Looking at bare transport coefficients in fluctuating hydrodynamics

TL;DR

This paper investigates how bare transport coefficients, especially shear viscosity, manifest in fluctuating hydrodynamics and proposes methods to measure them directly, emphasizing their microscopic origin and behavior near boundaries.

Contribution

It introduces a methodology to determine bare shear viscosity from measurable quantities and analyzes the influence of an ultraviolet cutoff in fluctuating hydrodynamics.

Findings

Bare shear viscosity dominates near solid walls where fluctuations are suppressed.

Theoretical and numerical results confirm the suppression of fluctuations at boundaries.

Bare viscosity is determined by microscopic details below the atomic scale.

Abstract

Hydrodynamics at the macroscopic scale, composed of a vast ensemble of microscopic particles, is described by the Navier-Stokes equation. However, at the mesoscopic scale, bridging the microscopic and macroscopic domains, fluctuations become significant, necessitating the framework of fluctuating hydrodynamics for accurate descriptions. A central feature of this framework is the appearance of noises and transport coefficients, referred to as bare transport coefficients. These coefficients, generally different from the macroscopic transport coefficients of the deterministic Navier-Stokes equation, are challenging to measure directly because macroscopic measurements typically yield the latter coefficients. This paper addresses the questions of how bare transport coefficients manifest in measurable physical quantities and how practical methodologies can be developed for their determination. As a prototype example, we examine the shear viscosity of two-dimensional dense fluids. The numerical simulations of the fluctuating hydrodynamic equations reveal that near solid walls, where hydrodynamic fluctuations are significantly suppressed, the bare shear viscosity governs the fluid dynamics. The theoretical calculations, based on perturbation expansion of the fluctuating hydrodynamic equations, confirm this suppression of hydrodynamic fluctuations at walls and yield analytical expressions for the observed shear viscosity. Based on this finding, we develop a methodology to accurately determine the bare shear viscosity using a controlled shear flow. Furthermore, we provide detailed numerical investigations of the role of an ultraviolet cutoff length in fluctuating hydrodynamics. These establish that the lower bound of the ultraviolet cutoff length is on the order of atomic diameter and highlight that bare viscosity is determined solely by microscopic details below this scale.