Why do superfluids even climb walls? The question I have been puzzling over is how can superfluids climb walls?
I know there is a force that overcomes gravity. I thought perhaps the van de Waals force is so weak between superfluid atoms that the atoms are just attracted to the container walls much more than they are attracted to each other. So they stick to the walls. But it still doesn't sit right with me. Could you please provide a mathematical answer if possible?
 A: Superfluids are described by a zero viscosity $\eta = 0$. Microscopically, this means that the intermolecular forces between molecules are so small that the individual atoms move together instead of colliding against each other.

Any fluid has a natural attraction to another surface. The forces of surface tension causes the surface of the fluid to deform as in the above image, also known as capillary action. (Note that superfluids still have surface tension because it arises from the energy excess of intermolecular forces at an interface $\Delta E = \gamma \Delta A$.)
Once the superfluid initially moves upward from capillary action, a thin stream of atoms (about 30 nm) can continue to flow along the walls due to there being no viscosity to stop them.
This process is suprisingly similar to how you can siphon water out of a tank or tub. Siphons work because the fluids flowing through the siphon lowers its total energy. All that is required is for water to initially move together along the tube. In a similar fashion, the superfluid is simply attempting to lower its energy. A famous setup related to this discussion is called a Rollin film.
