Modelling of bubble merging submerge on water

Carlos

Hi everyone, Can anyone please tell me about mathematical models which allows to compute (numerically) the dynamic of a creation, growth an detachment of an air bubble submerged into water?

This is the situation:

1-a circular cavity half-filled with water (water on bottom, air on top)

2-a little inyection zone placed at -135 degrees (relative to the center of the cavity, and clockwise), under the water zone.

3-Isothermal regime. Merging only due to density differences

4-fluid (water) incompressible.

I would like to solve this problem numerically with the Finite Element Method, but I have some trouble in the modelling. The litterature shows many different models, someone with only the rising, others with the cavity filled with water. Anywhere, these references are not so clear for me. Can anyone help a little on this "bubbly" subject?

Many thanks in advance

Carlos