# Conditions for and Characteristics of the Dispersion of Gel Fuel Droplets during Ignition
## 2 Materials and Methods
### Analytical Studies  
Insignificant impurities in liquids and environmental conditions significantly affect the surface tension and its parts (polar and dispersive) [33]. Therefore, the surface tension of the liquids was measured, and the parts of the surface tension were calculated. The surface tension of the liquids used in the studies was measured by using a K20 tensiometer (KRUSS, Hamburg, Germany) according to the Du Nouy and Wilhelmy methods at a liquid \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Liquid**} & \multicolumn{2}{c}{**Chemical**} & \multicolumn{4}{c}{**Reference Data**} \\ \cline{2-6}  & **Formula/Boiling** & **Manufacturer** & \(\sigma_{L}\)**, **mN/m** & \(\sigma_{L}^{P}\)**, **mN/m** & \(\sigma_{L}^{D}\)**, **mN/m** & **Ref.** \\ \hline Water & H\({}_{2}\)O/100.0 & \multicolumn{2}{c}{Mill-Q water treatment system, Sigma-Aldrich, St. Louis, MO, USA} & 72.8 & 51.0 & 21.8 & [28] \\ Monoethanolamine & C\({}_{2}\)H\({}_{7}\)NO/170.0 & Ekos-1, Moscow, Russia & 48.2 & 29.4 & 18.8 & [29] \\ Glycerol & C\({}_{3}\)H\({}_{8}\)O\({}_{3}\)/290.0 & Tula Pharm Factory, Tula, Russia & 63.4 & 26.4 & 37.0 & [28] \\ Ethylene glycol & C\({}_{2}\)H\({}_{6}\)O\({}_{7}\)/197.3 & Ekos-1, Moscow, Russia & 47.7 & 16.8 & 30.9 & [28] \\ Acetone & C\({}_{3}\)H\({}_{4}\)O\({}_{7}\)/56.0 & Ekos-1, Moscow, Russia & 25.2 & 3.1 & 22.1 & [30] \\ Ethyl alcohol 95\% & C\({}_{2}\)H\({}_{6}\)O/78.3 & Rosbio, St. Petersburg, Russia & 22.1 & 4.6 & 17.5 & [31] \\ Diiodomethane & CH\({}_{2}\)I\({}_{2}\)/182.1 & Alfa Aesar, Heysham, UK & 50.8 & 0.0 & 50.8 & [28] \\ Dodecane & C\({}_{2}\)H\({}_{2}\)/216.3 & Ekos-1, Moscow, Russia & 25.4 & 0.0 & 25.4 & [32] \\ Synthetic engine oil & \(-\)/190.4 & Gazprommeft, St. Petersburg, Russia & 33.4 & 1.4 & 32.0 & [25] \\ Compressor oil & \(-\)/190.5 & Gazprommeft, St. Petersburg, Russia & 28.01 & 0.01 & 28.0 & [25] \\ Oil TEDEX TU 32 & \(-\)/208.0 & Gazprommeft, St. Petersburg, Russia & 36.1 & 1.1 & 35.0 & [25] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristics of components in composite fuels. and ambient temperature of 22 \({}^{\circ}\)C. The error in determining the surface tension did not exceed 0.5%, which was several tenths of a mN/m. According to the [PERSON], [PERSON], [PERSON], and [PERSON] (work) method, the polar (\(\sigma_{L}^{P}\)) and dispersive (\(\sigma_{L}^{D}\)) parts of the surface tension (\(\sigma_{L}=\sigma_{L}^{P}+\sigma_{L}^{D}\)) of the liquids presented in Table 1 were determined by using the following system of equations [34]:  
\[\left\{ \begin{array}{ll}\frac{\sigma_{L}(\cos\theta_{1}+1)}{2\sqrt{\sigma_{ L}^{D}}}=\frac{\sqrt{\sigma_{S1}^{P}}\sqrt{\sigma_{L}^{P}}}{\sqrt{\sigma_{L}^{D}}} +\sqrt{\sigma_{S1}^{D}}\\ \frac{\sigma_{L}(\cos\theta_{2}+1)}{2\sqrt{\sigma_{L}^{D}}}=\frac{\sqrt{\sigma _{S2}^{P}}\sqrt{\sigma_{L}^{D}}}{\sqrt{\sigma_{L}^{D}}}+\sqrt{\sigma_{S2}^{D}} \end{array} \right. \tag{1}\]  
where \(\sigma_{L}\), \(\sigma_{L}^{P}\), and \(\sigma_{L}^{D}\) are the surface tension and its polar and dispersive parts (target values from Equation (1)) in mN/m; \(\theta_{1}\) and \(\theta_{2}\) are static contact angles on test surfaces #1 and #2 (determined experimentally) in \({}^{0}\); \(\sigma_{S1}^{P}\), \(\sigma_{S1}^{D}\) and \(\sigma_{S2}^{P}\), \(\sigma_{S2}^{D}\) are the polar and dispersive parts of the surface free energy (SFE) of test surfaces #1 and #2 (calculated from Equation (2)) in mN/m. As test surfaces #1 and #2, aluminum-magnesium alloy AMG-6 (ROSTEHKOM, Yekaterinburg, Russia) and fluoropolymer PTFE (APC Group, Yekaterinburg, Russia) were chosen. Surfaces #1 and #2 were made in the form of a disk with a diameter of 50 mm and a thickness of 4 mm, and they had a very low roughness that was close to molecularly smooth. By using the known surface tensions of the test liquids (Table 1), we determined \(\sigma_{S1}^{P}\), \(\sigma_{S1}^{D}\) and \(\sigma_{S2}^{P}\), \(\sigma_{S2}^{D}\) by solving the following system:  
\[\left\{