## 3 Results and Discussion
### Liquid-Liquid Equilibrium (LLE) Data  
The experimental LLE for the pseudo-ternary system containing lactic acid, water, and AE at 308.15 K are presented in Figure 3 and Table 2. The obtained tie-lines indicate that lactic acid has preferential attraction or miscibility to the aqueous phase. This suggests an ineffective extraction process if the AE surfactant is to be used as a lactic acid extraction solvent. As previously mentioned, the studied temperature (308.15 K) is lower than the cloud point of the AE surfactant. Thus, the two-phase region of its ternary system can be accounted solely on its HLB or water miscibility (i.e., the system is not dictated by the closed loop miscibility gap). Since the water miscibility of nonionic surfactants decreases with temperature [36], raising the extraction temperature could possibly improve the effectiveness of the extraction. Nevertheless, this can possibly be explored for the extraction of other metabolites or for extraction configuration other than extractive fermentation. As for the case of this work, the AE surfactant had to be assessed at the temperature (308.15 K), as dictated by the target application. Figure 2: Concentration of phases formed as a function of incubation time for the system lactic acid (1) + water (2) + AE (3) at \(T\) = 308.15 K and \(P\) = 0.1 MPa (atmospheric pressure). To further assess the capability of AE and to be able to compare it to others that have been considered as lactic acid extraction solvent, distribution coefficients, separation factors, and extraction efficiencies were estimated from the experimental tie-lines. The distribution coefficients, \(D_{i}\), and separation factors, \(S\), of the LLE data for lactic acid (\(i\) = 1) and water (\(i\) = 2), and the lactic acid extraction efficiency, \(E\)(%), were calculated using the following equations [28; 41]:  
\[D_{i}=\frac{w_{i}^{I}}{w_{i}^{II}}, \tag{1}\]  
\[S=\frac{D_{1}}{D_{2}}, \tag{2}\]  
\[E(\%)=\frac{D_{1}}{1+D_{1}}\times 100, \tag{3}\]  
where: \(w_{1}^{I}\) and \(w_{1}^{II}\) are mass fractions of the lactic acid in the surfactant and aqueous phases, respectively, and; \(w_{2}^{I}\) and \(w_{2}^{II}\) are mass fractions of water in surfactant and aqueous phases, respectively. The calculated values are presented in Table 3 and Figure 4. \begin{table}
\begin{tabular}{c c c c c} \hline \multicolumn{5}{c}{**Surfactant Phase (Phase 1) Mass Fraction**} & \multicolumn{2}{c}{**Aqueous Phase (Phase II) Mass Fraction**} \\ \hline \(w_{1}\) & \(w_{2}\) & \(w_{3}\) & \(w_{1}\) & \(w_{2}\) & \(w_{3}\) \\ \hline
0.0000 & 0.1561 & 0.8439 & 0.0000 & 0.9965 & 0.0035 \\
0.0265 & 0.2676 & 0.7059 & 0.0456 & 0.9481 & 0.0064 \\
0.1252 & 0.2748 & 0.5999 & 0.2051 & 0.7907 & 0.0041 \\
0.2594 & 0.3526 & 0.3880 & 0.3077 & 0.6900 & 0.0023 \\
0.2956 & 0.4366 & 0.2678 & 0.3265 & 0.6735 & 0.0000 \\ \hline \end{tabular} \({}^{1}\) Standard uncertainties \(u\) are \(u(T)\) = 0.5 K, \(u(P)\) = 10 kPa, \(u_{\text{rel}}(w)\) = 0.004.  
\end{table} 
Table 2: Experimental tie-line data in mass fraction, \(w\), for the ternary system containing lactic acid (1), water (2), and AE (3): \(T\) = 308.15 K and \(P\) = 0.1 MPa (atmospheric pressure) \({}^{1}\). Figure 3: Experimental ternary phase liquid–liquid equilibria (tie-lines) for lactic acid + water + alcohol ethoxylate (AE) at \(T\) = 308.15 K and \(P\) = 0.1 MPa (atmospheric pressure). The distribution coefficient, \(D_{1}\), is an indication of the capacity of AE as a lactic acid extraction solvent [42]. For the liquid-liquid extraction process, higher values of \(D_{1}\) are preferred to minimize the amount of solvent needed for extraction. Nevertheless, this is not the main requirement of an effective extraction process [43]. On the other hand, the separation factor or selectivity indicates the ability of a solvent to separate lactic acid from water [44] and can be viewed as an indicator of the number of extraction stages needed for extraction [42]. Similar to \(D_{1}\), higher \(S\) is also preferred for liquid-liquid extraction.