# Can an air bubble in a liquid be faster than its terminal velocity

The title says it pretty much. I am wondering if an air bubble in a liquid can move faster (relative to the surrounding liquid) than its terminal velocity?

• By definition terminal velocity means that no higher velocity will occur. A gas bubble rising against gravity in a fluid, if given enough time will reach a dynamic equilibrium, the terminal velocity. If you want to change the velocity, you have to either change the liquid, the gas, or gravity. Feb 10, 2015 at 20:50
• @docscience - By definition terminal velocity means that no higher velocity will occur. That's not true. Terminal velocity is the velocity at a object that is falling vertically experiences zero net force. An object falling faster (through the air) than terminal velocity will slow down, an object falling slower than terminal velocity will speed up. An air bubble moving faster than its terminal velocity won't last long. Instead of slowing down, it most likely will break up into smaller air bubbles. Feb 10, 2015 at 21:52
• Bullets or other massive objects (denser than the surrounding fluid) frequently travel faster than their terminal velocity. Consequently, they will slow down to their terminal velocity when no forces other than gravity and drag act. Feb 11, 2015 at 8:59
• The reason I ask is, I would like to know if there are situations in which bubbles are faster than their terminal velocity. You can't grab them and accelerate like a ball. Feb 11, 2015 at 9:01
• @Dohn Joe right, there's another force to consider as David Hammen referred to with regards to the bubbles breaking apart -surface tension. Pulling or pushing will likely shear the bubble rather than speed it's progress. Like nailing jelly to a tree. Feb 11, 2015 at 20:15

## 1 Answer

Terminal velocity by definition means the zero acceleration condition for the bubble. It won't get faster or slower unless a property of the system which affects the terminal velocity changes.

Because the air bubble rising also means that liquid is falling, the terminal velocity depends on the viscosity of the fluid, the gravitational field, the size of the bubble and any restrictions in the path of the bubble. If the bubble reaches a spot in the fluid where the viscosity changes, the bubble may move faster or slower.

A very interesting experiment is the speed of an air bubble in hydraulic fluid in a tube. When the tube is inverted, the bubble quickly reaches terminal velocity for its conditions and the speed can be measured. The terminal speed is strongly dependent not only on the temperature but also the angle the tube is held after inversion. The maximum speed is close to 45 degrees (which would seem reasonable) but experimentally isn't exactly that. Also, at not vertical angles the bubble takes on odd shapes, especially near its fastest speed. The trailing edge of the bubble has a small curl (or depression) in it.

Various science equipment vendors stock these tubes.

• Changes in total fluid pressure can also affect the terminal velocity as the bubble will either shrink or expand in size. This decreases or increases the buoyant force, but also shrinks or enlarges the projected area respectively considering the opposing drag force. Feb 10, 2015 at 22:05