Can you swim in a superfluid?

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TheQuestionIsYes
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Can you swim in a superfluid?

Postby TheQuestionIsYes » Tue Sep 21, 2010 2:56 am UTC

Rather simple concept on this one.
I've been trying to wrap my head around(god that's a grotesque image) the implications of the concept of literally zero viscosity, and this is the thought experiment I can't seem to resolve.
So, ignoring the more mundane difficulties like insanely low temperature, would a person (or other swim-worthy body) be able to propel themselves through the superfluid or would they just flail around like a looney tunes character on a block of ice?
Is viscosity a necessary property of the material?

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Re: Can you swim in a superfluid?

Postby Josephine » Tue Sep 21, 2010 3:00 am UTC

It would be like trying to swim in air, probably.
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Re: Can you swim in a superfluid?

Postby TheQuestionIsYes » Tue Sep 21, 2010 3:09 am UTC

You can swim in air though, that's basically what flying is. As long as you have a large enough area on your wings/pushing surface, or low enough gravity to not pull you back. I think air has nonzero viscosity though.

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Re: Can you swim in a superfluid?

Postby scarecrovv » Tue Sep 21, 2010 4:32 am UTC

I'm not a physicist, so perhaps everything I say is wrong, but this is what it seems like to me:

Instead of a person trying to swim, let's imagine a simpler object. Suppose you have a fairly long hollow cylinder with small mass and with walls of negligible thickness, floating in the superfluid. Now put a membrane with small mass relative to the cylinder across the front end, and then sweep that membrane down the cylinder. It seems to me that regardless of the viscosity of the fluid, it still has density, and therefore inertia. I think it would be easier for the cylinder to move forward and the membrane and fluid to stay stationary rather than for the cylinder to remain stationary and for the membrane to accelerate lots of fluid. Now turn the membrane 90 degrees so it's edge on to the fluid, and bring it back to the front of the cylinder. Repeat. I think the cylinder will move forward with each stroke.

Now given that it's possible for some machine to swim in a superfluid, it seems reasonable that a human should be able to as well, albeit with lesser efficiency.

I think. :?

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Re: Can you swim in a superfluid?

Postby Interactive Civilian » Tue Sep 21, 2010 4:32 am UTC

Hmmm... My instinct says "no", because it seems to me that if there is no resistance to flow, then flow will be instantaneous around any object moving through it. Therefore, you could never create the pressure difference needed to produce the drag or lift (depending on which style of swimming you are doing) needed to generate thrust.

I may be wrong, but it seems to me that it would be no different than trying to swim in a vacuum. That is what my instinct says. However, instincts often seem to be wrong when it comes to stuff like this, so I, too, am very interested in the real answer.

[edit]
scarecrovv wrote:It seems to me that regardless of the viscosity of the fluid, it still has density, and therefore inertia.


See, this is where I'm not so sure. IS there such a thing as a zero-viscosity fluid? Or is it just a thought concept to illustrate points in physics, like frictionless surfaces and spherical cows? ;) It seems to me that viscosity must be tied into inertia somehow... :?
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Re: Can you swim in a superfluid?

Postby phlip » Tue Sep 21, 2010 4:51 am UTC

But think about where the actual force is in that scenario... in a normal fluid, the membrane moving down the tube leaves an area of low pressure behind it, and high pressure in front of it... while the fluid will flow to equalise this pressure, the viscosity stops this from being instant, so there's a pressure difference on the membrane, which provides the reaction force to the tube and the thing moves. With a superfluid, that pressure difference won't be there. So there can't be any force on the membrane, and the tube will stay stationary.

For the inertia point... while there will be fluid in the tube moving from front to back, there'll also be fluid around the tube moving from back to front, with the same total flow rate. Now, with a normal fluid, the flow outside happens after the flow inside, with a propagation delay... but in a superfluid, it would be much faster, and there would be no net change in momentum of the fluid. The fluid has no resistance to flowing around the tube like this, by definition, since it's a superfluid.

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Re: Can you swim in a superfluid?

Postby PhoenixEnigma » Tue Sep 21, 2010 4:56 am UTC

Interactive Civilian wrote:See, this is where I'm not so sure. IS there such a thing as a zero-viscosity fluid? Or is it just a thought concept to illustrate points in physics, like frictionless surfaces and spherical cows? ;) It seems to me that viscosity must be tied into inertia somehow... :?
At very low tempertures, helium becomes a superfluid, and I believe there are others. These have been experimentally verified, as well. Those are certainly real matter, with real mass and volume, and therefore density.

Unfortunately, that's just about all I know about superfluids. My best guess that is you could generate thrust with some sort of piston setup, but not with a swimming motion. You can still invoke Newton's third law, but swimming relies heavily on resistance to shear in the fluid.
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Re: Can you swim in a superfluid?

Postby BlackSails » Tue Sep 21, 2010 5:03 am UTC

In low viscosity liquid, you cannot swim by any sort of reciprocal motion. You need to do what bacteria do and turn like a corkscrew

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Re: Can you swim in a superfluid?

Postby Nlelith » Tue Sep 21, 2010 5:24 am UTC

I know that for liquid helium below the lambda point, there's still viscosity in the sense that you would experience drag when passing a metal plate over the surface. This is explained by a two-fluid model where the fluid is composed of both superfluid and normal fluid (the fraction of which depends on the temperature). Only the superfluid part is supposed to be involved in the capillary flow while there's always some normal fluid present to retard the motion of objects passing through it. I suspect this is true for all superfluids so I think you would still be able to swim in it, though it would be more difficult the further below the lambda point you were.

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Re: Can you swim in a superfluid?

Postby scarecrovv » Tue Sep 21, 2010 5:34 am UTC

phlip wrote:But think about where the actual force is in that scenario... in a normal fluid, the membrane moving down the tube leaves an area of low pressure behind it, and high pressure in front of it... while the fluid will flow to equalise this pressure, the viscosity stops this from being instant, so there's a pressure difference on the membrane, which provides the reaction force to the tube and the thing moves. With a superfluid, that pressure difference won't be there. So there can't be any force on the membrane, and the tube will stay stationary.

For the inertia point... while there will be fluid in the tube moving from front to back, there'll also be fluid around the tube moving from back to front, with the same total flow rate. Now, with a normal fluid, the flow outside happens after the flow inside, with a propagation delay... but in a superfluid, it would be much faster, and there would be no net change in momentum of the fluid. The fluid has no resistance to flowing around the tube like this, by definition, since it's a superfluid.

But wouldn't that imply that it takes no force to accelerate the fluid? Viscosity aside, F=ma should still hold. Right?

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Re: Can you swim in a superfluid?

Postby phlip » Tue Sep 21, 2010 5:55 am UTC

No, I can't say I know what I'm talking about...

But it doesn't seem like there would strictly need to be any force involved in making the fluid accelerate in a loop... since there's no net acceleration, every bit accelerating left is balanced by another bit accelerating right...

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Re: Can you swim in a superfluid?

Postby Qaanol » Tue Sep 21, 2010 6:50 am UTC

All right, take your hollow tube and put it inside another hollow tube, so it’s extendable (like a curtain rod or a toy lightsaber or a radio antenna). Let the inner tube fill with liquid, then seal the ends. This is now a solid rod with substantial mass thanks to the trapped liquid. Extend the two tubes apart with a little motor. Since the outer tube is hollow it is much lighter, so it travels a lot further. The center of mass of the tube system does not move though.

Open the ends of the inner tube. In this instant of unsealing the inner tube, a lot of mass—namely the formerly-trapped liquid—suddenly stops being part of the tube system. That mass had been off-center, so the center of mass of the tube system immediately changes from its original location to a new location.

Now the inner and outer tubes have comparable mass. Use the little motor to retract them together again. They both move about the same distance, so the center of mass of the tube system does not change. Reseal the ends of the inner tube. We have now returned to the initial state, but the tubes have moved. Therefore motion is possible.
Last edited by Qaanol on Tue Sep 21, 2010 7:19 am UTC, edited 4 times in total.
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Re: Can you swim in a superfluid?

Postby scarecrovv » Tue Sep 21, 2010 6:58 am UTC

phlip wrote:But it doesn't seem like there would strictly need to be any force involved in making the fluid accelerate in a loop... since there's no net acceleration, every bit accelerating left is balanced by another bit accelerating right...

But there's no net acceleration in a flywheel either, but you need a force on the edge to make it change speed.

Qaanol wrote:All right, take your hollow tube and put it inside another hollow tube, so it’s extendable (like a curtain rod or a toy lightsaber or a radio antenna). Let the inner tube fill with liquid, then seal the ends. This is now a solid rod with substantial mass thanks to the trapped liquid. Extend the two tubes apart with a little motor. Since the outer tube is hollow it is much lighter, so it travels a lot further. The center of mass of the tube system does not move though.

Open the ends of the inner tube. Now the inner and outer tubes have comparable mass. Use the little motor to retract them together again. They both move about the same distance, so the center of mass of the tube system does not change.

Reseal the ends of the inner tube. We have now returned to the initial state, but the tubes have moved. Therefore motion is possible.


Ooooh, that could work even less confusingly.

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Re: Can you swim in a superfluid?

Postby Qaanol » Tue Sep 21, 2010 7:23 am UTC

Example:

Denote the position of the outer tube by its endpoints, say x = [-1, 1] initially.
Denote the position of the inner tube by its endpoints, say y = [-1, 1] initially.
Call the mass of the outer tube m. Call the mass of the inner tube n. Initially n = m.
Call the center of mass c. In general [imath]c = \frac{m}{m+n}\frac{x_1+x_2}{2}+\frac{n}{m+n}\frac{y_1+y_2}{2}[/imath]. Initially c = 0.

We seal the inner tube, so its total mass increases. Say n = 9m.

We extend the tubes. The outer tube moves nine times as far. Say it moves 0.9 units.
x = [-0.1, 1.9]
y = [-1.1, 0.9]
Now the center of mass of the system is c = (0.1)(0.9) + (0.9)(-0.1) = 0, unchanged as expected.

Unseal the inner tube, so its total mass reverts to n = m.
x = [-0.1, 1.9]
y = [-1.1, 0.9]
Now the center of mass of the system is c = (0.5)(0.9) + (0.5)(-0.1) = 0.4, which has changed.

Retract the tubes. They both move the same distance since their masses are equal. Since they are 1 unit apart, they each move 0.5.
x = [-0.6, 1.4]
y = [-0.6, 1.4]
Now the center of mass of the system is c = (0.5)(0.4) + (0.5)(0.4) = 0.4, still.

Seal the inner tube. It now has mass n = 10m. We are in the same situation we began, but the system has advanced by 0.4. This is repeatable, so the tubes can move.

We can do a lot better, for starters by having the tubes move all the way through each other in both directions, not just part way in one direction. But this was just a proof-of-concept. Also note that it may be difficult to float in the superfluid. You may need constant propulsion of this sort just to maintain vertical position.

By combining several of these pumps it is plausible to get a constant velocity.

To show how a human could use this in a sort of “swimming”, take a bucket in each hand. Stretch your hands forward in the direction you want to move. Put lids on the buckets to seal them. Bring your arms behind you in the direction you want to leave. Open the buckets. Bring your arms forward again. Seal the buckets again. Repeat ad nauseum.

The basic idea here is that, no matter how you move your limbs, your center of mass does not change because the superfluid flows effortlessly and you have no friction with which to push on it. But you can grab it without friction, using a bucket. This increases your total mass. You still can’t move your center of mass, but you can move your body’s center of mass relative to the buckets (and more importantly, relative to their contents). Then you can unseal the buckets and find your center of mass suddenly changed. Flailing about here still won’t move your center of mass, but it means you can move the buckets forward without losing any ground.
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Re: Can you swim in a superfluid?

Postby Zamfir » Tue Sep 21, 2010 7:38 am UTC

BlackSails wrote:In low viscosity liquid, you cannot swim by any sort of reciprocal motion. You need to do what bacteria do and turn like a corkscrew

But bacteria swim in extremely high viscous fluids, relative to other forces. More in general, without viscosity (and without compressibility) the Navier-Stokes equations collapse to potential flow, basically a Laplace equation. I am pretty sure any closed body in potential flow cannot have a net force on it. So a propeller or corkscrew in a perfectly non-viscous fluid would not produce thrust.

It is possible to model things like wings and propellers using potential flow by applying artificial conditions (in particular the Kutta condition), but those conditions simulate the effects of locally strong viscous effects in reality.

Qaanol wrote:All right, take your hollow tube and put it inside another hollow tube, so it’s extendable (like a curtain rod or a toy lightsaber or a radio antenna). Let the inner tube fill with liquid, then seal the ends. This is now a solid rod with substantial mass thanks to the trapped liquid. Extend the two tubes apart with a little motor. Since the outer tube is hollow it is much lighter, so it travels a lot further. The center of mass of the tube system does not move though.

Open the ends of the inner tube. In this instant of unsealing the inner tube, a lot of mass—namely the formerly-trapped liquid—suddenly stopped being part of the tube system. It was off-center, so the center of mass of the tube system immediately changed from its original location to a new location.

Now the inner and outer tubes have comparable mass. Use the little motor to retract them together again. They both move about the same distance, so the center of mass of the tube system does not change. Reseal the ends of the inner tube. We have now returned to the initial state, but the tubes have moved. Therefore motion is possible.

I think this would indeed work.

For an analogous situation, we can imagine a spacecraft in vacuum, next to long row of pebbles floating in space, and at rest relative to the pebbles. The spacecraft can extend an arm, take a pebble in front of it, and deposit the pebble behind it. The space craft will then be stationary relative to the pebbles again, but somewhat further down the line. In the same way, an object in a superfluid can extend an arm forward, close a container, and deposit it behind it. That's basically the same as your double-tube.

Of course, the spacecraft could accelerate a pebble backwards, and accelerate itself forward. I think a superfluid swimcraft could do the same: fill a container with fluid, accelerate the container backwards, open the container, then move the arm forward again. I think it would not even matter on which side the container was opened.

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Re: Can you swim in a superfluid?

Postby Qaanol » Tue Sep 21, 2010 7:52 am UTC

Zamfir wrote:Of course, the spacecraft could accelerate a pebble backwards, and accelerate itself forward. I think a superfluid swimcraft could do the same: fill a container with fluid, accelerate the container backwards, open the container, then move the arm forward again. I think it would not even matter on which side the container was opened.

Beautiful. I was trying to figure out how to make it work like a squid’s jet, and you nailed it. Seal in fluid, accelerate container, unseal container, repeat as necessary. Now we have acceleration, and by combining a few of these we can get constant acceleration. Well done.
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Re: Can you swim in a superfluid?

Postby Certhas » Tue Sep 21, 2010 8:46 am UTC

Nicely done. So you could swim by swalloing the liquid and pooping it out. Returning briefly to the propeller idea I think this case is somewhat problematic as vortices are tricky. They are topological defects in the fluid so the standard idea of 0 viscosity fluids might not apply. the rotational motion is inherently quantized (http://en.wikipedia.org/wiki/Quantum_vortex).
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Re: Can you swim in a superfluid?

Postby xepher » Tue Sep 21, 2010 12:54 pm UTC

Maybe you could swim in a superfluid, but right now I'm going to say no because of the low temperatures they have. I don't think it would be very... healthy to swim in one.

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Re: Can you swim in a superfluid?

Postby Tass » Tue Sep 21, 2010 2:13 pm UTC

xepher wrote:Maybe you could swim in a superfluid, but right now I'm going to say no because of the low temperatures they have. I don't think it would be very... healthy to swim in one.


Not the point.

TheQuestionIsYes wrote:So, ignoring the more mundane difficulties like insanely low temperature, would a person (or other swim-worthy body) be able to propel themselves through the superfluid or would they just flail around like a looney tunes character on a block of ice?

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Re: Can you swim in a superfluid?

Postby Scyrus » Tue Sep 21, 2010 8:02 pm UTC

Temperature aside, if you found an element which is superfluid at a temperature bearable to us humans,
and if you were immersed in a pool of superfluid, wouldn't it (with 0 viscosity) creep all over you and enter any holes in your body in a rather... "impossible to shake off" manner and drown you? I mean if it can creep along vertical walls as if it could defy gravity, what prevents it from climbing along your body, reach your mouth and try to fill the inside to attempt to equalize the pressure?

My guess is that arguing wether you can swim in it seems quite... irrelevant considering you can't be alive in it.

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Re: Can you swim in a superfluid?

Postby gorcee » Tue Sep 21, 2010 8:07 pm UTC

I believe that you can.

When you study basic aerodynamics, you work with inviscid fluid mechanics, and you just sort of ignore things like D'Alembert's Paradox. You can quite easily do things like calculate the lift or drag of a body in an inviscid flow, because viscosity effects operate primarily in the boundary layer. I would expect the same to hold true in a superfluid.

Now, the question is how do we solve D'Alembert's Paradox with a superfluid? I'm not sure on the answer, but I would be willing to bet that the dominant factor is flow separation.

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Re: Can you swim in a superfluid?

Postby jmorgan3 » Tue Sep 21, 2010 8:48 pm UTC

gorcee wrote:When you study basic aerodynamics, you work with inviscid fluid mechanics, and you just sort of ignore things like D'Alembert's Paradox. You can quite easily do things like calculate the lift or drag of a body in an inviscid flow, because viscosity effects operate primarily in the boundary layer.

You can calculate the lift on a body fairly accurately with inviscid theory. You can not use it to accurately predict drag, though, because skin friction drag and drag due to boundary layer separation are viscous phenomena. The only kinds of drag you can calculate with inviscid theory are finite-wing drag (due to wingtip vortices) and wave drag. If superfluids are incompressible or nearly so, I would expect wave drag to be undetectable. Finite-wing effects wouldn't come into play unless you used a non-conservative body force to induce circulation in the fluid. I believe that there would be no drag at all on a moving object.

gorcee wrote:Now, the question is how do we solve D'Alembert's Paradox with a superfluid? I'm not sure on the answer, but I would be willing to bet that the dominant factor is flow separation.

D'Alembert's Paradox is a paradox because we can empirically measure a drag force on moving objects in a viscous fluid. It won't be a paradox if, as I explain above, there is no drag on a body in inviscid flow. Flow separation, by the way, is a viscous phenomenon, and won't occur in a truly inviscid fluid. If there is any drag, it will be wave drag caused by the not-perfectly-incompressible nature of a superfluid.
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Re: Can you swim in a superfluid?

Postby Qaanol » Tue Sep 21, 2010 11:00 pm UTC

How do you contain a superfluid? In particular, if you have a “blob” of superfluid just floating in the vacuum of space, will it stay together (like water does thanks to surface tension) or will it sort of disperse into a fine mist of individual particles? What about in a gravity well, if you fill a beaker (or swimming pool) will a significant volume of fluid stay put, or will it all climb up the walls and just spread out as much as possible? I suppose what I’m asking is essentially, to contain a superfluid in a volume sufficient to have a reasonable notion of “swimming through it”, is it necessary to completely enclose it (in a box)?
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Re: Can you swim in a superfluid?

Postby Mavrisa » Wed Sep 22, 2010 12:05 am UTC

I'd have to say that you can. The only force that is no longer helping you out with swimming is surface friction. And it seems to me that surface friction doesn't really help that much in propelling you forward, and if it does, it has just as great an effect in slowing you down.
If you take a propeller and begin to whirl it around, it acts to reflect the particles in one direction. And as long as I can assume that Newton's third law applies in a superfluid (I'm sure there would be energy conservation problems if it didn't), then the system is propelled in the opposite direction. Yes, it may end up spinning around so that its angular momentum is conserved, but the propeller should still spin relative to the fluid. In my mind, this should mean that motion is possible, BUT, of course humans cannot do this.
Now imagine a motion similar to the way olympic rowers move their oars (I say olympic, because they have the most precise technique and it was the first thing I pictured). In one direction, the flat side is turned to face the water, so that when the rower pulls, the paddle forces a bunch of water in one direction. The paddle is then turned 90 degrees so that only a very small surface area is being pulled through the water (if it was being pulled through the water... which would be stupid, but humour me). The majority of the drag is then caused by skin friction. Again, this wouldn't exist in a superfluid.
Wikipedia's article on drag has a helpful table of form drag vs. skin friction which shows pretty much this idea in the first and last rows. If skin friction was completely negated, then you can imagine the result.
I have noticed that I do a variation on this when swimming completely submerged.
So yeah, possible I think.
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Re: Can you swim in a superfluid?

Postby scarecrovv » Wed Sep 22, 2010 12:08 am UTC

Scyrus wrote:Temperature aside, if you found an element which is superfluid at a temperature bearable to us humans,
and if you were immersed in a pool of superfluid, wouldn't it (with 0 viscosity) creep all over you and enter any holes in your body in a rather... "impossible to shake off" manner and drown you? I mean if it can creep along vertical walls as if it could defy gravity, what prevents it from climbing along your body, reach your mouth and try to fill the inside to attempt to equalize the pressure?

My guess is that arguing wether you can swim in it seems quite... irrelevant considering you can't be alive in it.

But you could wear a dry suit, and scuba gear with a full face mask. You'd be fine if nothing broke :wink:.

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Re: Can you swim in a superfluid?

Postby Zamfir » Wed Sep 22, 2010 5:28 am UTC

jmorgan3 wrote:
gorcee wrote:When you study basic aerodynamics, you work with inviscid fluid mechanics, and you just sort of ignore things like D'Alembert's Paradox. You can quite easily do things like calculate the lift or drag of a body in an inviscid flow, because viscosity effects operate primarily in the boundary layer.

You can calculate the lift on a body fairly accurately with inviscid theory. You can not use it to accurately predict drag, though, because skin friction drag and drag due to boundary layer separation are viscous phenomena. The only kinds of drag you can calculate with inviscid theory are finite-wing drag (due to wingtip vortices) and wave drag. If superfluids are incompressible or nearly so, I would expect wave drag to be undetectable. Finite-wing effects wouldn't come into play unless you used a non-conservative body force to induce circulation in the fluid. I believe that there would be no drag at all on a moving object.

gorcee wrote:Now, the question is how do we solve D'Alembert's Paradox with a superfluid? I'm not sure on the answer, but I would be willing to bet that the dominant factor is flow separation.

D'Alembert's Paradox is a paradox because we can empirically measure a drag force on moving objects in a viscous fluid. It won't be a paradox if, as I explain above, there is no drag on a body in inviscid flow. Flow separation, by the way, is a viscous phenomenon, and won't occur in a truly inviscid fluid. If there is any drag, it will be wave drag caused by the not-perfectly-incompressible nature of a superfluid.


You cannot predict lift, or any fluid dynamic force, using inviscid theory alone. It would be a bit weird if inviscid flow could tell which parts of a force we call drag and which we call lift.

Prediction of lift on wings use the Kutta condition: you add artificial vorticity to the flow solution until the trailing edge flow is nicely parallel. But in reality, it is because of viscosity that the flow is parallel to the trailing edge. In real inviscid flow, flow would just curve around the trailing edge to a stagnation point on the top of a wing, and there would be no lift.

That's why you cannot use a propeller in a superfluid: the blades will not produce a net force on the flow.

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Re: Can you swim in a superfluid?

Postby jmorgan3 » Wed Sep 22, 2010 6:03 am UTC

Correct. I didn't mean to imply that lift is possible in an actual inviscid fluid, just that the lift on a body in a viscous fluid can be calculated using inviscid theory. I include the Kutta condition as part of inviscid theory, since it's pretty much a requisite for getting any useful data out of inviscid simulations of wings. As stated in my link above, a body in an inviscid fluid will not be able to induce any circulation in the fluid. As a result the Kutta condition obviously cannot hold, and, unless the fluid already has some circulation, there can be no lift force on the body.
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