# Secondary Atomization of a Biodiesel Micro-Emulsion Fuel Droplet Colliding with a Heated Wall
## 3 Results and Discussion
### Hydrodynamic Interaction Regimes of WiDME and WiBDME Droplets  
The analysis of the experimental results, like in [32], established that there are three possible regimes of WiDME and WiBDME droplet interaction. Figure 3 shows the images corresponding to the established regimes: (a) drop deposition (including drop spreading and receding), (b) drop hydrodynamic breakup, (c) drop rebound. This indicates that the bio-additive to the fuel micro-emulsion had no significant effect on the hydrodynamic interaction between the droplets and heated surface. The effect of inertial forces, viscosity, and surface tension results in different outcomes of the impact characterized by specific thermodynamic processes. In the case of drop deposition regime (Figure 3a), just like for distilled water [29], a micro-emulsion fuel droplet is wetting the surface during its whole lifetime and does not rebound after the impact. After the impact, the droplet evaporation is accelerated under the effect of convection or bubble boiling, depending on \(T_{0}\). For the distilled water, the authors of [29] describe drop dancing as a transient regime between drop deposition and drop rebound. In the experiments with WiDME and WiBDME droplets, this regime was not observed, most likely, because their viscosity is higher than that of water. No transient boiling was identified by video-recording in the micro-emulsion under study. The drop rebound regime (Figure 3c) is characterized by high surface heating temperature \(T_{0}\). After spreading and receding, the drop rebounds. The reason for this behavior is a vapor layer between the substrate surface and the droplet. Film boiling during droplet interaction is described in [33; 34]. In terms of practical secondary atomization, the hydrodynamic breakup regime (Figure 3b) is of the highest interest. This regime produces a lot of secondary droplets, also known as child droplets. In real internal combustion engines, this regime will accelerate the ignition of the air-fuel mixture. The numerical characteristics of this interaction regime will be presented further. The transition boundary between the regime of hydrodynamic breakup of micro-emulsion fuel droplets and their rebound for various \(D_{0}\) and \(U_{0}\) is shown in Figure 4 and is given by \(Re=-1466.7 Oh+349.33\). More details on this transition and the analysis of the regime map in Figure 4 can be found in [32]. Figure 3: WiDME and WiBDME drop collision with a heated surface within different hydrodynamic regimes: (**a**) drop deposition (including drop spreading and receding), \(T_{0}=225\)\({}^{\circ}\)C, \(D_{0}\approx 3\) mm, \(U_{0}\approx 1.72\) m/s, (**b**) drop hydrodynamic breakup, \(T_{0}=320\)\({}^{\circ}\)C, \(D_{0}\approx 2.7\) mm, \(U_{0}\approx 2.69\) m/s, (**c**) drop rebound, \(T_{0}=330\)\({}^{\circ}\)C, \(D_{0}\approx 3\) mm, \(U_{0}\approx 1.72\) m/s. When generalizing the results using \(Re\) and \(Oh\), we attempt to determine the balance of inertial forces, viscosity, and surface tension that leads to a transition from one droplet-wall interaction regime to another. The overall shape of the transition boundary in Figure 4 demonstrates the possible transition to extensive atomization of droplets with high viscosity to surface tension ratio, even at relatively low \(Re\) (below 100). For actual advancement of the technology, this result can be used to rationalize that lower pressures are sufficient for fuel injection (with lower velocity and \(Re\)). The experiments showed that the higher the liquid viscosity, the faster the child droplets take spherical shape. It requires higher aerodynamic force to disrupt spherical drops than elliptical or disk-shape ones [35]. It decreases the probability of recurrent breakup, i.e., high-viscosity liquid can be atomized by an injection nozzle (primary) and by wall impact (secondary), but all the following stages will not provide many child droplets. In general, high-viscosity liquid is characterized by the lower amount and larger dimensions of child droplets.