There is some interesting research being done at Worcester Polytechnic Institute on how bubbles interact in a rising column.
By using DNS on the complex motions of a large number of bubbles, the researchers have shown that rising bubbles do follow some fundamental structure -- for spherical bubbles at least.
Spherical bubbles tend to rise in pairs, if one bubble is behind, following in the wake of another, it gets speeded up in the upward-moving wake, catches up, hits the top bubble, they tumble, and then both travel in horizontal alignment.
However, the shape of the bubble is dependent on the surface tension of the fluid.
"But as the surface tension drops and the bubbles flatten, this forces the flow to go around in a different way. The ellipsoidal bubbles become little winglets, and that changes the direction of the lift, completely reversing it so that it draws them into the faster moving fluid found in the wakes of passing bubbles. As a result, unlike spherical bubbles, flattened bubbles will sometimes stream together, following each other up in narrow columns,"
To do this, the researchers have developed a method for tracking the deforming bubble surface as a triangulated 2-D grid as it progresses across a fixed grid. This allows for the accurate simulation of 3D systems with a large number of bubbles over a long period of time.
In the future, the researchers hope to extend the model to include phase change and mass transfer as well as modeling fundamentally different bubble behavior, for example large single bubbles which can wobble and follow a spiraling pattern as they ascend.