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Name: Nathan W.
Status: student
Age: 17
Location: N/A
Country: N/A
Date: 9/12/2004


Question:
I noticed while scuba diving that my larger exhaled air bubbles rose faster than my smaller ones. Obviously the buoyancy force must be greater on the larger bubbles, but surely they have greater resistance too. I am wondering what the relationship (if any) is between the size of a bubble and its rate of ascension.


Replies:
The buoyant force on a bubble is proportional to its volume, but the drag is proportional to its surface area. The ratio of volume to surface area of a bubble is 4/3*pi*r^3 / 4*pi*r^2 = r/3, so a large bubble will have a greater buoyant-force/drag ratio than a small bubble.

The exact relationship between size and rate of ascent will be pretty complicated, because drag forces are strongly dependent on speed.

Tim Mooney


The relationship between bubble size and rate of rising velocity is very complicated. It depends upon size, water purity, turbulence, the number of bubbles/volume present, and a host of other things. Roughly speaking the rising velocity increases with bubble radius -- about 0.03meters/second (m/s) for a bubble radius of 1x10^-4 (m) increasing to about 0.25m/s for a bubble radius of 6x10^-4(m), then decreases to about 0.2(m/s) at a radius of about 3x10^-3(m), then increases again back to about 0.25(m/s) at a bubble radius of 1x10^-2(m). This refers to the "terminal" velocities. How quickly a bubble attains its "terminal" velocity is a whole other problem. In some regimes bubbles that are too large break up, which raises a whole other set of problems. Bubbles can be spherical or mushroom shaped depending upon the various parameters. It is fair to say that such a simple problem as the rise of a bubble in a fluid is not well understood in general. It is under certain special conditions, but not in general.

See NEWTON BBS archive:

http://www.newton.dep.anl.gov/askasci/phy00/phy00505.htm for some more info and further reading.

Vince Calder


Hi,

Buoyancy is related to the volume of the object. Resistance (drag) is related to the frontal area. In the case of a sphere, these are proportional to R^3 and R^2, respectively. Buoyancy force wins out: bigger bubbles move faster.

Dr. Ali Khounsary
Argonne National Laboratory


Large bubbles flatten out as they try to rise fast. I'm not going to try to figure the net effect of that change, just now.

Small-to-medium bubbles stay roughly spherical in the water. Buoyancy force is proportional to volume, which goes as diameter cubed. Drag force at a given speed is proportional to frontal area, the area of a circle, which goes as diameter squared.

So, yes, as the diameter increases, buoyancy increases faster than drag, and speed will then increase until drag force is again equal to buoyancy force.

Drag in turbulent, fast, "mass-like", non-viscous liquids goes as the square of speed. So spherical bubbles will rise with speed proportional to the square-root of their diameter.

Extremely tiny bubbles may have a different power-law: speed linearly proportional to size. Most fluids tend to act viscous rather than inertial, at sufficiently small sizes.

Tiny dust falls slowly in the air, and tiny bubbles rise slowly in water. Same effect. Someday I must ask whether a 6-foot-tall skyjumper tends to overtake a 4-foot-tall skyjumper, before they open their chutes.

Jim Swenson



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