# How does a rising bubble take a dome-like shape?

Since I have swam on the swim team for most of my life, I am very familiar with bubbles. I know a raindrop falling through the sky gets its shape because it is the most aerodynamic shape, but how come a bubble rising through water has a different, rather jellyfish-like or dome shape? is an example of what I am referencing. (As a side note, I have found this property to be shown mostly in larger bubbles.)

• Have a look at this article from Nature and in particular figure 1. Sadly the full article is behind a paywall. – John Rennie Dec 1 '15 at 7:59
• No, raindrops do not take an aerodynamic shape. They wobble and jiggle due to complicated interactions with local atmospheric phenomenon (and their shape history). – Carl Witthoft Dec 1 '15 at 15:28
• @JohnRennie thank you, that was a great article. It looks like this is a public pre-print – New Alexandria Dec 8 '15 at 0:25

As the bubble rises it pushes the water above it out of the way, so we get a water flow created around the bubble. With a large bubble the flow velocities will be relatively high because a large bubble has to push aside a large volume of water.

Water flowing around a bubble will pull it out of shape. the obvious simple example is a bubble in a shear flow, that gets pulled out into an ellipsoid:

For a bubble rising through water the flow is going to be complicated and there is no simple way to calculate it. We have to reach for a finite element analysis program and a large computer. I did some Googling and managed to find this paper reporting calculations of this type$^1$. If you look at for example figure 3 in the paper it shows the hemisphere bubble shape that you show in your photo.

The trouble with the computer modelling is that it can be hard to get an intuitive feel for what is going on, so I've attempted to draw my own diagram of how the bubble is pulled out of shape by the water flow:

You shouldn't take this too literally as it's just an illustration of the flow. The arrows show the water flow, and how it pulls the bubble out of shape. There are more detailed (if more confusing!) diagras of the flow in figure 15 of the paper I have linked.

$^1$ Jinsong Hua and Jing Lou, Numerical simulation of bubble rising in viscous liquid, Journal of Computational Physics 222 (2007) 769–795

• Your answer talks about the cause, without elaborating on the principle, which defines the phenomenon. It's like introducing the concept of friction, without taking the time to distinguish between static and kinetic friction. An oversimplification of a complex process, isn't exactly the way forward, right? – Garvit Sharma Dec 1 '15 at 16:45
• Minor comment to the post (v1): Please consider to mention explicitly author, title, etc. of link, so it is possible to reconstruct link in case of link rot. – Qmechanic Dec 8 '15 at 1:40

The bubble maintains a spherical shape, because of surface tension, which I am sure you are aware of. It does so , because it wants to store maximum volume of the fluid involved, using minimum surface area, which can be done using a spherical shape. Thus, the layer of the bubble acts like a stretched membrane. When the pressure inside the bubble, for whatever reason, increases more than what the surface tension can balance, it breaks apart into a semi-spherical, or dome like structure. Now, even though it is not a complete bubble, it still has surface tension, and thus possesses some concavity.

The reason behind the bubble's desire to minimise it's surface area, is that all objects want to stay at the lowest energy possible. When you increase the surface area of the bubble, you increase the number of particles being affected by adhesive forces of the surrounding, and thus increasing it's energy( surface potential energy).

• I don't see how this answers the question. The "bowl" shape is going to be some balance between surface tension and the hydrodynamic forces created as the bubble rises. – John Rennie Dec 1 '15 at 7:56
• @JohnRennie If you read the last line of the first paragraph, you might just learn something. – Garvit Sharma Dec 1 '15 at 7:59
• @Garvit: It isn't obvious to me how your first paragraph's conclusion follows from its predicates. – RedGrittyBrick Dec 1 '15 at 10:29
• @RedGrittyBrick The first paragraph talks about the reason behind the spherical shape, i.e., surface tension. The last line suggests that there isn't sufficient surface tension to balance the external pressure, hence it's shape changes. But, since surface tension still acts, we continue to see an incomplete spherical shape. My answer is a direct answer to why do bubbles get their spherical shape and not any other. – Garvit Sharma Dec 1 '15 at 16:36
• I find this answer to lack directness, too. Sorry. Probably you are being too generalistic — i.e. a bubble does not maintain spherical shape under all situations, so you cannot lead with that 'bare' assertion. – New Alexandria Dec 7 '15 at 23:42