## 3 Results and Discussions
### The Influence of Surface Roughness  
To explore the influence of roughness on droplet spreading dynamics, this section compares the impact images of droplets on different roughness surfaces at similar _We_, as shown in Figure 6. The outcomes of droplet impingement are similar on four roughness surfaces. No obvious breaking splashes were observed within the range of _We_ studied.  
Droplet impingement on a groove-textured solid surface may experience one of the following states [21]. (i) Cassie state [41], in which liquid is suspended on the grooves and air is occupied in the valleys of the surface. (ii) Wenzel state [42], in which the liquid impales the valleys. (iii) Intermediate state, in which liquid is partially impa  
Figure 5: \(\beta\)-\(\tau\) curves at different _We_. (**a**) _Ra_ = 0.8 \(\upmu\)m. (**b**) _Ra_ = 1.6 \(\upmu\)m. (**c**) _Ra_ = 3.2 \(\upmu\)m. (**d**) _Ra_ = 6.3 \(\upmu\)m.  
Figure 6: Spreading process of R1336 mzz(Z) droplets impinging on different roughness surfaces at medium _We_ (_We_\(\approx\) 520). (**a**) _Ra_ = 0.8 \(\upmu\)m, (**b**) _Ra_ = 1.6 \(\upmu\)m, (**c**) _Ra_ = 3.2 \(\upmu\)m and (**d**) _Ra_ = 6.3 \(\upmu\)m.  
force of droplets increases or the surface conditions changes, more liquid will squeeze into the groove gap occupied by air originally, which induces the transition from the Cassie state to the Wenzel state. This transition leads to an increase in the adhesion between the droplet and the wall and high hysteresis in the Wenzel state, making it \"sticky\" on the textured surface [43]. There are two possible mechanisms for the transition as reported [21, 44, 45, 46]: sag and de-pinning. Sag means that when the depth of roughness valleys is small enough, the liquid-vapor interface directly contacts the bottom of the valley. In the de-pinning mechanism, when the magnitude of net downward force at TPCL is large enough, the droplet de-pins and causes the liquid to impale the valleys when the depth of roughness valleys increases. Forces acting on the TPCL include droplet impact pressure related to impacting velocity and three interfacial tensions [21].  
This study changed the depth of valleys through changing surface roughness. The variable \(Ra\) is commonly used to reflect the height characteristics of surface microscopic geometry. Figure 7 presents the curves of droplet spreading factors with dimensionless time on different roughness surfaces. Similar phenomena can be observed at three different _We._ The \(\beta_{\text{max}}\) first increases with the increase in surface roughness from 0.8 \(\upmu\)m to 1.6 \(\upmu\)m but decreases obviously with the increase in surface roughness from 1.6 \(\upmu\)m to 3.2 \(\upmu\)m. When the roughness increases to 6.3 \(\upmu\)m, the maximum spreading factors are basically unchanged, but they are always smaller than the \(\beta_{\text{max}}\) of the surface with \(Ra\) = 0.8 \(\upmu\)m. The first increase in \(\beta_{\text{max}}\) can be explained by the Cassie state. That is, the viscous dissipation is relatively small since the liquid film is suspended on the grooves. As a result, the \(\beta_{\text{max}}\) increases with the increase in roughness. With the continued increase in the depth of the grooves, the Cassie-Wenzel transition takes place, leading to a rapid decrease in \(\beta_{\text{max}}\) due to the de-pinning mechanism. The partially impaled state between the Cassie state and the Wenzel state consumes part of the energy input to conquer the energy barriers induced by the state transition [47]. What is more, the pinning force at TPCL increases, which leads to an increase in energy dissipation and a significant decrease in the maximum spreading diameter.  
Figure 7: Influence of surface roughness on \(\beta\)-\(\tau\) curve at three different _We._ (**a**) Low _We._ (**b**) Medium _We._ (**c**) High _We._