# Superfluids in areogel and porous media: why?

Aerogels are materials that are like ~90% or more air. As I understand, the topology of the material (i.e. of that part of the aerogel that is not air) is not such that air is contained into bubbles. Rather, the structure is similar to that of a "jungle-gym" (see this this answer).

Now, it is possible to soak aerogels in a superfluid like Helium-II or He-3. As I understand it is possible to make the aerogel absorb the superfluid in two different ways:

• "Partially filled": the superfluid does not fill all the vacuum contained into the aerogel, but it sticks to the internal "aerogel surface", namely it covers the topologically intricate surface of the "jungle-gym" structure (i.e. we have a superfluid film on a complex substrate, a system first studied by Reppy and collaborators1). The superfluid domain is 2D.

• "Completely filled": the superfluid fills all the vacuum space that constitutes the "pores". The superfluid domain is 3D but it is not simply connected (see e.g. this article2).

My question is: why are these systems studied and interesting and what are we supposed to learn from these kinds of experiments? Is there any difference between porous media "partially" (or "completely") filled with Helium-4 and Helium-3?

1. J. E. Berthold, D. J. Bishop, and J. D. Reppy, "Superfluid Transition of $$\require{mhchem} \ce{^4He}$$ Films Adsorbed on Porous Vycor Glass", Phys. Rev. Lett. 39, 348 (1977).
2. G. K. S. Wong, P. A. Crowell, H. A. Cho, and J. D. Reppy, "Superfluid critical behavior in $$^{4}\mathrm{filled}$$ porous media", Phys. Rev. Lett. 65, 2410 (1990).