Shear viscosity of liquid helium 4 above the lambda point

TL;DR

This paper investigates how Bose statistics influence the shear viscosity of liquid helium 4 above the lambda point, deriving a formula that explains the viscosity's gradual decrease near the transition.

Contribution

It introduces a new theoretical formula linking shear viscosity to Bose statistics and susceptibility, providing insights into superfluid behavior above the lambda point.

Findings

Shear viscosity decreases gradually from 3.7K to the lambda point.

Derived a formula connecting viscosity with Bose statistics.

Explained the influence of Bose statistics on liquid helium 4's flow properties.

Abstract

In liquid helium 4, many features associated to Bose statistics have been masked by the strongly interacting nature of the liquid. As an example of these features, we examine the shear viscosity of liquid helium 4 above the lambda point. Applying the linear-response theory to Poiseuille's formula for the capillary flow, the reciprocal of the shear viscosity coefficient is considered as a transport coefficient. Using the Kramers-Kronig relation, we relate a superfluid flow in a capillary with that in a rotating bucket, and express the reciprocal of the shear viscosity coefficient in terms of the susceptibility of the system. A formula for the kinematic shear viscosity is obtained which describes the influence of Bose statistics. Using this formula, we study the gradual fall of the kinematic shear viscosity from 3.7K to the lambda point in liquid helium 4 at 1 atm.