THE PHYSICS OF BUBBLE RINGS AND OTHER DIVER'S EXHAUSTS

ABSTRACT
Dolphins and, more recently, scuba divers are able to blow ring shaped bubbles. This page describe the physics behind it.

Bubble rings

Figure 1 The bubble ring

Figure 2 Diver blowing bubble rings (photos: Wim Bakker)

The photographs above shows a diver blowing bubble rings. You can blow bubble rings performing the following steps:

• Squeeze your lips to a small orifice. Keep it closed though. Your lips should look like being ready for a kiss, though a light one (not that wet smacker of your mother in law...).
• Slightly increase the air pressure in your mouth.
• Now very quickly open and close your lips so they pop out a very small amount of air. Abrupt closing is essential. The air shall really pop out. When all goes right, the air will form a ring.
• Keep trying till you blow the nicest and smoothest rings and the dolphins are no longer ashamed of being a ring blowing mammal.

The photographs show various shapes of rings: small thick ones and large thin ones.

Refer to http://www.bubblerings.com for splendid photos and videos of bubble rings and even a bubble ring machine.

Dolphins and certain whales are known to blow bubble rings. Two ways of creating such rings have been reported: one way is by letting a ring out of their blow hole, the other by creating a water vortex ring and blowing air in the vortex ring.

Figure 3 Dolphin blowing bubble ring

The physics of bubbles

Bubbles in water

The bubble is the most stable situation for an amount of gas phase in water (liquid phase). A surface tension is associated with the surface between the gas phase and the liquid phase, the surface tension tends to minimize the surface area. This is also described in the section on bubbles in bubble models. Given a volume of gas, the sphere (bubble) shape is the shape that has the smallest surface area with respect to the containing volume.

The situation of a bubble in water is comparable to a balloon. The balloon surface is elastic. The tension of it tries to minimize the surface: if you don't tie a knot in the balloon after blowing it up, air escapes and the surface of the balloon is minimized to the initial unstretched situation.

Distorting the bubble to any other shape enlarges the surface area. Force has to be exerted to the bubble to distort its shape.

The ratio between surface area and enclosed volume is not constant. Surface area A increases with the square of the radius r of the bubble (sphere)

Volume V of the bubble increases with r to the third power:

V  =   4 3  π r 3

(2)

The ratio of surface area and volume is proportional to 1/r. This means a large bubble has less surface compared to its volume (equally, it is wiser to buy large apples if you don't eat the skin: you eat more apple per kg of apples bought in that case).

So the bubble shape is most stable situation for an amount of gas in water, like the diver's exhaust air. However, this only applies in a static situation. When Archimedes comes in and bubbles start to float and move to the water surface. The bubble shape is distorted by the flow of air and surrounding water. Bubble movement and velocity is quite complicated to describe.

Small bubbles

Small bubbles are bubbles with a diameter of a millimeter or below. These bubbles are spherical. When the bubble moves upward with continuous velocity (steady state), the forces on the bubble cancel out. The forces are:

• Weight of the bubble F_W, pointing down
• Archimedes force F_A, pointing up
• Drag force F_D, pointing down

The drag force acting on the bubble is given by Stokes Law:

F_D

Drag force (pointing down)

ν

Viscosity of the fluid (water)

v

Velocity of the bubble

r

Radius of the bubble

The net force is

6 π ν v r +  4 3  π g r 3  ( ρ air - ρ water )   =  0

v  =   2 g  ( ρ water - ρ air )  9 ν  r 2

(4)

Velocity is proportional to the square of the bubble radius.

For larger bubbles than approximately 1 millimeter, bubbles are no longer perfectly spherical. Shapes and trajectories start to oscillate: bubbles become ellipsoidal. Bubble rising speed is constant and about 25 cm/second.

Large bubbles

Large bubbles are bubbles with an diameter of 10 cm and larger. These bubbles are quite popular amongst starting divers that are not fully capable of controlling breathing.

Surface tension is proportional to 1/r. Surface tension is the force that keeps bubble in shape. The larger the surface tension, the more force has to be applied to the bubble to distort the shape. For larger bubbles surface tension is weaker. Bubbles are more floppy. On the other hand, volume is relatively larger (as we have seen, ration between surface and volume is proportional to 1/r). Hence Archimedes force is relatively larger on large bubbles. This results in the bubble shape getting distorted, since a sphere is not the most economical shape in a flow situation.

For large bubbles, flow is turbulent. Shapes end up in mushroom shapes, heavily oscilating.

The physics of bubble rings

Bubbles do not turn into rings naturally. Something has to be done for that. However, they have long lives and often make it up to the surface. Hence they are stable structures.

How bubble rings are created

Bubble rings are an example of vortex rings. Other vortex rings are smoke rings blown by the experienced smoker.

There are few ways on how bubble rings can be created:

1. Rings can be created by letting air escape through an orifice that is opened and closed abruptly. A bubble-blowing diver falls in this category.
2. Rings can be created by letting a fixed amount of air escape through an orifice that is permanently opened. The bubble machine of David Whiteis falls in this category
3. Dolphins create bubble rings by blowing air in a water vortex ring: by flipping a fin they create a vortex ring of water. The then blow air in the ring, which goes to the center of the vortex ring. In the water vortex ring the natural location of the air is in the center of the vortex. When air and water move in a circular path like they do in the vortex ring, air and water are separated due to the centripetal force. Since density of water is larger than air, water moves at the outside, while the air ends up in the middle.

In this article we stick to creating bubble rings by letting air escape through an orifice. I think there is no big difference in the creation process between type 1 and type 2 bubble rings. The photographs below show the phases in the creation of type 2 bubble rings. The sequences were taken as separate photos of more bubble rings. Hence the time scale might not be linear. The sequence only covers a fraction of a second (in fact I had to take about 200 photographs to end up with the sequence below. Most photos were to early or to late)

The following steps are visible in the photo sequence:

1. The air starts to escape through the orifice
2. Air keeps flowing into the bubble. The bubble grows. Water is pushed aside and because the bubble moves up, the water starts moving down.
3. Air keeps flowing into the bubble. Air starts flowing to the sides. The upward motion of the bubble is dampened by the water. Therefor the bubble is squashed and becomes flattened.
4. The velocity of air flowing into the bubble increases since the entrance is surrounded by air now instead of water. When the bubble grows larger, it becomes easier to grow. The larger the bubble, the smaller the surface tension. Air starts accelerating trough the orifice. Due to upward flow through the orifice hitting the upper side of the bubble the bubble bulges out at the upper side due to the air flow. Air start to circulate in the bubble.
5. The entering air starts to drag water with it into the bubble. The in flowing air is surrounded by a fountain of water. The bubble is now mushroom shaped, like the atomic bomb explosion mushroom. (stated otherwise: atomic bombs might possibly be used to blow Guiness Book of Records bubble rings)
6. More water is dragged into the bubble. The fountain increases.
7. The airflow is finished. The bubble is now free of the orifice. Due to the momentum of flowing air and water, more water is now sucked into the bubble.
8. More water enters the center of the bubble. The bubble moves upward.
9. Due to the momentum, the water now breaks through the top of the bubble. The breaking through s fairly explosive, expelling small bubbles of air.
10. The vortex movement is now complete. Due to the centripetal forces the expelled air is re-centered.
11. All the air is now re-centered and the bubble has become a nice smooth ring.
12. The bubble ring continues it movement upward towards the sunshine

Figure 5 above shows another sequence showing the constiction of the mushroom stem ending up in water entering the bubble. The breaking through is clearly visible in the right most picture: small air bubbles are expelled.

Figure 6 Close-up of the water entering the bubble

In Figure 6 beside a close-up is shown of the stage when water gets dragged into the bubble. Clearly visible is the airflow from the orifice into the bubble (the stem of the mushroom). Water is dragged from the side by this flow into the bubble. The beginning of break-through is visible at the top of the bubble. The moment of break-through varies per bubble.

How bubble rings evolve

Bubble rings have long lives. After creation they usually end up at the surface. The ring bubble experiences an upward Archimedes force which makes the bubble float and move upward. When moving upward water flows outside along and through the bubble (actually the water does not flow but the bubble does). This is shown in Figure 7. The water flowing outside along the bubble flows in the direction of the vortex flow. Hence, this flowing enhances the vortex movement. The water flowing through the ring flows in the opposite direction to the vortex flow. The water flow slackens the vortex movement. However the frontal area of the outside part (blue part in Figure 7) of the ring is larger than the inside part (red part in Figure 7). Hence the net effect of the water flow on the vortex movement is positive. This net effect keeps the vortex moving.

Figure 7 Bubblering moving upward

The outer frontal area of a bubble ring with radius r and thickness d is

A outer  =  π     r +  d 2     2  - π r 2  =  π     r d +  d 2 4

(5)

Similar, the inner area is:

A inner  =  π r 2 - π     r -  d 2     2   =  π     r d -  d 2 4

(6)

The difference in area is

A diff  =  A outer - A inner  =  π     r d +  d 2 4     - π     r d -  d 2 4      =   π d 2 2

(7)

Assuming the net force affecting (driving) the vortex movement is proportional to to the difference in area, this means the driving force is proportional to the thickness of the bubblering.

Gallery