The nature of superfluid helium in porous structures
We report observations of the behavior of superfluid 4He in two porous membranes, Nuclepore and Anopore. Using capacitive measurements, M. P. Lilly had observed hysteresis, return-point memory and avalanche behavior in Nuclepore  when superfluid 4He in capillary condensed in its pores. Additionally, he found that the avalanches of draining pores were global on the substrate, and the pore-pore connections as well as the superfluid film enabled the avalanches. We have continued that work to characterize the statistics of the avalanches in Nuclepore. We have seen that the statistics of the avalanches in Nuclepore are dependent on temperature and rate of removal of 4He from the sample cell. We have also observed two distinct regions of avalanche type in Nuclepore, which we propose is due to the pore-pore connections. We have observed power law behavior in the statistics of the avalanche size and measured the correlation of the avalanche events and sizes under various conditions.
We have also observed hysteresis, return-point memory and avalanche behavior in Anopore using the same type of capacitive measurement. Anopore differs from Nuclepore in that nominally it has no pore-pore connections. In Anopore, we observed only one type of avalanche draining, and exponential behavior in the statistics of the avalanches instead of power law tendencies. We also measured the correlation of the avalanche events and sizes, and compared our results to those for Nuclepore.
We performed simulations of draining on Nuclepore, artificially including and excluding third sound from our “avalanches”. We find that our results are similar to our laboratory measurements. We also performed a simple version of semi-local draining on Anopore, and saw some similarities to our measured results.
We conclude that the behavior and statistics of the avalanches in a porous material are good indications of whether one is looking at a substrate that is percolated (Nuclepore) or a substrate that has no internal connections (Anopore).