Axisymmetric and three-dimensional boundary integral simulations of bubble growth from an underwater orifice

The formation of bubbles from an underwater orifice is studied by means of a boundary integral method. Since the bubble process is highly transient the flow field is assumed to be irrotational. A potential-flow boundary-integral formulation is employed to simulate the growth of a bubble from a needle in an unbounded domain and in a tube. The geometry of the problem is axisymmetric in these cases. A good agreement is found between the simulations and the experiment for air bubbles of radii ranging from a few hundred microns to several millimeters in water. A three-dimensional boundary integral method is developed to simulate bubble detachment from a non-vertical needle in an unbounded domain. Numerical instabilities commonly associated with the boundary integral technique are found to be even more severe for the three dimensional case and therefore an artificial damping term is introduced to eliminate these instabilities. Even though the simulations often fail just before the pinchoff point, the results compare favorably with the experiment.