# Temperature Dependence of Density and Viscosity of Biobutanol-Gasoline Blends
## 3 Results and Discussion
### Mathematical Models
#### 3.4.3 Mathematical Models for Kinematic Viscosity
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Vogel** & \(\mathbf{\eta_{0}\) **(mPa-s)** & \(\mathbf{b}\) **(K)** & \(\mathbf{c}\) **(K)** & \(\mathbf{R^{2}}\) & **SSE** \\ \hline B0-95 & 0.4717000 & 12.59 * & \(-\)233.8 & 0.9572 & 0.0013480 \\ B5-95 & 0.51300000 & 9.758 * & \(-\)235.9 & 0.9493 & 0.0012490 \\ B10-95 & 0.54120000 & 8.194 & \(-\)244.4 & 0.9700 & 0.0015740 \\ B85-95 & 0.0079680 * & 1500 & \(-\)31.16 * & 0.9996 & 0.0047340 \\ B0-98 & 0.40190000 & 25.06 * & \(-\)216.5 & 0.9782 & 0.0006507 \\ B5-98 & 0.0008957 * & 2703 * & 50.67 * & 0.9989 & 0.0133100 \\ B10-98 & 0.58500000 & 3.513 * & \(-\)250.8 & 0.9321 & 0.0147100 \\ B85-98 & 0.000895 * & 2703 * & 50.66 * & 0.9989 & 0.0133100 \\ B100 & 0.0037680 * & 1737 & \(-\)33.16 * & 0.9997 & 0.0093950 \\ \hline \hline \end{tabular}  
* coefficient is not statistically significant for confidence level \(p<0.05\).  
\end{table} 
Table 7: Coefficients of Vogel dynamic viscosity model and statistical indicators (\(R^{2}\)—coefficient of determination, SSE—sum of squared estimate of errors). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Exponential** & \(\mathbf{\
u_{0}\) **(mm\({}^{2}\)-s\({}^{-1}\))** & \(\mathbf{b}\) **(K–1)** & \(\mathbf{R^{2}}\) & **SSE** \\ \hline B0-95 & 3.2970 & \(-\)0.004905 & 0.8745 & 0.006032 \\ B5-95 & 0.8766 & \(-\)0.003729 & 0.7472 & 0.008742 \\ B10-95 & 4.1030 & \(-\)0.005324 & 0.7760 & 0.017080 \\ B85-95 & 2465 & \(-\)0.022790 & 0.9961 & 0.072730 \\ B0-98 & 3.0930 & \(-\)0.004876 & 0.9157 & 0.003430 \\ B5-98 & 1.3070 & \(-\)0.001549 & 0.7127 & 0.001855 \\ B10-98 & 2.0960 & \(-\)0.003125 & 0.5800 & 0.013700 \\ B85-98 & 2356 & \(-\)0.021870 & 0.9950 & 0.131700 \\ B100 (butanol) & 8691 & \(-\)0.026090 & 0.9980 & 0.093450 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Coefficients of Exponential kinematic viscosity model and statistical indicators (\(R^{2}\)—coefficient of determination, SSE—sum of squared estimate of errors). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Arrhenius** & \(\mathbf{\
u_{0}\) **(mm\({}^{2}\)-s\({}^{-1}\))** & \(\mathbf{E_{a}}\) **(J-mol\({}^{-1}\))** & \(\mathbf{R^{2}}\) & **SSE** \\ \hline B0-95 & 0.194500 & 3384 & 0.8962 & 0.004991 \\ B5-95 & 0.279800 & 2594 & 0.7751 & 0.007778 \\ B10-95 & 0.187100 & 3711 & 0.8129 & 0.014270 \\ B85-95 & 0.006053 & \(1.518\times 10^{4}\) & 0.9995 & 0.010040 \\ B0-98 & 0.186200 & 3356 & 0.9345 & 0.002662 \\ B5-98 & 0.534300 & 1070 & 0.7247 & 0.001777 \\ B10-98 & 0.337500 & 2211 & 0.6217 & 0.012340 \\ B85-98 & 0.009614 & \(1.459\times 10^{4}\) & 0.9991 & 0.022710 \\ B100 & 0.003469 & \(1.725\times 10^{4}\) & 0.9950 & 0.240900 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Coefficients of Arrhenius kinematic viscosity model and statistical indicators (\(R^{2}\)—coefficient of determination, SSE—sum of squared estimate of errors). In Figures 3-7, a relatively nonlinear decrease in the kinematic viscosity during the heating of gasolines, biobutanol, and their blends (especially when the Vogel model is used) can be seen. The lowest values in the kinematic viscosity were determined for B0 (pure gasoline) and the highest values in the kinematic viscosity were determined for B100 (pure biobutanol). The viscosity properties of the B5 and B10 blends approached that of the pure gasoline, which applies to both RON95 and RON 98. The viscosity behaviour of the B85 blend is close to the pure biobutanol viscosity behaviour. Similar results and conclusions were reached in [4,21].