The clustering morphology of freely rising deformable bubbles

We investigate the clustering morphology of a swarm of freely rising deformable bubbles. A three-dimensional Voronoï analysis enables us to distinguish quantitatively between two typical preferential clustering configurations: a regular lattice arrangement and irregular clustering. The bubble data are obtained from direct numerical simulations using the front-tracking method. It is found that the bubble deformation, represented by the aspect ratio ¿, plays a significant role in determining which type of clustering is realized: nearly spherical bubbles form a regular lattice arrangement, while more deformed bubbles show irregular clustering. Remarkably, this criterion for the clustering morphology holds for different diameters of the bubbles, surface tensions and viscosities of the liquid in the studied parameter regime. The mechanism of this clustering behaviour is most likely connected to the amount of vorticity generated at the bubble surfaces.