## 3 Results and Discussion
### Evaluation of Bubble Generation for Various Types of Electrodes  
When reactions occur at the electrode, gas bubbles are generated at the electrode surface, as represented by Equations (2) and (4). The generated bubbles are subject to buoyancy force (\(F_{b}\)) and surface tension (\(F_{\varphi}\)) at the electrode, and the buoyancy force can be expressed using Equations (5) and (6) (Figure 4a,b) [52]:  
\[F_{b}=\frac{4}{3}\pi\left(\rho_{liquid}-\rho_{gas}\right)gr^{3} \tag{5}\]  
Figure 3: Bubble generation for (**a**) aluminum, (**b**) titanium, and (**c**) copper electrodes; (**d**) comparison of bubble production rates across materials. \[F_{\sigma}=p\sigma sin\theta \tag{6}\]  
where \(\rho_{liquid}\) is the liquid density of the electrolyte, \(\rho_{gas}\) is the gas density, \(g\) is gravitational acceleration, and \(r\) is the radius of the bubble. \(p\) is the length of the contact line and \(\sigma\) is the dynamic surface tension between the bubble and the electrode surface. When surface tension exceeds buoyancy, larger bubbles are formed, and the buoyancy force increases. Once the buoyancy force surpasses surface tension, the bubbles detach from the electrode surface into the solution. The larger bubble size observed with the titanium electrode (Figure 3) is attributed to the higher surface tension (\(\sigma\)) of titanium (Ti > Cu > Al) compared to other materials [53; 54; 55]. According to Equation (6), on a pristine surface, where the contact angle \(\theta\) is 90\({}^{\circ}\), the maximum cohesive force acts on the bubbles, resulting in the formation of larger bubbles. When bubbles form on the electrode surface, no reaction occurs in the area covered by the bubbles, which negatively affects electrode efficiency. Therefore, the generation of large bubbles can hinder the electrode's overall performance. In contrast, when micro-nano structures are present on the electrode surface, the value of \(\theta\) changes, reducing the cohesive force and promoting the consistent formation of smaller bubbles. The continuous release of fine bubbles ensures that the electrolyte infiltrates the electrode surface, allowing for further reactions and enhancing the overall efficiency. Additionally, the use of micro-nano structures increases the surface area of the electrode, providing more active sites for reactions compared to a pristine surface (Figure 4c,d). Based on this theoretical framework, we investigated the effect of surface structures on bubble size and distribution by fabricating four types of aluminum electrodes: Plate-Pristine (PP), Plate-Micro/Nano (PMN), Mesh-Pristine (MP), and Mesh-Micro/Nano (MMN). Mesh electrodes were chosen because they offer a simple method to increase surface area. The surface morphology of the fabricated electrodes was examined using Scanning Electron Microscopy (SEM) to confirm the successful formation of the micro/nano structures (Figure 5). In particular, the interfacial bonds between the micro/nano structures and substrates consist of hydrogen bonding with the hydroxyl groups, which leads to a condensation reaction and covalent bonding to the substrate. This chemical treatment ensures improved durability and stability, as demonstrated in previous studies [37; 38; 39; 40; 41]. Figure 4: Schematic force diagram and generation of bubble on (**a,c**) pristine and (**b,d**) micro-nano structured surface. To assess the effect of surface structures on bubble generation, the macroscopic process of bubble generation during electrolysis was observed using a high-speed camera, and the size and distribution of bubbles were evaluated using optical instruments under identical experimental conditions (Figure 6). Figure 6a,b show images of bubbles generated by the MP and MMN electrodes, respectively. In the MP electrode, large bubbles visible to the naked eye predominantly formed. In contrast, the MMN electrode exhibited very few visible bubbles, with most bubbles appearing as a mist due to their significantly smaller size.