A lattice Boltzmann study on Brownian diffusion and friction of a particle in a confined multicomponent fluid

TL;DR

This study uses fluctuating lattice Boltzmann models to analyze how a small particle diffuses and experiences friction in a confined, multicomponent fluid, highlighting the effects of boundary conditions and wettability on particle dynamics.

Contribution

It introduces a numerical approach combining fluctuating lattice Boltzmann models with confinement effects to accurately predict particle diffusivity and friction in multicomponent fluids.

Findings

Periodic boundary conditions induce random advection over time.

Wall boundary conditions reduce advection effects.

Matching the Stokes-Einstein relation requires considering confinement effects.

Abstract

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)