[varsigma (OP)]

Superfluid Helium in a glass container, suspended above a larger volume of the same liquid, flows up the sides, forms drops which fall into the larger volume and slowly empties.

Obviously gravity is involved and the liquid has inertia. It looks like it wants to get to a lower gravitational potential.
Does anyone know how to explain the inertia of a superfluid?

[varsigma (OP)]

Sorry I meant to say the suspended glass container is what empties.

But what if you start with an empty beaker and push it so the bottom is below the surface in the reservoir? Will the fluid climb the sides and go into the beaker?

[hamdani yusuf]

Sorry I meant to say the suspended glass container is what empties.

But what if you start with an empty beaker and push it so the bottom is below the surface in the reservoir? Will the fluid climb the sides and go into the beaker?

Assuming symmetry, I predict that the superfluid will fill the beaker.

[varsigma (OP)]

Assuming symmetry, I predict that the superfluid will fill the beaker.

Hokay. Well, leaving aside what symmetry you mean. What does a superfluid do when it rotates? rotating a ball or a sphere, "breaks the symmetry", now the sphere has two distinguished points and an axis of rotation. The ball of superfluid has to conserve momentum.

It also has a 'cross-section' in that every small disk of fluid has a perimeter where it interacts with the glass; glass isn't a Fermi liquid. It has to be factored in, but how

[Eternal Student]

Hi.

Does anyone know how to explain the inertia of a superfluid?

   When you say "inertia" you could be talking about the movement and in the first post that was the movement up the sides of the beaker.  I know very little about superfluids, sorry but I have seen some explanations for that.

   Most fluids show a capillary action, they cling to the sides of the glass and there is initially a net movement up the side.  However, most fluids have enough friction among the molecules within them that the progress of more particles trying to keep flowing up the glass is effectively stopped.  Superfluids don't have that friction, so once some molecules are in motion and moving up the glass then there is nothing to stop them.  As the molecules move up the glass there would be bare glass left behind and the remaining molecules in the bottom of the glass can then start their capillary action on that.  Given enough time all of the superfluid will flow up the sides of the glass beaker and over the top.

  Anyway, applying the same reasoning to the second situation where the empty beaker is pushed into the larger container of super fluid,  I would have to guess that the molecules start their capillary action on the glass walls of the beaker and will ultimately flow up the sides over the top and into the beaker.

   The energy considerations are strange.  It almost seems that you could get a superfluid to move to a location as high as you wanted (where it has high gravitational potential energy) just by dipping a long glass tube into the superfluid.   The molecules probably are slowing down as they move higher, so effectively the temperature is dropping.  This should mean that something like superfluid Helium can't climb very high before all of it's internal energy is depleted (it's only about 2 degrees above absolute zero at the best of times).   However, most experiments are done in a warm lab where energy is constantly flowing into the superfluid from the environment and effectively warming it up.  So perhaps a flow up the sides of standard beaker height can be explained by the cooling of the environment.  I don't really know, this is speculation.

Best Wishes.

[hamdani yusuf]

Hokay. Well, leaving aside what symmetry you mean. What does a superfluid do when it rotates? rotating a ball or a sphere, "breaks the symmetry", now the sphere has two distinguished points and an axis of rotation. The ball of superfluid has to conserve momentum.

It's just the similarities in both cases.  Superfluid flows from higher level to lower level place even when there is a barrier between them. I'm still curious how tall the barrier could be until the super fluid can no longer overcome it.

[varsigma (OP)]

The rotation of the superfluid part of the bulk liquid increases its effective moment of inertia and as a result it is energetically beneficial. Thus, even for an arbitrarily small velocity of rotation, an infinite number of layers occur, the radii of which are asymptotically concentrated with respect to direction toward the axis of the cylinder.

--https://www.sciencedirect.com/science/article/pii/B9780080363646500296

What do you think this rearrangement means in terms of the inertia? Recall, inertia is the resistance to motion of any object with 'Newtonian' mass. Is the superfluid distributing the mass into layers, when rotating, to conserve the inertial response?

And a clue about what liquid He might be able to tell us, one day, about superfluids and superconductors:

When Cornell physicists Robert Richardson, David Lee and Douglas Osheroff received the 1996 Nobel Prize for their discovery of the superfluid state of liquid helium, it was only the beginning. Now a new team of Cornell researchers, building on that work, have found new complexities in the phenomenon, with implications for the study of superconductivity and theoretical models of the origin of the universe.

“We wanted to see new phase transitions,” said Jeevak Parpia, professor of physics. As it turned out, he saw a more “efficient” transition compared to any observed before in helium.
--https://news.cornell.edu/stories/2017/07/secrets-superfluid-helium-explored

Sorry about the formatting; I'll pick that up as I go.

[varsigma (OP)]

One other view of the flow over the sides of a beaker.

The superfluid is trying to conserve its own 'kinetic' potential, so it tunnels through a 'static' potential barrier--the drops form and fall into the reservoir because the suspended fluid has a higher probability of being in the least potential of the 'well'.

 The flow is minimal, like the least action in the most time. The asymptotic concentration (in the rotation experiment above) is because of rotational motion in the bulk of a suspended fluid, it responds by trying to look like it has more mass near the centre.

[hamdani yusuf]

Hokay. Well, leaving aside what symmetry you mean. What does a superfluid do when it rotates? rotating a ball or a sphere, "breaks the symmetry", now the sphere has two distinguished points and an axis of rotation. The ball of superfluid has to conserve momentum.

It's just the similarities in both cases.  Superfluid flows from higher level to lower level place even when there is a barrier between them. I'm still curious how tall the barrier could be until the super fluid can no longer overcome it.

I think the quantity of the superfluid plays a role here. If it's only 1 milligram, it's unlikely to pass a 1 meter tall barrier.

[varsigma (OP)]

What I'm interested in is what the experiment did and what the meaning of the formation of layers of superfluid says about the 'moment of inertia' I, for a rotating disk of material--a solid body.

Mathematics tells you I is the integral of all the small volumes in the disk. To get the integral you can sum over a lot of small rings of material (actually it doesn't really matter how you "address" the volumes). The superfluid state, when rotated separates into this integral, but asymptotically arranged--not what a solid does.

There's something being said about inertia and what I actually is. Mathematically, I is what addresses all the tiny volumes dV of the material--a solid ring of material requires at least two coordinates to do this. It follows that I  is a (0,2) tensor, which we can write Iij.

The superfluid is physically 'factoring' the scalar inertia into rings (asymptotic near the centre), when the bulk rotates. Although drops forming is "ordinary stuff" for a liquid, something about how the drops form and become 'inertial lumps of matter' might need a closer look.

But what do I know?

[hamdani yusuf]

Thus, even for an arbitrarily small velocity of rotation, an infinite number of layers occur

But we know that it must contain a finite number of atoms.