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 study how varying the Péclet number (Pe) affects the steady state sedimentation of colloidal particles that interact through short-ranged attractions. By employing a hybrid molecular dynamics simulation method we demonstrate that the average sedimentation velocity changes from a non-monotonic dependence on packing fraction φ at low Pe numbers, to a monotonic decrease with φ at higher Pe numbers. At low Pe number the pair correlation functions are close to their equilibrium values, but as the Pe number increases, important deviations from equilibrium forms are observed. Although the attractive forces we employ are not strong enough to form permanent clusters, they do induce transient clusters whose behaviour is also affected by Pe number. In particular, clusters are more likely to fragment and less likely to aggregate at larger Pe numbers, and the probability of finding larger clusters decreases with increasing Pe number. Interestingly, the lifetime of the clusters is more or less independent of Pe number in the range we study. Instead, the change in cluster distribution occurs because larger clusters are less likely to form with increasing Pe number. These results illustrate some of the subtleties that occur in the crossover from equilibrium like to purely non-equilibrium behaviour as the balance between convective and thermal forces changes.

We use a mesoscopic simulation technique to study the effect of short-ranged interparticle attractions on the steady-state sedimentation of colloidal suspensions. Attractions increase the average sedimentation velocity vs compared to the pure hard-sphere case, and for strong enough attractions, a nonmonotonic dependence on the packing fraction φ with a maximum velocity at intermediate φ is observed. Attractions also strongly enhance hydrodynamic velocity fluctuations, which show a pronounced maximum size as a function of φ. These phenomena arise from a complex interplay between nonequilibrium hydrodynamic effects and the thermodynamics of transient cluster formation.

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.

We apply a hybrid molecular dynamics and mesoscopic simulation technique to study the steady-state sedimentation of hard sphere particles for Peclet number (Pe) ranging from 0.08 to 12. Hydrodynamic backflow causes a reduction of the average sedimentation velocity relative to the Stokes velocity. We find that this effect is independent of Pe number. Velocity fluctuations show the expected effects of thermal fluctuations at short correlation times. At longer times, nonequilibrium hydrodynamic fluctuations are visible, and their character appears to be independent of the thermal fluctuations. The hydrodynamic fluctuations dominate the diffusive behavior even for modest Pe number, while conversely the short-time fluctuations are dominated by thermal effects for surprisingly large Pe numbers. Inspired by recent experiments, we also study finite sedimentation in a horizontal planar slit. In our simulations distinct lateral patterns emerge, in agreement with observations in the experiments.

We describe in detail how to implement a coarse-grained hybrid molecular dynamics and stochastic rotation dynamics simulation technique that captures the combined effects of Brownian and hydrodynamic forces in colloidal suspensions. The importance of carefully tuning the simulation parameters to correctly resolve the multiple time and length scales of this problem is emphasized. We systematically analyze how our coarse-graining scheme resolves dimensionless hydrodynamic numbers such as the Reynolds number Re, which indicates the importance of inertial effects, the Schmidt number Sc, which indicates whether momentum transport is liquidlike or gaslike, the Mach number, which measures compressibility effects, the Knudsen number, which describes the importance of noncontinuum molecular effects, and the Peclet number, which describes the relative effects of convective and diffusive transport. With these dimensionless numbers in the correct regime the many Brownian and hydrodynamic time scales can be telescoped together to maximize computational efficiency while still correctly resolving the physically relevant processes. We also show how to control a number of numerical artifacts, such as finite-size effects and solvent-induced attractive depletion interactions. When all these considerations are properly taken into account, the measured colloidal velocity autocorrelation functions and related self-diffusion and friction coefficients compare quantitatively with theoretical calculations. By contrast, these calculations demonstrate that, notwithstanding its seductive simplicity, the basic Langevin equation does a remarkably poor job of capturing the decay rate of the velocity autocorrelation function in the colloidal regime, strongly underestimating it at short times and strongly overestimating it at long times. Finally, we discuss in detail how to map the parameters of our method onto physical systems and from this extract more general lessons-keeping in mind that there is no such thing as a free lunch-that may be relevant for other coarse-graining schemes such as lattice Boltzmann or dissipative particle dynamics.

We show how to implement stick boundary conditions for a spherical colloid in a solvent that is coarse-grained by the method of stochastic rotation dynamics. This allows us to measure colloidal rotational velocity auto-correlation functions by direct computer simulation. We find quantitative agreement with Enskog theory for short times and with hydrodynamic mode-coupling theory for longer times. For aqueous colloidal suspensions, the Enskog contribution to the rotational friction is larger than the hydrodynamic one when the colloidal radius drops below 35 nm.

The interplay between hydrodynamic and Brownian fluctuations during steady-state sedimentation of hard sphere particles for Peclet numbers (Pe) ranging from 0.1-15 was studied using a mesoscopic computer simulation. A stochastic rotation dynamics (SRD) to the problem of sedimenting HS was adapted to perform the simulations. It was shown that the hydrodynamic interactions (HI) induce backflow effects that dominate the reduction of the average sedimentation velocity with increasing particle packing fraction, even when the they were an order of magnitude weaker than Brownian forces. It was observed that the velocity fluctuations begin to show nonequilibrium hydrodynamic character for Pe>1.