Stability of a bubble containing fluid of different density to a surrounding fluid

The situation is that we have a bubble containing a fluid of density p1 surrounded by a fluid of
density p2. We will be looking at the stability of the bubble surface when the pressure difference
across the bubble boundary differs. If the surrounding fluid pressure is greater than the interior of
the bubble the radius starts to decrease. It would be interesting to see the bubble collapse under such
pressure changes. Later in the project we aim to include other interesting effects such as rotation
or added boundaries. The stability analysis will be closely related to M. Plesset's paper [1] which
describes the stability of a bubble surface using spherical harmonics. We will be able to potentially
verify the theory developed with experimental simulations by using the magnet lab provided by the
Physics department. We can create a 'levitating' bubble in a volume of liquid within the magnetic
bore. It is because of this laboratory that we are able to perform such experiments without using
expensive methods conducted in space. Looking at this problem could give a better insight into
cavitating bubbles which can cause damage to structures such as propeller blades on ships as well
as possible applications to inertial connement fusion.