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Old Jun 19th 2014, 08:37 AM   #1
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Fluids Displacement Help

Hi all,

I was wondering if you guys can help me with the physics of this scenario. Let's consider a tube with two immiscible fluids of equal volume, separated by a barrier. The bottom of the tube contains the lighter fluid, fluid A while the top has a heavier fluid, fluid B. At time t = 0, we remove the barrier. Describe the physics of the process. You can make any other necessary assumptions. (The only force acting is gravity, no external forces applied, and the tube is positioned vertical)

Eventually, the heavier fluid will displace the lighter fluid, at time t>>0. How will the process occur immediately following the removal of the barrier though. What kind of forces act on the system. Please help, also if you can find a similar study on this scenario, please share!! I have found several studies done using porous media, etc. but can't find a study that simply studies the phenomenon in a tube/pipe. Thanks in advance for your input!
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Old Jun 19th 2014, 09:12 AM   #2
MBW
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If you had a "perfect" situation:
where the barrier is removed without disturbing the fluids
and there are no other external disturbances of any kind
then nothing will happen.
The heavy liquid will stay on top of the light one.

While this might be statically stable, it is obviously dynamically unstable,
any slight disturbance of the balance such that one portion of the heavy fluid is lower than the rest
(and thus a portion of the lighter fluid is higher than the rest)
will cause bouyancy forces to pull the low portion of the heavy fluid even further down,
and push the raised portion of the light fluid even further up.
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Old Jun 20th 2014, 06:20 AM   #3
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Originally Posted by MBW View Post
If you had a "perfect" situation:
where the barrier is removed without disturbing the fluids
and there are no other external disturbances of any kind
then nothing will happen.
The heavy liquid will stay on top of the light one.

While this might be statically stable, it is obviously dynamically unstable,
any slight disturbance of the balance such that one portion of the heavy fluid is lower than the rest
(and thus a portion of the lighter fluid is higher than the rest)
will cause bouyancy forces to pull the low portion of the heavy fluid even further down,
and push the raised portion of the light fluid even further up.

Why would the heavy liquid stay on top in a "perfect" situation? Wouldn't the forces acting on the fluids (weight of the fluid and gravity) drive the heavier molecules downward and then the buoyancy effect driving the lighter fluid upwards? Thanks for the reply! Also, do you know of any studies related to this scenario? Can you direct me towards them, studies with a model of the situation, perhaps?
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Old Jun 20th 2014, 09:37 AM   #4
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Upon doing some further research, I actually think I have found the phenomenon explained well by the Rayleigh-Taylor instability theory. I found literature explaining the phenomenon, http://www.maths.bris.ac.uk/~marrk/paper_SKM

Thanks for your help MBW and you're right as that in a "perfect" situation, the heavier fluid will stay atop the lighter fluid, but any disturbance would cause the movement in fluids and a displacement of the heavier fluid to the bottom while pushing the lighter fluid on top.
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