Enhancement of Diffusive Transport by Nonequilibrium Thermal Fluctuations

TL;DR

This paper investigates how nonequilibrium thermal fluctuations enhance diffusive transport in fluid mixtures, revealing size-dependent effects and confirming the importance of nonlinear advective terms through theory, simulations, and numerical methods.

Contribution

It demonstrates the significant role of thermal velocity fluctuations in enhancing diffusion and emphasizes the necessity of including nonlinear advective terms in fluctuating hydrodynamics models for small systems.

Findings

Diffusive flux is enhanced by long-range correlations due to thermal fluctuations.

Enhancement depends on system size, growing logarithmically in quasi-two dimensions.

Theoretical predictions agree well with particle simulations and numerical solutions.

Abstract

We study the contribution of advection by thermal velocity fluctuations to the effective diffusion coefficient in a mixture of two identical fluids. The steady-state diffusive flux in a finite system subject to a concentration gradient is enhanced because of long-range correlations between concentration fluctuations and fluctuations of the velocity parallel to the concentration gradient. The enhancement of the diffusive transport depends on the system size L and grows as \ln(L/L_{0}) in quasi-two dimensional systems, while in three dimensions it grows as L_{0}^{-1}-L^{-1}, where L_{0} is a reference length. The predictions of a simple fluctuating hydrodynamics theory, closely related to second-order mode-mode coupling analysis, are compared to results from particle simulations and a finite-volume solver and excellent agreement is observed. We elucidate the direct connection to the long-time tail of the velocity autocorrelation function in finite systems, as well as finite-size corrections employed in molecular dynamics calculations. Our results conclusively demonstrate that the nonlinear advective terms need to be retained in the equations of fluctuating hydrodynamics when modeling transport in small-scale finite systems.