A numerical study on the clustering characteristics of rising air bubbles in stagnant water

We perform numerical simulations of rising air bubbles in stagnant water to investigate their clustering characteristics. Monodispersed rising bubbles are simulated in a periodic computational box for three cases of bubble equivalent diameters ($d_{eq}=0.5,1$ and 1.5 mm), respectively. The bubble cluster is identified based on an inter-bubble-distance criterion (Ma et al., 2023) and its characteristics is analyzed. Initially, the bubbles are uniformly distributed throughout the domain. The bubbles with $d_{eq}=0.5\mathrm{mm}$ retain their initial distribution, while those with $d_{eq}=1$ and 1.5 mm interact among themselves, leading to clustering. For the larger bubbles ($d_{eq}=1$ and 1.5 mm), simulations with a small horizontal domain size result in a stable formation of domain-full horizontal bubble clustering. However, when the horizontal domain size is sufficiently large, such clustering no longer occurs, but local sheet-like clustering, aligned nearly parallel to the horizontal direction, occurs. During bubble collision and bouncing-off, a counter-rotating vortex pair is generated and induces a downward velocity on the bubbles, which decreases their rising velocity and keeps the bubbles horizontally aligned.