## 3 Results and Discussions
### The Influence of We  
Firstly, we discuss the results of droplet morphology under three different _We_ on the low-roughness surface (\(Ra=0.8\)\(\upmu\)m as shown in Figure 4a-c) and high-roughness surface (\(Ra=6.3\)\(\upmu\)m as shown in Figure 4d-f). Scale bars were labeled for each group of impacting images. As shown in Figure 4a for the low _We_ number case (\(We=77\)), the droplet deforms once it impacts the surface, forming a truncated spherical shape at first, and subsequently, a thin liquid layer is formed at the bottom of the droplet (0.60 ms). Then, the thin layer of liquid gradually spreads. Finally, the droplets spread to the maximum diameter (16.00 ms), forming a thin central part bordered by a thick cylindrical rim. The droplet front is pinned at the edge of solid grooves. The viscosity prevents the advancing motion of the three-phase contact line (TPCL), leading to a rapid change in the velocity along the normal direction. This causes an increase in the convexity of the advancing droplet periphery [21]. In the whole process of droplet spreading, it is usually assumed that the initial kinetic energy is mainly consumed by the surface energy and by viscous dissipation [36; 37; 38; 39]. The viscous dissipation comes from the attraction force between molecules in the droplets, the adsorption capacity of the solid wall to droplet molecules, and the momentum exchange between droplet flow layers. Figure 3: Parameters of droplet. (**a**) droplet spreading diameter. (**b**) droplet diameters in horizontal and vertical directions. Figure 4b shows the evolution process of droplet morphology under low surface roughness (\(Ra=0.8\)m) and medium \(We\) number case (\(We=521\)). The droplet morphology is similar to that at low \(We\) of 77, but the difference is that the time for droplets to reach the maximum spreading diameter is obviously shortened, and the thickness of the liquid film is thinner when reaching the maximum spreading diameter \(\beta_{\text{max}}\) due to the greater spreading kinetic energy of droplet. In addition, \"finger-like\" disturbance (9.20 ms, Figure 4b) can be observed at the final stage of spreading, which will be discussed in detail in a later section. Different from the low \(We\), when \(\beta_{\text{max}}\) is reached, the outer edge of the droplet has been boiled and evaporated (9.20 ms, Figure 4b). These phenomena are more obvious under a high \(We\) number (\(We=948\)), as demonstrated in Figure 4c. In addition, when the maximum spreading diameter is reached under a high \(We\) number, the boiling has propagated from the outer boundary to the inside of the liquid film (6.70 ms, Figure 4c). This can be explained by the fact that the larger kinetic energy at a high \(We\) number causes the droplets to spread into a thinner and larger liquid film, promoting the heat exchange and evaporation of the liquid film. At the same time, the dynamic evolution of droplet impinging on high roughness surface of \(Ra=6.3\)\(\upmu\)m under low, medium, and high \(We\) are presented in Figure 4d-\(f\) as a comparison. The dynamic behaviors are similar to those under low roughness surfaces. In all the roughness and Weber number ranges studied, no obvious phenomena such as broken splash, recede, rebound, and satellite droplets were observed. The spreading factor \(\beta\) is able to represent droplet spreading kinetics quantitatively. Figure 5 presents the variations of \(\beta\) with dimensionless time \(\tau\) under low, medium, and high \(We\) numbers on different roughness surfaces. As can be seen from this figure, the \(\beta\)-\(\tau\) curves of different \(We\) coincide at each roughness in the initial stage of droplet spreading (\(\tau<0.1\)), which means that the spreading speed and behavior of droplets at this stage are highly similar. [PERSON] et al. [40] believed that the evolution of \(\beta\) was not affected by any factors at the early stage of droplet motion (\(\tau<0.1\)). Near \(\tau=0.1\), the \(\beta\)-\(\tau\) curve of low \(We\) separates from the curve of medium and high \(We\).