Diffusive Transport Enhanced by Thermal Velocity Fluctuations

TL;DR

This paper investigates how thermal velocity fluctuations enhance diffusion in fluid mixtures, revealing size-dependent effects and emphasizing the importance of nonlinear terms in fluctuating hydrodynamics for small systems.

Contribution

It provides a theoretical and computational analysis of fluctuation-induced diffusion enhancement, highlighting the necessity of nonlinear advective terms in small-scale modeling.

Findings

Diffusive enhancement depends on system size, scaling as ln(L/L_0) in 2D.

In 3D, enhancement scales as L_0^{-1}-L^{-1}.

Fluctuating hydrodynamics predictions agree with simulations.

Abstract

We study the contribution of advection by thermal velocity fluctuations to the effective diffusion coefficient in a mixture of two indistinguishable fluids. 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 scales as L_0^{-1}-L^{-1}, where L_0 is a reference length. The predictions of a simple fluctuating hydrodynamics theory are compared to results from particle simulations and a finite-volume solver and excellent agreement is observed. 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.