# Experimental Investigation on the Dynamic Characteristics of Bubble-in-Chain Near a Vertical Wall
## 4 Conclusions  
The experimental investigation focused on studying the motion of near-wall bubble-in-chain with three distinct generation frequencies using a two-camera orthogonal shadow method. Image processing and feature matching techniques were employed to track the motion of the bubble-in-chain. Various motion characteristics such as velocity, size, Reynolds number (Re), and Weber number (We) were determined for these bubbles. Additionally, this study has discussed statistical properties and analyzed motion modes while exploring the dynamic characteristics and energy evolution in detail.  
The results demonstrate that both the generation frequency and wall effect significantly influence the behavior of bubbles in a chain. Increasing the generation frequency leads to a more pronounced deviation of bubble trajectories from the wall, resulting in an amplified trajectory amplitude and weakened inhibitory effect of the wall on bubble velocity. It is worth noting that there is a particularly noticeable deviation in xz-plane bubble trajectories and an expanded distribution range for the trajectories in the yz plane. Additionally, with an increase in generation frequency, there is a slight increase in the equivalent diameter of bubbles. The rise in generation frequency intensifies changes in bubble shape and motion instability while partially disrupting periodicity, whereas the wall effect can regulate this periodicity.  
The drag coefficients of bubbles with different frequencies consistently decrease as the Reynolds number increases, and higher generation frequencies lead to a wider distribution range for drag coefficients. The wall effect has varying influences on bubbles with different migration modes: for non-colliding bubbles, the drag coefficient increases with greater distance; whereas for colliding bubbles, the drag coefficient decreases as the distance from the wall increases. The conversion of kinetic energy to surface energy during bubble-wall collisions plays a crucial role in determining the motion state. At high generation frequencies, bubbles exhibit more prominent peaks in surface energy, indicating an enhanced capacity for storing and converting energy efficiently.  
Conceptualization, R.C., J.S. and W.C.; methodology, R.C. and J.S.; software, R.C.; validation, R.C., J.S. and W.C.; formal analysis, R.C., J.S. and W.C.; investigation, R.C.; resources, J.S. and W.C.; data curation, R.C. and J.S.; writing--original draft preparation, R.C.; writing--review and editing, J.S.; visualization, R.C.; supervision, W.C.; project administration, W.C.; funding acquisition, J.S. and W.C. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by National Natural Science Foundation of China (11602077, 11572357) and Natural Science Foundation of Hebei Province, China (A2021202009).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data that support the finding of this study are available from the corresponding author upon reasonable request.  
**Conflicts of Interest:** The authors declare no conflicts of interest.