## 3 Results and Discussion
### Viscosity of the Binary Mixtures
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multicolumn{3}{c}{**Mixtures**} \\ \cline{2-4}  & **MDEA (1) + H\({}_{2}\)O (2)** & **DMEA (1) + H\({}_{2}\)O (2)** & **DEEA (1) + H\({}_{2}\)O (2)** \\ \hline \(A_{0}\) & 98.13 & 99.61 & 123.5 \\ \(A_{1}\) & \(-\)0.4163 & \(-\)0.4218 & \(-\)0.528 \\ \(A_{2}\) & 5.008 \(\times\) 10\({}^{-4}\) & 5.013 \(\times\) 10\({}^{-4}\) & 6.291 \(\times\) 10\({}^{-4}\) \\ \(A_{3}\) & \(-\)29.09 & \(-\)33.79 & \(-\)45.8 \\ \(A_{4}\) & 0.0838 & 0.1083 & 0.1498 \\ \(A_{5}\) & \(-\)10.47 & \(-\)14.69 & \(-\)18.31 \\ \hline AARD (\%) & 1.7 & 2.7 & 4.7 \\ AMD (mPa-s) & 6.4 & 1.3 & 2.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Coefficients (\(A_{i}\)) for the viscosity deviation \(ln(\eta_{\gamma})\) of different aqueous amine mixtures. The [PERSON]'s three-body model:  
\[ \begin{array}{rl}ln(v)=&x_{1}^{3}ln(v_{1})+3x_{1}^{2}x_{2}ln(v_{12})+3x_{1}x_{2} ^{2}ln(v_{21})+x_{2}^{3}ln(v_{2})\\ &\qquad\qquad-ln(x_{1}+x_{2}\cdot[M_{2}/M_{1}])+3x_{1}^{2}x_{2}\\ &\qquad\qquad\cdot ln([2+M_{2}/M_{1}]/3)+3x_{1}x_{2}^{2}ln([1+2M_{2}/M_{1}]/3)+ x_{2}^{3}ln(M_{2}/M_{1})\end{array}  \tag{25}\]  
[PERSON]'s three-body model have two fitting parameters of \(v_{12}\) and \(v_{21}\). For each type of \(\Delta G^{*}\) considered during the model development, a corresponding kinematic viscosity were assigned as shown in Equations (26)-(30). With the assumption of temperature independent enthalpies and entropies of activation for viscous flow, it provides a kinematic viscosity model with both composition and temperature as independent variables. The unknown enthalpies and entropies can be calculated by fitting kinematic viscosity data at different compositions and temperatures to the model. Our previous work based on kinematic viscosities of MEA (monoethanol amine) + H\({}_{2}\)O mixtures provided acceptable accuracies by following this method [47]. \[\Delta G^{*}=\Delta H^{*}-T\Delta S^{*} \tag{26}\]  
\[v_{1}=\frac{hN}{M_{1}}e^{-\Delta s_{1}^{*}/R}e^{\Delta H_{1}^{*}/RT} \tag{27}\]  
\[v_{12}=\frac{hN}{M_{12}}e^{-\Delta s_{12}^{*}/R}e^{\Delta H_{12}^{*}/RT} \tag{28}\]  
\[v_{21}=\frac{hN}{M_{21}}e^{-\Delta s_{21}^{*}/R}e^{\Delta H_{21}^{*}/RT} \tag{29}\]  
\[v_{2}=\frac{hN}{M_{2}}e^{-\Delta s_{2}^{*}/R}e^{\Delta H_{2}^{*}/RT} \tag{30}\]  
The explained approach was adopted in this study to represent kinematic viscosities that were calculated via measured dynamic viscosities and densities. It was calculated accuracies as 23%, 17%, and 15% for MDEA + H\({}_{2}\)O, DMEA + H\({}_{2}\)O, and DEEA + H\({}_{2}\)O mixtures. These deviations are relatively high and questioning that adopted method with [PERSON]'s three-body model is viable to use for correlating kinematic viscosities of the considered mixtures. Accordingly, kinematic viscosity data were fitted at different temperatures instead of a temperature range using Equation (25) to see improvements in the accuracies. The reported AARD using Equation (25) are 8.4 %, 9.2% and 16% for MDEA + H\({}_{2}\)O, DMEA + H\({}_{2}\)O, and DEEA + H\({}_{2}\)O mixtures. It indicates that data fitting at different temperatures improves the accuracies of viscosity representation except for the DEEA + H\({}_{2}\)O. Table 8 lists the calculated parameters of Equation (25) at different temperatures. [PERSON] stated the necessity of taking into account other interactions that are involving more than three molecules in a three dimensional space instead of one plane for the scenario of two types of molecules having a size (radius) difference by more than a factor of 1.5 [46]. [PERSON]'s four-body model discusses such interactions however the fitting of kinematic viscosity data into four-body model is not discussed in this work.