We study the contribution of advection by thermal velocity fluctuations to the effective diffusion coefficient in a mixture of two identical fluids. We find good agreement between a simple fluctuating hydrodynamics theory and particle and finite-volume simulations. The enhancement of the diffusive transport depends on the system size L and grows as ln(L/L0) in quasi-two-dimensional systems, while in three dimensions it scales as L0-1-L-1, where L0 is a reference length. Our results demonstrate that fluctuations play an important role in the hydrodynamics of small-scale systems.
Alejandro Garcia, A. Donev, A. de la Fuente, and J. B. Bell. "Diffusive Transport Enhanced by Thermal Velocity Fluctuations" Physical Review Letters (2011): 204501-1-204501-4. doi:http://dx.doi.org/10.1103/PhysRevLett.106.204501