## 5 Conclusions  
Simplified solutions are derived and have been shown to closely approximate the bulk vaporization behavior described by the more detailed theory, particularly for the prediction of the total vaporization time [15]. It is also demonstrated that the behavior of hydrocarbon droplets of modern fuels and their blends during vaporization and ignition processes can be adequately estimated by using the simplified solutions of [PERSON]'s 'Diffusion Theory' offered by this model. These results qualitatively agree with experimental observations, implying that the various assumptions of the model that the influence of the kinetic factor exists are realistic. Finally, the model proposes a modified and accurate approach to ignition delay studies considering the difference in the gas phase diffusivity of diesel fuel \begin{table}
\begin{tabular}{c c c} \hline \hline
**Atoms, Groups, Bonds** & **Diesel Fuel** & **RME** \\ \hline Chemical formula & C\({}_{16}\)H\({}_{34}\) & C\({}_{19}\)H\({}_{36}\)O\({}_{2}\) \\ \hline Molecular weight & 226.43 & 292.00 \\ \hline Density at \(T\) = 293 K, kg/m\({}^{3}\) & 860 & 900 \\ \hline Thermal conductivity, W/m\(\cdot\)K & 95.72 & 66.46 \\ \hline Heat capacity (liquid phase) at \(T\) = 293 K, J/(g\(\cdot\)K) & 1.85 & 2.12 \\ \hline Dynamic viscosity at \(T\) = 288 K, Pa\(\cdot\)s & 2.44\(\cdot 10^{-6}\)[55] & 4.54\(\cdot 10^{-6}\) \\  & & 4.21\(\cdot 10^{-6}\) \\ \hline Specific heat capacity at \(T\) = 323 K, J/(gK) & 1.63 & 2.12 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Physico-chemical characteristics of test fuels. and RME vapors. Comparison with experimental data shows that the proposed equation can accurately predict the ignition delay of a binary droplet. With the assumption that droplets can serve as moving flameholders within the injected spray, some insights about droplet vaporization during the ignition delay can also be formulated. From the present study, it is evident that the blend vaporizing time can be reduced by either increasing the ambient temperature or decreasing the droplet size. Along with the above, the following conclusions can be drawn:  
* Single droplets of biodiesel, diesel and their 20% blend were suspended in a relatively static environment with an ambient temperature of 935 K to 1010 K to validate the model proposed in this paper. The semi-theoretical model can well describe the droplet ignition delay and the error between the predicted results, and the experimental data are within 1-13%. * The upper limit of the temperature range for this experiment exceeds the critical ignition temperature of the RME by 294 K.
* The longest ignition delay was established for diesel fuel and the shortest for RME, while blended fuel exhibited intermediate values. The time of combustion followed the opposite trend: fuels that exhibit longer ignition delays had shorter periods of combustion. This can be explained by the fact that the initial fuel mass per droplet from the thermocouple correlates with the fuel density and viscosity (see Table 2), i.e., biodiesel mass > diesel mass. * In terms of simulation accuracy assessed for six different temperatures, the average level of correspondence of the ignition delay values with the ones experimentally obtained for different types of fuel arranged in decreasing order: DF80/RME20 (average \(r=0.95\)) > DF (average \(r=0.95\)) > RME (average \(r=0.92\)). The data presented here can be used to predict or verify the ignition characteristics of yet less-investigated alternative fuels, such as microalgal oil blended with diesel fuel. The future scope of this study is primarily focused on the integration of the obtained findings to analyze the liquid jet atomization and the breakup of droplets of different alternative fuels. The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app15137488/s1](https://www.mdpi.com/article/10.3390/app15137488/s1)]([https://www.mdpi.com/article/10.3390/app15137488/s1](https://www.mdpi.com/article/10.3390/app15137488/s1)).