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Fluctuation-dissipation relation from a FLB-BGK model

A two-dimensional colloidal fluctuating lattice-Boltzmann (FLB-BGK) model was formulated by adopting the most popular version of the fluctuating lattice-Boltzmann algorithm in the literature and explicitly incorporating the finite size and shape of particles. In this formulation, random noise was added to the fluid to simulate thermal fluctuations of the fluid at mesoscopic length scales. The resulting random perturbations acting on the particle surface were responsible for particle Brownian motion. FLB-BGK simulations with a thermally perturbed fluid in a confined channel involving a Brownian particle near a channel wall displayed perfect equipartitioning and thermalization in the absence of any external force. The simulations captured a crossover from a ballistic regime to a diffusive regime at which particle velocity autocorrelation vanished. FLB-BGK simulations with an inert particle in thermally perturbed, creeping or low-medium Reynolds number flows in confined channels showed that particle motion obeyed the fluctuation-dissipation theorem if the wall effects on particle motion were absent or small. On the other hand, the fluctuation-dissipation theorem was found not to hold in the presence of significant wall effects on particle motion.