# Secondary Atomization of a Biodiesel Micro-Emulsion Fuel Droplet Colliding with a Heated Wall
## 2 Experimental
### Methods  
The experiment determined the quantitative characteristics (Table 2) of hydrodynamic disintegration of micro-emulsion fuel droplets interacting with a heated wall: \(d_{\rm s}\) is the arithmetical mean diameter of child droplets generated by hydrodynamic disintegration (also known as \(d_{10}\)); \(N\) is the number of child droplets; \(S_{1}\) is the total evaporation surface area of child droplets. The latter characteristic is determined as the area of a single fragment with the diameter \(d_{\rm s}\) further multiplied by \(N\) (see the calculation method for \(d_{\rm s}\) and \(N\) below). In addition, the initial surface area \(S_{0}\) of a parent droplet was calculated as the area of a sphere of the known diameter \(D_{0}\). The parameter \(d_{\rm s}\) was calculated in the Mathematica software package. A custom program was developed to analyze the resulting disintegration of fuel micro-emulsion droplets (i.e., the mean diameter of the generated fragments). A binarization threshold was set individually for each processed image. Then the program identified the elements and calculated their dimensions in pixels. The software subtracted the background and rejected the elements adjacent to the image border. Since the substrate had a mirror-like finish, the reflection of fragments was erased from the image during the frame processing. The designed technique is discussed in detail in [30]. \(N\) is a parameter calculated by: (1) determining the volume of a single child droplet with the mean diameter \(d_{\rm s}\); (2) determining the \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Fuel Composition**} & \multicolumn{2}{c}{**Volumetric Ratio**} & \multicolumn{2}{c}{**Emulsifier Concentration (vol. \%)**} \\ \cline{2-4}  & **D/FAME** & **D+FAME/Water** & \\ \hline C-1 & 90/10 & 80/20 & 20 \\ C-2 & 70/30 & 80/20 & 20 \\ C-3 & 50/50 & 80/20 & 20 \\ C-4 & 90/10 & 90/10 & 20 \\ C-5 & 50/50 & 80/20 & 10.45 \\ C-6 & 100/0 & 80/20 & 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Component composition of the fuel under study. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Fuel Composition** & \(\sigma\) **(mN/m) at 25 \({}^{\circ}\)C** & \(\rho\) **(kg/m3) at 25 \({}^{\circ}\)C** & \(\
u\)**10\({}^{6}\) (mm2/s) at 25 \({}^{\circ}\)C** & \(\mu\)**10\({}^{3}\) (mPa*) at 25 \({}^{\circ}\)C** \\ \hline C-1\({}^{*}\) & 29.7 & 902.42 & 39.89 & 36 \\ C-2\({}^{*}\) & 30 & 902.75 & 51.84 & 46.8 \\ C-3\({}^{*}\) & 29.9 & 910.36 & 46.14 & 42 \\ C-4\({}^{*}\) & 29.8 & 892.4 & 31.33 & 27.96 \\ C-5\({}^{*}\) & 30.9 & 892.11 & 32.01 & 28.56 \\ C-6\({}^{**}\) & 29.03 & 893.13 & 45.16 & 40.33 \\ \hline \hline \end{tabular} Note: \({}^{*}\) WiBDME; \({}^{**}\) WiDME.  
\end{table} 
Table 3: Water-in-diesel and water-in-biodiesel micro-emulsion properties: surface tension (\(\sigma\)), density (\(\rho\)), kinematic viscosity (\(\
u\)), and dynamic viscosity (\(\mu\)). Figure 2: Water-in-diesel and water-in-biodiesel fuel compositions under study. initial volume of a droplet with the diameter \(D_{0}\). Next, the initial volume of a droplet with the diameter \(D_{0}\) was divided by the volume of a fragment with the diameter \(d_{\rm s}\). The resulting value was an estimate of \(N\). There are several papers, for example [31], describing the evaluation of the number of fragments generated from a droplet breakup after heating or collision with a wall, another droplet or a group of droplets (aerosol).