How small hydrodynamics can go

TL;DR

This paper investigates the limits of linear hydrodynamics in liquids, revealing that the convergence radius is determined by microscopic atomic distances and varies with temperature and electromagnetic interactions.

Contribution

It combines recent theoretical concepts to analyze the convergence of hydrodynamics in real liquids using experimental and simulation data, highlighting microscopic bounds.

Findings

Radius of convergence increases with temperature

Radius decreases with electromagnetic coupling

Microscopic inter-atomic distance sets the convergence limit

Abstract

Numerous experimental and theoretical results in liquids and plasmas suggest the presence of a critical momentum at which the shear diffusion mode collides with a non-hydrodynamic relaxation mode, giving rise to propagating shear waves. This phenomenon, labelled as "k-gap", could explain the surprising identification of a low-frequency elastic behaviour in confined liquids. More recently, a formal study of the perturbative hydrodynamic expansion showed that critical points in complex space, such as the aforementioned k-gap, determine the radius of convergence of linear hydrodynamics, its regime of applicability. In this work, we combine the two new concepts and we study the radius of convergence of linear hydrodynamics in "real liquids" by using several data from simulations and experiments. We generically show that the radius of convergence increases with temperature and it surprisingly decreases with the electromagnetic interactions coupling. More importantly, for all the systems considered, we find that such radius is set by the Wigner-Seitz radius, the characteristic inter-atomic distance of the liquid, which provides a natural microscopic bound.