## 4 Experimental Results and Discussion
### Droplet Size and Velocity Distribution on Radial Direction  
Based on the analysis of the surface tension and viscosity change in the axial direction, this study further investigates the effect of these factors on droplet size in the radial direction. The Z = 15 cm section was selected for analysis and discussion due to its section position, data amount, and quality. Figure 8 shows the variation of droplet size in the radial direction under different surface tension and viscosity conditions.  
As shown in Figure 8, the droplet size exhibits two stages of change as the radial distance increases. The first stage occurs between X = 101 cm and X = 141 cm, during which the droplet size increases rapidly. This phenomenon can be attributed to two reasons. First, droplets with lower surface tension at the center of the radial section are more prone to breaking, forming high-speed small droplets due to the impact of internal energy. However, due to increased viscosity, these droplets are more likely to collide with surrounding droplets during radial movement, forming larger droplets. Second, during the radial expansion of droplets, heat exchange occurs between high-viscosity droplets, resulting in inelastic collisions and rapid droplet size increase. During the diffusion process, the surface tension of 2% dodecyl alcohol solution was 38.37 mN\(\cdot\)m\({}^{-1}\) lower than that of pure water, the viscosity increased by 0.23 \(\times\) 10\({}^{-3}\) Pa\(\cdot\)s, and the droplet size increased by 70 \(\upmu\)m. Thus, the interplay between surface tension and viscosity causes a rapid droplet size increase during radial movement.  
Figure 8: Droplet size distribution on the radial direction.  
The second stage of droplet size change occurs between \(X=\left\lvert\,4\,\right\rvert\) cm and \(X=\left\lvert\,8\,\right\rvert\) cm, during which the droplet size increases slowly. The droplet size of the dodecyl solution at \(X=\left\lvert\,4\,\right\rvert\) cm was not significantly different from that of pure water. In this stage, changes in surface tension and viscosity had no significant effect on droplet velocity. It can be seen that in the process of optimizing the fog field, the surface tension should be properly reduced to keep the droplet at the radial center with a smaller droplet size. At the same time, it is necessary to reduce the viscosity of the dust suppression solution so that the droplets increase steadily in the first radial expansion process and smoothly transition to the second stage so that the fog field maintains a large coverage area and uniform droplet size distribution.  
The variation of radial droplet velocity is depicted in Figure 9, which shows a two-stage change, with the first rapid decline followed by a slow decline. The velocity of the dust suppression solution reaches 0 m/s at \(X=\left\lvert\,8\,\right\rvert\) cm, which is due to the balance of surface tension, viscous force, inertial force, and air resistance of the droplet at the edge of the fog field, leading to slow droplet movement only under the influence of gravity. Between \(X=0\) cm and \(X=\left\lvert\,2\,\right\rvert\) cm, the droplet velocity of 2% dodecyl solution reduces by 53%, and that of 5% dodecyl solution reduces by 51%, with a much higher droplet velocity reduction rate of dust suppression solution compared to pure water. This indicates that the velocity of high-viscosity droplets drops faster during the change of radial expansion. Combining the analysis of Figure 8, it can be inferred that, in the process of optimizing the fog field, reducing surface tension can ensure small droplet size and large velocity at the radial center while reducing viscosity can prevent sudden changes in droplet size and velocity during radial expansion.