We study the motion of a spherical particle driven by a constant volume force in a confined channel with a fixed square cross-section. The channel is filled with a mixture of two liquids under the effect of thermal fluctuations. We use the lattice Boltzmann method to simulate a fluctuating multicomponent fluid in the mixed-phase, and particle-fluid interactions are tuned to reproduce different wetting properties at the particle surface. The numerical set-up is first validated in the absence of thermal fluctuations; to this aim, we quantitatively compute the drift velocity at changing the particle radius and compare it with previous experimental and numerical data. In the presence of thermal fluctuations, we study the fluctuations in the particles velocity at changing thermal energy, applied force, particle size, and particle wettability. The importance of fluctuations with respect to the mean drift velocity is quantitatively assessed, especially in comparison to unconfined situations. Results show that confinement strongly enhances the importance of velocity fluctuations, which can be one order of magnitude larger than what expected in unconfined domains. The observed findings underscore the versatility of the lattice Boltzmann simulations in concrete applications involving the motion of colloidal particles in a highly confined environment in the presence of thermal fluctuations.
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