# Temperature Dependence of Density and Viscosity of Biobutanol-Gasoline Blends
## 3 Results and Discussion
### Mathematical Models
#### 3.4.3 Mathematical Models for Kinematic Viscosity  
For practical use, modelling the temperature dependence of the kinematic viscosity of the biobutanol-gasoline blends is the most suitable, because the kinematic viscosity contains information about the values of both the dynamic viscosity and the volumetric mass density of the blends [35]. Therefore, in the industrial and petrochemical fields, this viscosity is preferred, especially for temperature-dependent fluids. \begin{table}
\begin{tabular}{c c c c c} \hline
**Newton** & \(\mathbf{\eta_{0}}\) **(mPa-s)** & \(\mathbf{b}\) **(K\({}^{-1}\))** & \(\mathbf{R^{2}}\) & **SSE** \\ \hline B0-95 & 0.13290 & 437.1 & 0.9101 & 0.002831 \\ B5-95 & 0.17350 & 371 & 0.8994 & 0.002481 \\ B10-95 & 0.11940 & 497.3 & 0.8563 & 0.007531 \\ B85-95 & 0.003794 & 1896 & 0.9996 & 0.005149 \\ B0-98 & 0.118700 & 456.2 & 0.9566 & 0.001295 \\ B5-98 & 0.316800 & 204.3 & 0.8742 & 0.001015 \\ B10-98 & 0.208800 & 330.4 & 0.7397 & 0.006637 \\ B85-98 & 0.003084 & 1942 & 0.9989 & 0.013940 \\ B100 & 0.001479 & 2233 & 0.9997 & 0.010480 \\ \hline \end{tabular}
\end{table} 
Table 6: Coefficients of Newton 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
**Exponential** & \(\mathbf{\eta_{0}}\) **(mPa-s)** & \(\mathbf{b}\) **(K\({}^{-1}\))** & \(\mathbf{R^{2}}\) & **SSE** \\ \hline B0-95 & 2.785 & \(-\)0.005277 & 0.8904 & 0.003453 \\ B5-95 & 2.291 & \(-\)0.004474 & 0.8800 & 0.002957 \\ B10-95 & 3.753 & \(-\)0.005958 & 0.8234 & 0.009255 \\ B85-95 & 2.785 & \(-\)0.005277 & 0.8904 & 0.003453 \\ B0-98 & 2.855 & \(-\)0.005526 & 0.9412 & 0.001755 \\ B5-98 & 1.318 & \(-\)0.002481 & 0.8729 & 0.001026 \\ B10-98 & 2.040 & \(-\)0.003918 & 0.7008 & 0.007626 \\ B85-98 & 2926 & \(-\)0.024320 & 0.9974 & 0.033080 \\ B100 & \(1.141\times 10^{4}\) & \(-\)0.028090 & 0.9971 & 0.088950 \\ \hline \end{tabular}
\end{table} 
Table 4: Coefficients of Exponential 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
**Arrhenius** & \(\mathbf{\eta_{0}}\) **(mPa-s)** & \(\mathbf{E_{a}}\) **(J**-mol\({}^{-1}\))** & \(\mathbf{R^{2}}\) & **SSE** \\ \hline B0-95 & 0.1329 & 3634 & 0.9101 & 0.002831 \\ B5-95 & 0.1735 & 3085 & 0.8994 & 0.002481 \\ B10-95 & 0.1194 & 4134 & 0.8563 & 0.007531 \\ B85-95 & 0.003794 & 1.576 \(\times\) 10\({}^{4}\) & 0.9996 & 0.005149 \\ B0-98 & 0.118700 & 3793 & 0.9566 & 0.001295 \\ B5-98 & 0.316800 & 1698 & 0.8742 & 0.001015 \\ B10-98 & 0.208800 & 2747 & 0.7397 & 0.006637 \\ B85-98 & 0.003084 & 1.615 \(\times\) 10\({}^{4}\) & 0.9989 & 0.013940 \\ B100 & 0.001479 & 1.856 \(\times\) 10\({}^{4}\) & 0.9997 & 0.010480 \\ \hline \end{tabular}
\end{table} 
Table 5: Coefficients of [PERSON] dynamic viscosity model and statistical indicators (\(R^{2}\)—coefficient of determination, SSE—sum of squared estimate of errors). The temperature dependence of the kinematic viscosity of the biobutanol-gasoline blends were also modelled using four mathematical models (see Section 2.4). The coefficients of these models are shown in Tables 8-11. Again, it has been proven that with an increasing temperature, the kinematic viscosity of the gasolines (RON 95 and RON 98) and biobutanol nonlinearly decreases [36], which is confirmed by the coefficients of the mathematical models in Figures 3-5. In Table 11 (the coefficients of the Vogel model), several statistically insignificant coefficients can be seen, despite the Vogel model being the most accurate according to the highest average value of the coefficient of determination \(R^{2}\) (0.9411) and average value of sum of squared estimate of errors SSE (0.0040) without SSE of B100. The Newton and Arrhenius models followed with an average \(R^{2}\) value 0.8621 and SSE value 0.0353, and the exponential model has the lowest accuracy (but still very high), according to the results of the average value \(R^{2}\) (0.8440) and SSE (0.0387).