Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2011-03-27
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
Draft; please send comments to corresponding author. For a concise summary, see arXiv:1103.5532
Scientific paper
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.
Bell John B.
Donev Aleksandar
García Abey López
la Fuente Anton de
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