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

情况是，我们有一个气泡，里面有密度为p1的流体，周围环绕着密度为p2的流体。当气泡边界上的压差不同时，我们将观察气泡表面的稳定性。如果周围的流体压力大于气泡内部，则半径开始减小。如果能看到泡沫在这种压力变化下破裂，那将是一件有趣的事情。在稍后的项目中，我们的目标是包括其他有趣的效果，如旋转或添加边界。稳定性分析将与M.Plesset的论文[1]密切相关，后者用球谐函数描述气泡表面的稳定性。我们将能够利用物理系提供的磁铁实验室，潜在地验证通过实验模拟开发的理论。我们可以在磁孔内的大量液体中产生一个“悬浮”气泡。正是因为有了这个实验室，我们才能在不使用昂贵的太空方法的情况下进行这样的实验。研究这个问题可以更好地洞察空化气泡，这种气泡会对舰船上的螺旋桨叶片等结构造成破坏，并可能应用于惯性连接聚变。

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