Double Fountain Effect in Superfluid Helium

A double fountain pressure model is used to analyze the recent measurements of Yu and Luo (arXiv2211.02236v4) of superfluid $^4$He flow between two chambers held at different temperatures via two superleaks and an intervening third chamber that spontaneously achieves a temperature higher than both fixed temperatures. The physical origin of the increased temperature in the intervening chamber is attributed to the balance between the rate of mechanical energy deposited by superfluid transport and the rate of convection back to the lower temperature chambers. An equation is given for the pressure of the third chamber, the measurement of which would confirm or refute the theory.