# Experimental Investigation on the Dynamic Characteristics of Bubble-in-Chain Near a Vertical Wall
## 3 Results
### Motion Mode of the Bubble-in-Chain
The bubble generation frequency of (**a**) is \(F1\), that of (**b**) is \(F2\), and that of (**c**) is \(F3\). The initial wall distance is \(L1\). significant changes in their aspect ratios, suggesting that the high generation frequency itself can induce substantial alterations in bubble shape. Figure 9 illustrates the variation in the velocity component of bubbles with rising height under different initial wall distances, wherein the velocity and height data have been normalized using the equivalent radius of bubbles and the average velocity (\(z^{*}=z/r_{eq}\), \(V_{x}*=V_{x}/\overline{V_{b}}\), \(V_{y}*=V_{y}/\overline{V_{b}}\), \(V_{z}*=V_{z}/\overline{V_{b}}\)). In the scenario where bubbles collide with the wall, the velocity components along the x-axis and z-axis (\(V_{x}\) and \(V_{z}\)) exhibit periodic variations akin to those observed in a single bubble, with their extremum positions closely aligned. However, the wall-normal velocity component \(V_{y}\) also demonstrates a corresponding relationship; nevertheless, its fluctuations are more pronounced, thereby slightly disrupting its regularity. When the bubble does not collide with the wall, the velocity component \(V_{z}\) becomes more stable and no longer exhibits obvious periodicity. However, \(V_{x}\) and \(V_{y}\) continue to show periodic variations, but their changing trends are not synchronized and there is a fixed phase difference. It is worth noting that even when there is no collision, \(V_{z}\) displays quasi-periodic oscillations at an initial wall distance of \(L3\). This indicates that the influence of the initial wall distance on bubble motion is complex and can cause changes in velocity components even without collisions. Figure 10 illustrates the variation of bubble velocity components with height at different generation frequencies. Irrespective of the generation frequency, when bubbles collide with the wall, the velocity components exhibit periodic changes, and the extreme points of different velocity components are closely aligned. However, in cases where bubbles do not collide with the wall, there is no longer consistency in the extreme positions of velocity components and a weakening of \(V_{z}\)'s periodic characteristics can be observed. This suggests that collision processes regulate the periodic features of bubble velocities and synchronize extreme points across different velocity components. As the generation frequency increases, particularly reaching \(F3\), there is a disruption in the periodicity of bubble velocity components to some extent, indicating heightened instability in bubble motion at high frequencies. This instability may arise from complex interactions between bubbles as well as between bubbles and their surroundings, resulting in more intricate and unpredictable variations in velocity components. Figure 8: The relationship between the aspect ratio of bubbles with different generation frequencies and the Weber number. (**a**) The bubbles collide with the wall, (**b**) The bubbles do not collide with the wall.