## 3 Results and Discussion
### Bubble Motion
#### 3.1.2 Bubble Motion near an Elastic Cylinder with Different Tension Values  
A change in tension is achieved by adjusting the weight at the other end of the elastic cylinder. The weights used were 50 g, 100 g, 150 g, 200 g, 300 g, and 400 g. This section presents the bubble morphology images of different dimensionless distances \(\gamma\) under the  
Figure 4: Bubble morphology under the conditions of \(\gamma_{red}=0.064\), \(F=0.49\) N, (**a**) \(\gamma=0.24\), (**b**) \(\gamma=0.58\), and (**c**) \(\gamma=1.04\). conditions of 0.49 N, 1.96 N, and 3.92 N tension of the elastic cylinder. Figure 5 shows the bubble morphology at several typical dimensionless distances when the tension is 0.49 N and the dimensionless cylinder radius \(\gamma_{rad}=0.11\). For \(\gamma=0.36\), the bubble morphology is shown in Figure 5a. It is basically spherical during the expansion process. After it contacts the boundary at 0.48 ms, because the bubble wraps the elastic cylinder, the spherical radius of the bubble below is smaller than that of the normally growing bubble above. At 0.73 ms, after the bubble expands to its maximum size, it will wrap around the elastic cylinder and collapse, pulling the elastic cylinder to move in the direction of the collapse. The collapse speed of the bubble is greater than the movement speed of the elastic cylinder. In the late stage of bubble collapse, the bubble will separate from the elastic boundary. The bottom of the bubble will adhere to the elastic boundary, resulting in the bubble no longer being a regular sphere in the late stage of bubble collapse but a mushroom shape with different stem lengths, where the stem length is related to the dimensionless distance. Figure 5b shows the shape of the bubble when the distance is slightly long (\(\gamma=0.68\)). Since the boundary is elastic, during the expansion of the bubble, the bubble will push the elastic boundary to displace, so the bubble is basically spherical, with a slightly sharp shape at the bottom. During the collapse process, the boundary has attraction toward the bubble, and the bubble will produce a speed and acceleration opposite to that during expansion when it collapses, pulling the elastic boundary to displace. The side of the bubble far from the boundary remains spherical during the collapse process, while the side close to the boundary becomes sharp due to complex interactions, as shown in Figure 5b at 0.99 ms. Figure 5c shows the shape of the bubble at a slightly longer distance (\(\gamma=1.16\)). The bubble's expansion and collapse are both spherical, which is consistent with its movement in the free field. It can be seen that at this dimensionless distance, the elastic boundary has no effect on the shape of the bubble. Figures 6 and 7 show that under the same dimensionless cylinder radius experimental conditions, the tension of the elastic cylinder is changed. The maximum tension used was 3.92 N, and no elastic cylinder experiment with a larger tension was conducted. This is because the elastic cylinder will deform under a larger tension. This elongation will cause the thickness of the elastic cylinder, that is, the radius, to change. This invisibly increases the number of variables, making the experiment more complicated. The processing of the experimental data is also inaccurate. In comparing Figures 5-7, it can be found that under the tension conditions used in this study, the morphological changes in the bubbles are basically similar at typical dimensionless distances. When the bubble is close to the boundary, it make contact with the elastic cylinder. In the late expansion stage, the bubble no longer expands in a spherical shape and produces different collapse speeds during the collapse period, causing the jet phenomenon and the displacement of the elastic cylinder. When it is farther away, the spherical shape is maintained in the expansion stage; during the collapse, the elastic cylinder is attracted by the bubble and displaced in the direction of the collapse.