# Numerical Study on the Rising Motion of Bubbles near the Wall
## 3 Numerical Simulation Results
### Analysis of the Motion of Double Bubbles near the Wall
#### 3.2.2 Horizontally Arranged Rising Bubbles  
Horizontal arrangement with 2 times diameter spacing  
Figure 16 is a simulation of the upward motion of double bubbles arranged horizontally. The motion of the double bubble near the wall is similar to the motion of the free double bubble. The two bubbles separated first, then approached, and finally merged together. Compared with a single bubble, it can be found that the left bubble is not affected by the wall surface, and first deviates from the wall surface. Figure 14: Upward flow field diagram of double bubbles of different sizes near the wall at 110 ms: (**a**) Upper small and lower large, (**b**) Upper big and lower small. Figure 15: The rising shape of double bubbles of different sizes near the wall (upper large and lower small). Figure 17 shows the surrounding flow field distribution of two bubbles at 50 ms. At this time, the bubbles are beginning to move away from each other. When there is a single bubble near the wall, due to the influence of the left wall, the flow field on the left side of the fluid will flow closer to the left side of the bubble. The direction of the flow velocity is more the tangent direction of the left side of the bubble, and the flow velocity on the left will be faster than that of unbounded still water. As a result, the flow field at the bottom of the bubble forms a situation where the left side is less and the right side is more. In the case of double bubbles, it can be seen from the figure that two jets merge between the two bubbles, causing the two bubbles to have a fast flow velocity in the middle of the bubble and a slow flow velocity on both sides, thus forming a deflection of the two bubbles away from each other. The flow field on the left side of the left bubble is affected by the wall, and the flow field on the right side of the right bubble has no boundary. The bubble on the left will swing wider than the bubble on the right, and the overall path of the two bubbles will gradually deviate from the wall. (2) Double bubbles arranged horizontally at 3 times diameter spacing  
Figure 18 is the rising deformation diagram of the horizontally arranged double bubbles with the bubble spacing of 3 times the bubble diameter. It can be seen from the figure that the two bubbles did not coalesce, and the interaction between the bubbles became smaller due to the increase in the distance between the bubbles. So unlike the previous article, the bubbles are far away from each other, The left bubble also appeared to move away from the wall at 90 ms, and the left bubble came into contact with the wall  
Figure 16: The shape change of the rising double bubbles arranged vertically near the wall. Figure 17: The flow field distribution diagram of the horizontally arranged near-wall double bubbles at the initial stage of rise and after the coalescence: (**a**) Bubbles before merging, (**b**) The merged bubbles. at 500 ms. The rising form changes to bounce rising, and it is obvious that the left bubble rises faster at 850 ms. It is mutually corroborated with the conclusion of the bubble rising speed in the previous article. Figure 19 shows the flow field distribution of the bubble at 90 ms. It can be found that the deflection of the left bubble is slightly smaller than that of the right bubble. This is because the inducement of the deflection of the left bubble is that the influence of the wall surface is more obvious than the influence between the bubbles, and the jet formed on the wall promotes the deflection of the left bubble; The right bubble is the bubble deflection caused by the interaction between the bubbles, so compared with the two, the right bubble deflection is greater. (3) Double bubbles arranged horizontally at 4 times diameter spacing  
Figure 20 shows the rising deformation of horizontally arranged double bubbles with a bubble spacing of four times the diameter.