# Secondary Atomization of a Biodiesel Micro-Emulsion Fuel Droplet Colliding with a Heated Wall
## 3 Results and Discussion
### Effect of Rheological Properties of Fuel Micro-Emulsions and Bio-Additive  
We estimated how the FAME of rapeseed oil bio-additive affects the mean diameter of child droplets generated by the hydrodynamic breakup (Figure 8a). It was established that the additional component provides a decrease in \(d_{\text{s}}\). Also, the minimum considered amount of this component (D/RO = 90/10) leads to the most substantial decrease in the mean child droplet diameter. A further increase in the biodiesel proportion increases \(d_{\text{s}}\)/\(D_{0}\). This result can be explained by different kinematic viscosity of the examined fuel compositions. In particular, sample C-1 has the lowest viscosity and the smallest mean diameter of child droplets (Figure 8a). In other words, lower viscosity gives finer droplets. This pattern was observed throughout the range of the heating temperatures under study. Moreover, the droplet of C-1 with the lowest viscosity breaks up into the largest amount of child droplets as well (Figure 8b). Interestingly, adding the lowest examined amount of rapeseed oil caused a _several-fold_ (from \(\sim\)100 up to \(>\)1000) increase in the number of child droplets under the same experimental conditions. A further increase in the biodiesel fraction has a moderate effect on \(N\) (increasing it 2-5 times). Finally, it was no surprise that the estimated increase in the evaporation  
Figure 7: Effect of WiDME (C-6) drop interaction velocity on variation of the mean diameter of child droplets generated by hydrodynamic breakup (**a**), their number (**b**), and evaporation surface area (**c**) at various surface temperatures. surface area due to hydrodynamic breakup was maximum for the C-1 composition at \(T_{0}\) = 400 \({}^{\circ}\)C (Figure 8c). The initial drop surface area was exceeded by more than 10 times. Figure 8: Effect of FAME of rapeseed oil (RO) added to the hydrocarbon component of micro-emulsion in different volume fractions on **(a)** mean diameter of child droplets generated by hydrodynamic breakup, **(b)** their amount, and (**c–e**) fuel evaporation surface area; (**a–c**) \(T_{0}\) = 400 \({}^{\circ}\)C, **(d)**\(T_{0}\) = 300 \({}^{\circ}\)C, **(e)**\(T_{0}\) = 500 \({}^{\circ}\)C.  
The effect of inertial forces, viscosity, and surface tension results in different outcomes of the impact characterized by specific thermodynamic processes. The analysis of Figure 8 shows that a threshold _We_ was observed for almost every liquid. When \(S_{1}\)/\(S_{0}\) exceeds this threshold, its values do not change much, i.e., the curves tend to asymptotic values. These trends were observed at various temperatures and for various droplet component compositions. By considering them, we will be able to optimize the secondary atomization due to the wall impact. Indeed, it is unreasonable to increase the impact velocity or initial drop size trying to provide _We_ > 300, if the child to parent droplet size ratio (and, correspondingly, \(S_{1}\)/\(S_{0}\)) will only change by 15-20%. More rational parameters should be chosen in this case. Again, composition C-1 demonstrated the highest integral characteristics of hydrodynamic breakup with an increase in \(T_{0}\) (Figure 8e). At \(T_{0}\) = 300 \({}^{\circ}\)C, adding the minimum amount of biodiesel had no perceptible effect on \(S_{1}\)/\(S_{0}\) (Figure 8d). The results in Figure 8c-e indicate the following:  
1. Viscosity decrease due to adding a minimum amount of biodiesel provides a several-fold increase in the number of fine child droplets. 2. Wall surface temperature should be taken into an account when analyzing the integral characteristics of the hydrodynamic breakup of WiDME and WiBDME drops. 3. Fuel micro-emulsion drops with FAME of rapeseed oil break up into more child droplets with a smaller mean diameter, intensifying the air-fuel mixture preparation in the combustion chamber. The effect of rheological properties of a fuel composition on WiDME and WiBDME droplet spreading diameter versus time (Figure 9) was studied experimentally.