Bubble Velocity in Fluids
Name: Shihab K.
Date: Saturday, April 20, 2002 8:17:44 PM
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?
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
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
It will take a lot of careful reading.
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