How can superfluid liquid Helium have zero viscosity while retaining surface tension? (assuming something like surface tension is required for a liquid to form drops)
The short answer is that surface tension and viscosity are two totally separate properties for a fluid. To illustrate how one can exist without the other in a superfluid, we’ll imagine two different scenarios. For the first, imagine that you have a narrow vertical pipe. Any fluid you put in the pipe will flow downward due to the force of gravity. If you put water through the pipe, you’ll get some rate of outflow. Now imagine putting something like molasses through the pipe. Even with the same external forces on it, the molasses will never move through the pipe as quickly as the water does. This is because the molasses has higher viscosity and resists flowing. In a force balance, viscosity would act like friction, opposing the downward motion of the fluid.
Surface tension arises from a different balance of forces. Now imagine that you have a stationary droplet of one fluid (A) floating in a different fluid (B). Deep inside the droplet, each molecule of Fluid A is being pulled on all sides by other identical molecules of Fluid A. A molecule at the surface of the droplet, though, doesn’t experience that neighborly pull on all sides; it experiences different intermolecular forces from Fluid B. Our imaginary droplet is stationary, though, so all the forces on it and all the forces on its individual molecules have to balance, otherwise there’d be acceleration. Surface tension acts along the interface by pulling molecules of Fluid A in toward one another–much like the elastic of a balloon–thereby balancing the forces in the droplet and equalizing the force across the interface between Fluid A and Fluid B. (Illustration credit: Wikipedia)
In the superfluid, this balance of forces across the interface between air and helium-3 must still exist, despite the superfluid’s lack of viscosity.