Temperature Dependence of Viscosity in Normal Fluid $^3$He Below 800mK Determined by a Micro-electro-mechanical Oscillator

TL;DR

This study measures the viscosity of normal liquid helium-3 at very low temperatures using a micro-electro-mechanical oscillator, revealing a transition from classical to Fermi liquid behavior.

Contribution

It introduces a novel application of a micro-electro-mechanical oscillator to accurately determine helium-3 viscosity across a wide temperature range.

Findings

Viscosity decreases with temperature, showing a crossover from classical to Fermi liquid behavior.

Transition from $T^{-1}$ to $T^{-2}$ dependence indicates flow regime change.

Results agree with previous measurements and Fermi liquid theory predictions.

Abstract

A micro-electro-mechanical system vibrating in its shear mode was used to study the viscosity of normal liquid $^3$He from 20mK to 770mK at 3bar, 21bar, and 29bar. The damping coefficient of the oscillator was determined by frequency sweeps through its resonance at each temperature. Using a slide film damping model, the viscosity of the fluid was obtained. Our viscosity values are compared with previous measurements and with calculated values from Fermi liquid theory. The crossover from the classical to the Fermi liquid regime is manifest in the temperature dependence of viscosity. In the Fermi liquid regime, the temperature dependence of viscosity changes from $T^{-1}$ to $T^{-2}$ on cooling, indicating a transition from the Stokes flow to the Couette flow regime.