Double Fountain Effect in Superfluid Helium

TL;DR

This paper presents a double fountain pressure model to explain recent superfluid helium experiments, attributing the temperature increase in an intermediate chamber to energy balance mechanisms, and proposes an equation for experimental verification.

Contribution

It introduces a novel theoretical model for superfluid helium flow involving a double fountain effect and provides an equation to test this theory experimentally.

Findings

The model explains the temperature rise in the intermediate chamber.

An equation for the third chamber's pressure is derived.

The theory can be validated through specific measurements.

Abstract

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.