino-1,2-ethane dichloride, a purple-colored complex resulted. This complex's absorbance at 543 nm was then measured using a UV-visible spectrophotometer. The removal rate of nitrate (Y1%) and nitrite (Y2%) was calculated by Eq. (1):

$$\mathbf{Y\_{1}} \text{ or } \mathbf{2} \text{ (\%)} = \frac{\mathbf{C\_{0}} - \mathbf{C\_{e}}}{\mathbf{C\_{0}}} \times \mathbf{100} \tag{1}$$

where Ce is the nitrate and nitrite equilibrium concentration (mg/L) and C0 is the initial concentration of nitrate or nitrite (mg/L).

### **2.3 Doehlert design**

A Doehlert design based on the RSM was employed as the experimental strategy in this inquiry. The values of these parameters must be simultaneously optimized in order to achieve the best system performance. The optimal scenario was found by superimposing the contours of the response surfaces in a plot with multiple responses. In the three-dimensional plots of numerous variables used to represent the graphical optimization in the experimental field, the regions of optimal response would be highlighted in red. A close match between the experimental and projected values is required [24]. The total number of experiments for k factors is N = k<sup>2</sup> + k + 1. In fifteen tests, three duplicates at center field were employed [24–27].

The initial nitrate, nitrite, and counter-ion concentrations in the receiver compartment were the factors that were examined. With one component in the feed compartment, the range of these factors was set in accordance with the preliminary investigation. The experimental field of the factors under investigation is shown in **Table 2**.

*Removal of Nitrate and Nitrite by Donnan Dialysis: Optimization According to Doehlert… DOI: http://dx.doi.org/10.5772/intechopen.112482*


### **Table 2.**

*Range and levels of nitrate and nitrite removal.*

The variables that were examined included the initial nitrate, nitrite, and counterion concentrations in the receiver compartment. The range of these factors was established with one component in the feed compartment in accordance with the preliminary investigation. The experimental setting for the factors under investigation is shown in **Table 2**.

The Doehlert design, a matrix that can anticipate the values of the response at any point in the experimental area, can be used to estimate the coefficients of a secondorder function [28]. Using a polynomial equation (Eq. (2)), the selected model represents the predicted values of the answers Y. Bi represents the estimated major effect of component i, bii represents the estimated second-order effects, bij represents the estimated interactions between the factors i and j, and Xi represents the coded variable. NemrodW® Software was used to determine the model's coefficients.

$$\begin{aligned} Y\_{1\text{ or }2} &= b\_0 + b\_1 X\_1 + b\_2 X\_2 + b\_3 X\_3 + b\_{11} X\_1^2 + b\_{22} X\_2^2 + b\_{33} X\_3^2 + b\_{12} X\_1 X\_2 \\ &+ b\_{13} X\_1 X\_3 + b\_{23} X\_2 X\_3 \end{aligned} \tag{2}$$

The percentage absolute error of deviation (AED) and the regression coefficient (R2 ) between experimental and theoretical findings were employed as two metrics to assess the models. Eq. (3) was used to compute the AED.

$$\text{AED} \left( \% \right) = \frac{\mathbf{100}}{\mathbf{N}} \cdot \left| \frac{\mathbf{Y\_{exp}} - \mathbf{Y\_{theo}}}{\mathbf{Y\_{exp}}} \right| \tag{3}$$

where Ytheo represents the theoretical replies and Yexp represents the experimental responses. N is the total number of locations where measurements were made. The validation of the model is deemed valid when R<sup>2</sup> > 0.7 and AED 10% [29].
