We use a mesoscopic particle-based simulation technique to study the classic convection-diffusion problem of Taylor dispersion for colloidal discs in confined flow. When the disc diameter becomes non-negligible compared to the diameter of the pipe, there are important corrections to the original Taylor picture. For example, the colloids can flow more rapidly than the underlying fluid, and their Taylor dispersion coefficient is decreased. For narrow pipes, there are also further hydrodynamic wall effects. The long-time tails in the velocity autocorrelation functions are altered by the Poiseuille flow.

We apply a hybrid molecular dynamics and mesoscopic simulation technique to study the dynamics of two-dimensional colloidal disks in confined geometries. We calculate the velocity autocorrelation functions and observe the predicted t-1 long-time hydrodynamic tail that characterizes unconfined fluids, as well as more complex oscillating behavior and negative tails for strongly confined geometries. Because the t-1 tail of the velocity autocorrelation function is cut off for longer times in finite systems, the related diffusion coefficient does not diverge but instead depends logarithmically on the overall size of the system. The Langevin equation gives a poor approximation to the velocity autocorrelation function at both short and long times.

The crossover from single-file diffusion, where the mean-square displacement scales as 〈x²〉 ∼ t, to normal Fickian diffusion, where 〈x²〉 ∼ t, is studied as a function of channel width for colloidal particles. By comparing Brownian dynamics to a hybrid molecular dynamics and mesoscopic simulation technique, we can study the effect of hydrodynamic interactions on the single file mobility and on the crossover to Fickian diffusion for wider channel widths. For disc-like particles with a steep interparticle repulsion, the single file mobilities for different particle densities are well described by the exactly solvable hard-rod model. This holds both for simulations that include hydrodynamics, as well as for those that do not. When the single file constraint is lifted, then for particles of diameter σ and pipe of width L such that (L - 2σ)/σ = δ_c ≪ 1, the particles can be described as hopping past one-another in an average time t_hop. For shorter times t ≪ t _hop the particles still exhibit sub-diffusive behaviour, but at longer times t ≫ t_hop, normal Fickian diffusion sets in with an effective diffusion constant D_hop ∼ 1/√ t_hop. For the Brownian particles, t_hop ∼ δ_c ^-2 when δ_c ≪ 1, but when hydrodynamic interactions are included, we find a stronger dependence than δ_c^-2. We attribute this difference to short-range lubrication forces that make it more difficult for particles to hop past each other in very narrow channels.