Courtesy of the book Carl found we have an answer!



Consider the element of the liquid helium at a height $h$ above the fluid surface and distance $y$ from the wall. To raise that element above the fluid surface costs an energy $mgh$, but because there is a Van der Waals attraction between the helium atoms and the wall you get back an energy $E_{VdW}$. Dzyaloshinskii et al give the energy change per unit mass as:

$$ \Delta E = gh - \frac{\alpha}{y^n} $$

where $\alpha$ is constant giving the strength of the Van der Waals attraction and $n$ is in the range 3 - 4 depending on the film thickness. So it is energetically favourable to lift the fluid up the wall if the Van der Waals attraction outweighs the gravitational potential energy making $\Delta E$ negative. Since $y$ can be taken arbitrarily small (well, at least down to a few times the He atom size) $\Delta E$ will be negative for all heights $h$ and the film covers the whole wall.

The resulting equation for the film thickness $d$ as a function of height is given (without derivation) as:

$$ d \approx \left( \frac{\alpha}{gh} \right)^{1/n} $$

Since the liquid film will have a non-zero thickness at the top of the container wall it can flow over the wall and then down the outside. Even though the film thicknesses work out to be only a few tens of nanometres the zero viscosity of the superfluid helium allows an appreciable flow rate. Indeed, later in the book flow velocities of 30 cm/s are mentioned.

In principle this would apply to all fluids, however for normal fluids the flow rate in a film a few tens of nanometres thick would be infinitesimally small so the climbing is never observed.

A few comments of my own: I note that this derivation ignores the interfacial tensions of the helium/air, helium/wall and air/wall interfaces. I have no figures for what these would be for superfluid helium and possibly they are negligable. The predictions of the Dzyaloshinskii theory are claimed to agree well with experiment. Also you should note that one of the references provided by Carl challenges the above explanation, though without coming to any firm conclusions.

What kind of energy does superfluidity use?
I'm looking to create a bundle offer where customers can buy two items from a collection (30 products with varying prices) and they get a fixed third item which is a FREE product.

As the final price will vary depending on what the customer chooses, how do I make the basket subtotal add the two items but ignore the third priced item?

Hope that makes sense 
