## 4 Conclusions  
Previous research into controlling droplet jumping through macrostructures has primarily emphasized the coalescence stage, with less exploration into how macrostructures affect the motion of a descending jumping droplet. Moreover, many studies focused mainly on the theoretical jumping direction perpendicular to the substrate, although the velocity in the horizontal direction must be involved in practical applications due to various scenarios. This study analyzed numerically the effect of the distribution in ridge structure's wettability on the performance of coalesced droplet jumping. The jumping dynamics were discussed for varying contact angle ratios and the aspect ratios of the ridge, which were the initial values for the current model. The influence of the ridge's wettability asymmetry on droplet coalescence jumping was numerically analyzed. In the current study, while varying the contact angle ratio and the geometric aspect ratio of the ridges, the maximum height of the jumping and horizontal offset distance were predicted. The results showed that at the lowest \(\beta\), there was approximately a 30% decrease in the height compared to the case with homogenous symmetric wettability. Furthermore, at the lowest \(\beta\), there was an approximately 2.7-fold increase in the offset distance compared to the case with weak  
Figure 7: Temporal evolution of averaged jumping velocities of the merged droplets in the \(z\) direction for varying \(\beta\). The snapshots of the insets represent the morphological behavior of the coalesced droplet in the \(yz\) plane at three distinct times.  
asymmetry (\(\beta\) = 0.84). Ensuring uniform wettability of the ridges seems to play a crucial role in efficient droplet transport.  
Changes in bounce magnitude and the trajectory of the droplet could be explained by the components of the horizontal and vertical average velocities. Particularly, significant velocity changes occurred around 10-15 ms, when droplets detached from the ridge surface during contraction. This change stemmed from the significantly higher receding velocity on ridges with low wettability surfaces compared to those with high wettability surfaces. As ridge wettability asymmetry increased, the maximum vertical velocity generally decreased. In this study, substantial variations in \(U_{y}\) were observed from \(\beta\) = 0.75 (i.e., \(\theta_{R}\) = 120\({}^{\circ}\)). Here, we could classify the region where the influence of surface wettability difference on jumping is significant (wettability-dependent regime) for \(\beta\) values lower than 0.75, and the other region, where the influence of surface wettability difference was less significant (wettability-independent regime), for \(\beta\) values greater than 0.75. This study is expected to contribute to efficient droplet rebound control in applications such as anti-icing/frosting [4; 5], enhanced heat transfer [6; 7], and energy harvesting [33].  
Future studies will involve examining the primary hurdle in the practical implementation of droplet coalescence jumping. Typical superhydrophobic structures face challenges related to mechanical durability and chemical stability, particularly concerning their micro/nanostructures. In addition, practical applications may require further exploration of droplet coalescence jumping across various droplet sizes by using measurements [34]. Lastly, the introduction of multiple droplets brings about greater diversity in their arrangement and characteristics, resulting in a more intricate process and phenomena of coalescence jumping. The multiple droplet coalescence jumping may have a significant influence on the jumping dynamics of the merged droplet.  
This work was supported by the National Research Foundation of Korea (NRF) grant, funded by the Korean government (MSIT) (No. 2022R1C1C1003711).  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The author declares no conflicts of interest.