## 2 Materials and Methods
### Methods of Determining the Ignition and Combustion Characteristics of Fuel Droplets  
Each experiment was repeated at least five times under identical initial conditions for a mixed and conductive heat supply to a fuel droplet. The obtained video recordings of the ignition and combustion of fuel droplets were processed in accordance with previously developed algorithms [27] using Tema Automotive and Phantom Camera Control software. Figure 5 shows typical frames of video recording processing. In the experiments, the main  
Figure 4: Experimental setup of a conductive heat supply to a fuel droplet. 1—modified steel surface; 2—electromagnetic inductor; 3—induction spiral; 4—control unit for inductor; 5—thermal imaging camera; 6—chiller; 7—fuel droplet; 8—holder; 9—high-speed video camera; and 10—spotlight.  
characteristics of ignition and burnout of fuel droplets were determined, including the ignition delay time (\(\tau_{d}\)) (Figure 5b,e), the maximum size of the fuel burnout region (\(D_{\text{max}}\)) (Figure 5c,f), the number of puffing initiations (\(N\)) (Figure 5d,g), and the burnout time (\(\tau_{\text{burn}}\)). In experimental studies with a mixed heat supply, the contact diameter of the spreading of fuel droplets (\(d_{s}\)) was additionally determined (Figure 5a).  
The contact diameter of spreading fuel droplets \(d_{s}\) (Figure 5a) was registered 5-6 s after dosing a droplet on the surface under laboratory conditions. During such a period of time, a fuel droplet achieves a quasi-equilibrium state (balancing the forces acting on it). The systematic error in determining the contact diameter of fuel droplets due to the high-speed video camera resolution did not exceed 4%.  
The ignition delay time (Figure 5b,e) was determined from frames of videograms in monochrome colors. The ignition delay time was taken as a time period between two events. The first event is placing the steel with a fuel droplet at a given point in the ceramic tube of the furnace for a mixed heat supply (Figure 5b) or placing a special holder with a droplet placed on it on the steel surface preliminary heated to a given temperature for a conductive heat supply (Figure 5e). The second event is when the image brightness values exceeded 220 units. The fuel burnout time was determined from monochrome images from the start of ignition to the achievement of image brightness values of less than 219 units in terms of color range. The random error in determining \(\tau_{d}\) and \(\tau_{\text{burn}}\) did not exceed 10%.  
The maximum size of the fuel burnout region (Figure 5c,f) was determined from color videograms. The burnout region was automatically controlled (by image contrast) on the frames of high-speed video recording. By azimuth with a step of 45 degrees, the value of the width of the burnout region was determined. The maximum size of the fuel burnout region was determined as the arithmetic mean of the four measurements. The random error in determining \(D_{\text{max}}\) did not exceed 10%.  
The number of puffing initiations (Figure 5d,g) was determined from the statistical data on the separation of fragments of child droplets from the parent droplet by determining the change in the characteristic size of the burnout region. The number of puffing initiations was taken to be the value of positive peaks in the change in the characteristic size of the burnout region. The random error in determining \(N\) did not exceed 7%.  
Figure 5: Typical frames of video recording processing to determine the ignition and combustion characteristics of fuel droplets. Characteristics determined for a mixed heat supply were \(d_{s}\) (**a**), \(\tau_{d}\) (**b**), \(D_{\text{max}}\) (**c**), and \(N\) (**d**). Characteristics determined for a conductive heat supply were \(\tau_{d}\) (**e**), \(D_{\text{max}}\) (**f**), and \(N\) (**g**).