## 3 Results and Discussions  
### Viscosity Studies  
The viscosity of a liquid is affected by many factors such as temperature, size, molecular weight, inter-molecular forces and the presence of impurities. Viscosity determination helps in understanding the molecular interactions and properties of binary and ternary liquid systems. It is to be noted that attractive interactions can cause an increase in the viscosity of these systems. Regardless of the fact that viscosities can be used as the base data in a simulation, equipment design, solution theory or molecular dynamics, it is also essential in designing calculations involving heat transfer, mass transfer and fluid flow. The accurate prediction of the viscosities of binary mixtures is considered very important considering the above facts. A large number of viscosity models have been applied, but few reviews have described the application prospects of the models [43; 44]. Models that describe the viscosity of liquid mixtures can be classified into two categories: (i) empirical equations using only one adjusting parameter and simple algebraic formulations [28], and (ii) semi-empirical models which are deduced based on different theories, like [PERSON]'s absolute reaction-rate theory, the theory of corresponding states, and molecular dynamic models [45]. Table 1 infers the deviation between the experimental and the literature values for pure components. The viscosity of the binary liquid mixtures was calculated using the [PERSON] relation, Kendall and Monroe relation, [PERSON] relation, Arrhenius-Eyring relation, Croenauer-Rothfus Kermore relation and Gambrill relation as detailed below:  
[PERSON] relation (\(\eta_{\rm{H}}\))  
The following relations were proposed for the evaluation of the viscosity of binary liquid systems by [PERSON] et al. [28]: \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Liquid** & \multicolumn{2}{c}{**Density (kg/m\({}^{3}\))**} & \multicolumn{2}{c}{**Viscosity (\(\times\)10\({}^{-3}\) Nsm\({}^{-2}\))**} & \multicolumn{2}{c}{**Ultrasonic Velocity (m/s)**} \\ \cline{2-7}  & **Expt [27]** & **Literature** & **Expt [27]** & **Literature** & **Expt [27]** & **Literature** \\ \hline Ethanol & 783.9 & 780.5 [46] & 1.0090 & 0.983 [46] & 1133.3 & 1130 [46] \\ \hline
1-Hexanol & 807.6 & 810.0 [47] & 3.8951 & 3.513 [47] & 1281.7 & 1289 [47] \\ \hline
1-Octanol & 817.2 & 803.03 [48] & 6.4931 & 5.9424 [48] & 1327.5 & 1329 [48] \\ \hline APD of experimental and & & & 0.80\% & & 7.5\% & 0.3\% \\ literature value & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental values of the viscosity, density and ultrasonic velocity of pure liquids. \[\eta=x_{1}^{2}\eta_{1}+x_{2}^{2}\eta_{2}+2x_{1}x_{2}H_{12} \tag{2}\]  
\[H_{12}=\left(\eta-\eta_{calc}^{id}\right)/(2x_{1}x_{2})\eta_{calc}^{id}=x_{1}^{2 }\eta_{1}+x_{2}^{2}\eta_{2} \tag{3}\]  
where x is the mole fraction, \(\eta_{1}\) is the viscosity, the subscripts 1 and 2 refer to the components 1 and 2, respectively, and H\({}_{12}\) refers to cross-pair interactions, which can be obtained from Equation (3). [PERSON] and [PERSON] relation (\(\eta_{\rm{IKM}}\)) [29]  
[PERSON] and [PERSON] derived an equation for the analysis of viscosity of binary liquid systems based on a zero-adjustable parameter:  
\[\eta_{m}=\left(x_{1}\eta_{1}^{1/3}+x_{2}\eta_{2}^{1/3}\right)^{3} \tag{4}\]  
where \(x_{1}\), \(x_{2}\) and \(\eta_{1}\), \(\eta_{2}\) are the mole fraction and viscosity of the pure component, respectively. [PERSON] relation (\(\eta_{\rm{IB}}\)) [30]  
[PERSON] derived an equation for the analysis of viscosity of binary liquid systems based on a zero-adjustable parameter:  
\[\eta_{m}=\left(x_{1}\eta_{1}+x_{1}\eta_{1}\right) \tag{5}\]  
Arrhenius-Eyring relation (\(\eta_{\rm{AE}}\)) [30]  
[PERSON] derived an equation for the analysis of viscosity of binary liquid systems based on a zero-adjustable parameter.