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Name: Shihab K.
Status: student
Age: 17
Location: N/A
Country: N/A
Date: Saturday, April 20, 2002 8:17:44 PM


Question:
what is the relationship between size of a bubble traveling up in a liquid and the speed of the bubble. and the relationship between viscosity of the liquid and the speed of the bubble. as the bubbles rise there size increases due to pressure loss how can i find the difference in the size of the bubbles as they rise?


Replies:
There are relationships governing these, and I have run into them before. You can look them up in text books on "boiling heat transfer." For example, please see the boiling section in

Handbook of Heat Transfer Fundamentals, ed. WM Rohsenow, JP Hartnet and EN Ganic, McGraw-Hill, New York, 1985.

Ali Khounsary, Ph.D.
Argonne National Laboratory


The relationship between the size of a bubble (air) traveling up in a liquid (water)and the speed of the bubble is VERY COMPLICATED. Here are some of the factors that have to be taken into account [ in no particular order]:

1. The presence of surface active impurities, which accumulate at the surface of the air/water interface and "lubricate" the rise of the bubble increasing its speed. These surface active impurities are not necessarily uniformly distributed at the interface either. They tend to accumulate at the lower end of the rising bubble.

2. The size of the bubble.

3. The viscosity of the continuous phase, in this case water.

4. The Reynold's number, Re, of the bubble: Re = (Dv)*(Ut)*(r)/(m), where: Dv = [(6)*(V)/(pi)]^1/3 where V = volumetric rate of flow, and has dimensions, m^3/sec. (Ut) = the terminal speed of the bubble, meters/sec. (r) = density of the continuous phase (water). And (m) = viscosity of the continuous phase. As the value of Re increases in various ranges, the shape of the bubble will change from a sphere with no circulation, a sphere with the air circulating due to drag at the air/water interface, and oblate spheroid, to an irregular mushroom-shape.

And the equations of motion of the rise are solved numerically.

See the book "Viscous Flows -- The Practical Use of Theory" by S. W. Churchill, especially chapter 17, to see just how messy the problem's solution is. It will take a lot of careful reading.

Vince Calder



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