Hydrodynamics of Superfluid Helium in a Single Nanohole

TL;DR

This study investigates superfluid helium flow through a nanohole, demonstrating viscous flow in He I and superfluid flow in He II, with measurements aligning with existing models and data.

Contribution

First experimental analysis of helium flow in a nanohole, combining viscous and superfluid regimes with quantitative modeling.

Findings

Viscous flow in He I not clamped despite small diameter.

Superfluid velocities match existing critical superflow data.

Flow behavior well described by short pipe and two-fluid models.

Abstract

The flow of liquid helium through a single nanohole with radius smaller than 25 nm was studied for the first time. Mass flow was induced by applying a pressure difference of up to 1.4 bar across a 50 nm thick Si3N4 membrane and was measured directly by means of mass spectrometry. In liquid He I, we experimentally show that the fluid is not clamped by the short pipe with diameter-to-length ratio D/L~1, despite the small diameter of the nanohole. This viscous flow is quantitatively understood by making use of a model of flow in short pipes. In liquid He II, a two-fluid model for mass flow is used to extract the superfluid velocity in the nanohole for different pressure heads at temperatures close to the superfluid transition. These velocities compare well to existing data for the critical superflow of liquid helium in other confined systems.