  We study the diffusivity of a small particle immersed in a square box filled
with a non-ideal multicomponent fluid in the presence of thermal fluctuations.
Our approach is based on the numerical integration of fluctuating lattice
Boltzmann models (LBM) for multicomponent mixtures. At changing the wettability
on the particle's surface, we measure the mean square displacement (MSD) and
compare with the prediction of the Stokes-Einstein theory. Two main set-ups are
tested, involving periodic boundary conditions and wall boundary conditions
realized on the computational box. We find that full periodic boundary
conditions give rise to random advection after millions of lattice Boltzmann
time steps, while this effect is mitigated in the presence of wall boundary
conditions. The matching with the Stokes-Einstein relation is therefore
guaranteed when we use the appropriate frictional properties measured in the
presence of confinement. Our results will help the exploration of nanoscale
applications with multicomponent fluids using LBM in the presence of thermal
fluctuations. (This paper has been published in Journal of Computational
Science)

Fluid Dynamics