The Inverted Whirlpool Paradox

The tea leaf paradox explained. A spinning vortex and cause liquids to seemingly defy gravity

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[SteveMould]

One of those rare occasions where fluid dynamics makes sense!

[Viniter]

It would be interesting to see what would happen if you had three different liquids with different densities. The bottom layer would surely bulge up, but what would the boundary between the middle and top layer look like?

[sol_in.victus]

When we were kids our grandma's house had a circular pool, and when we were done playing late in the afternoon, me and all of my cousins would run in circles on the edge of the pool to Form a whirlpool, and all the dirt would bunch up in the middle making it easier to clean.

As a kid I always thought it unintuitive so this explanation was pretty interesting.

[adamhester]

"The fluid on the bottom is water. I've dyed it brown, fittingly, with tea leaves."
I hate to break it to you Steve, but you've just made tea.

[scheimong]

That genuine excitement from your kids is possibly the most compelling marketing I've ever seen.

[VeeloBird]

I haven't seen anyone mention this, but this video is probably the most comprehensive explanation of how Hilsch vortex tubes work from a fluid dynamics perspective. It's a shame that they are widely accepted as black magic, but a simple demonstration like the one you did with the liquids helps immensely in understanding the actual mechanics behind what's happening. Although there are a few differences, and you also have to account for pressure, the working principle is the same.
Amazing video! Thank you, Steve, for making the internet better!

[Nobody_is_my_name]

While the majority of what you describe here makes good sense, it also overlooks a fundamental reason this exists.
I learned about this when I was in school studying atmospheric physics in the Navy.
First of all, the pressure gradient you are describing and showing is accurate, water column depth is directly proportional to the "weight" of the column when measured at the bottom, but likely will not be the primary driver behind this phenomenon. If it were, then you should be able to set up a flat wave tank with the same different densities of liquid and see inverted wave patterns in the more dense liquid than in the lighter top liquid. I suspect you won't.
Secondly, you can observe in your videos portions where the vortex depth of the lighter liquid is nearly nil, yet the bulge height of the more dense liquid in the bottom doesn't diminish proportionally.
These observations alone should give anyone pause when considering the pressure gradient as the primary cause of this phenomenon.
Now lets consider what happens to a contained fluid in motion.
When you stir your cup of water, as you note, inertia wants the water/fluid to travel in a straight line, but because there is a physical barrier the fluid must turn. Starting at the glass, pressures build up to a peak from the SIDE of the glass, not from the height of the fluid. The real culprit of pressure related causes here is not the height of the fluid but instead the "traffic jam" of molecules being forced to follow the path of the curved glass, so that pressures near the glass are much higher than the pressure at the center of the glass because of this.(although, while there is a 'funnel' in the center of the vortex, there technically is a difference in 'column weight', but the resulting pressure gradient would not be enough to overcome or balance with the fluid inertia).
Even in an open body of water, such as an ocean we can see this horizontal pressure gradient have substantial impacts to fluid. In the Ocean, as you probably know, there exist eddy currents where for whatever reason (orographic disturbances, speed gradients, etc) closed circulations of water form. The same fundamental thing occurs where the area of max speed around the circulation is generally the highest pressures, despite the actual height difference of the water within the circulation compared to say, the center, is practically nil. And whatever difference that may exist there is certainly "washed out" by wind and swell wave features that move across the circulation. Now, in open ocean eddy currents, you get into other things that effect water density, such as temperature and salinity, where you can end up with a warm core eddy or a cold core eddy as those circulations become 'cut off' from the surrounding waters, but I digress.
Love the video, and I don't intend to be a muck raker, I just hope that you could better explain where the source of the pressure gradient that causes this comes from. Again, it is not the height difference of the less dense liquid, but instead the pressure gradient caused by the lateral motion of the water.
Cheers!
-A

[BrettBernier]

Used to do this as kids to make cleaning above-ground pools easier. Send the kids into the pool and do 20-30 laps, all the leaves and debris gathers in the middle.

[RobertMilesAI]

Experiment: Try a vessel with a very smooth bottom surface vs one with a very rough bottom surface. Like, sandblast the bottom of the flask or glue down some sandpaper. Rougher surface should mean more drag so a bigger effect

[joseph_soseph]

If I'm not mistaken, this effect doesn't have anything to do with density at all. It's just pressure and drag, so it also occurs if you only have water in the container, but you can't see it happening. That made the tea leave paradox look even more like magic to me. I'm glad I now know how it works

[rizowski]

The two fluids interacting with each other is so mesmerizing to watch.

[oregonboy]

I'm constantly amazed at the explanations you choose to give that I must have witnessed 1000x in my daily life but never questioned. Then, on top of that, you make it SO INTERESTING and easy to understand! Keep up the amazing work Steve.

[tagno]

9:24 It may have more do do with which liquid is primarily being stirred, not the horizontal stirring location.

I wonder if you had three liquids would you see the effect once, or twice. Or if you could get two liquids with different densities, but the same viscosity, what would happen?

[Mint_Robot]

Another nice video! I agree that "inverted whirlpool paradox" sounds much cooler than "tea leaf paradox".

7:20 The critical mechanism for this phenomenon is the drag from the bottom of the container.

I would explain it this way:

Only the heaviest liquid is in contact with the entire surface at the bottom of the container, which provides an exceptional amount of drag, lowering the moment of inertia for the heavier liquid as a whole. Since the lighter liquid does not experience as much drag, it has a higher rotational inertia, and it displaces some of the heavier liquid near the edges of the container.


So at 9:15 when the experiment was to use a magnetic stirrer at the bottom of the container I was certain that the inverted whirlpool paradox would not be present. Since the stirring action is coming from the bottom of the container, the rotational velocity of the heavier liquid would NOT be lower than that of the lighter liquid, and thus the whirlpool would be regular and not inverted.

[johnmcclain]

I've observed this for almost sixty years, as a mechanic, I never realized the questionable behavior, perhaps because I've never seen it behave any other way. This makes sense, it falls exactly in line with the rest of my physics experience. Thanks for making this video, very interesting, informative.

[scottleepeters]

Hey man, I've been watching your videos for many years. I'm an HVAC tech. I've never had formal training, but you and other channels like you taught me to analyze things on a fundamental energy transfer level. It seems like it should be obvious, but now I'm spending the slower months traveling across Texas teaching a 2 day class for my distributor to help other techs. This kind of stuff makes a real difference, even if we don't notice it all the time. Thank you!

[aidanclark]

It's amazing how I was stumped over this solution until you said 'when the container itself isn't spinning' and I got a bolt if lightning and suddenly had no idea how I didn't get it before. Your presentation skills are absolutely phenomenal

[judeevans]

Steve you're honestly such a treasure. I don't know where else I could have learned how this complex intermingling fluid-dynamic quirk of physics works, other than your channel. Breaking this down and iteration it in such an easy to understand way is such a gift. I truely feel like I understand our world a little more. Thank you Steve.

[wookieQutie]

Through most of the video, I kept thinking of how the fluids would perform using a magnetic stirrer. You cannot understand how unreasonably excited I got when you said you actually did this!!!

[DavidLee-jcbf]

Based on your turntable demonstration, this effect seems to have something to do with the velocity distribution in vortex flow versus uniform solid-like rotation. Another interesting experiment would be to have a higher level of the lower fluid, to get away from the boundary layer at the bottom, and also possibly a taller container for the same reason.