Theory of adiabatic fountain resonance

TL;DR

This paper clarifies the theory of adiabatic fountain resonance in superfluid helium, identifying it as a fourth sound resonance rather than a Helmholtz resonance, influenced by wafer flexing at low frequencies.

Contribution

It provides a corrected theoretical understanding of adiabatic fountain resonance, emphasizing the role of fourth sound and wafer flexing effects.

Findings

Resonance is a fourth sound mode, not Helmholtz resonance.

Resonance frequency is low due to wafer flexing.

Clarifies the physical mechanism behind the resonance.

Abstract

The theory of "Adiabatic Fountain Resonance" with superfluid $^4$He is clarified. In this geometry a film region between two silicon wafers bonded at their outer edge opens up to a central region with a free surface. We find that the resonance in this system is not a Helmholtz resonance as claimed by Gasparini and co-workers, but in fact is a fourth sound resonance. We postulate that it occurs at relatively low frequency because the thin silicon wafers flex appreciably from the pressure oscillations of the sound wave.