Explanation for the Fountain effect in superfluids

[BobGom]

I'm looking for an explanation for the fountain effect in superfluids using the 'two fluid model'. However the explanations I've come across are not very satisfactory

From the NASA website

http://cryo.gsfc.nasa.gov/introduction/liquid_helium.html

Here is the two fluid model explanation of the fountain effect. When the heater in the tube is turned on, the liquid helium in the tube begins to warm up. Since superfluid helium flows from cool areas to warm areas, superfluid helium flows into the tube through the porous plug. Normal fluid is too viscous to flow out through the porous plug. Therefore, when the tube fills with liquid helium, the only way out for the normal fluid is to squirt out the hole in the top.

But why does superfluid Helium flow from cool areas to warm areas? Unless I'm missing something that it is not a property of all fluids is it? The wiki article on Helium says

In the fountain effect, a chamber is constructed which is connected to a reservoir of helium II by a sintered disc through which superfluid helium leaks easily but through which non-superfluid helium cannot pass. If the interior of the container is heated, the superfluid helium changes to non-superfluid helium. In order to maintain the equilibrium fraction of superfluid helium, superfluid helium leaks through and increases the pressure, causing liquid to fountain out of the container.

But I don't see why the system needs to maintain the same fraction of superfluid helium. Surely at higher temperatures there is a lower equilibrium fraction of superfluid.

 

[0xDEADBEEF]

The analogy is that of partial pressure. Like with osmosis you get osmotic pressure if you have an uneven concentration of some salt. If you have an uneven concentration of suprafluid helium it is the same

 

[Minich]

I'm looking for an explanation for the fountain effect in superfluids using the 'two fluid model'. However the explanations I've come across are not very satisfactory

Yes, this fact is known. Even Feynman couldn't explore theory of superfluidity in details.
You can see his book on statistical mechanics (last edition) and see that Feynman suggest to publish anybody paper explaining lambda point curve in He4. He couldn't get second order phase transition curve himself (only third order phase transition for Bose codensation).

I also remember, that Feynman main paper on superfluidity didn't deal with the fountain effect. So we don't have so genius author to explain fountain effect now to all of us.

But at the same time we can find such instability in plasma and/or in hydrodynamics as "negative energy wave" (we can google out topical reviews on such instabilities). This instability is famous for moving frames could diminish total energy of the system. So "moving frame" (in our case "superfluid" fraction of He4 can fontain at the expense of total energy.