We study many-particle diffusion in 2D colloidal suspensions with full hydrodynamic interactions through a novel mesoscopic simulation technique. We focus on the behaviour of the effective scaled tracer and collective-diffusion coefficients DT(rho)/D0 and DC(rho)/D0 respectively, where D0 is the single-particle diffusion coefficient, as a function of the density of the colloids rho. At low Schmidt numbers Sc - 1, we find that hydrodynamics has essentially no effect on the behaviour of DT (rho)/D0. At larger Sc, DT (rho)/D0 seems to be enhanced at all densities, although the differences compared to the case without hydrodynamics are rather minor. The collective-diffusion coefficient, on the other hand, is much more strongly coupled to hydrodynamical conservation laws and is distinctly different from the purely dissipative case without hydrodynamic interactions.

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We study the submonolayer diffusion of hard disks and rodlike molecules on smooth surfaces through numerical simulations and theoretical arguments. We concentrate on the behavior of the various diffusion coefficients as a function of the two-dimensional ͑2D͒ number density in the case where there are no explicit surface-particle interactions. For the hard disk case, we find that while the tracer diffusion coefficient D T ( ) decreases monotonically up to the freezing transition, the collective diffusion coefficient D C ( ) is wholly determined by the inverse compressibility which increases rapidly on approaching freezing. We also study memory effects associated with tracer diffusion, and present theoretical estimates of D T ( ) from the modemode coupling approximation. In the case of rigid rods with short-range repulsion and no orientational ordering, we find behavior very similar to the case of disks with the same repulsive interaction. Both D T ( ) and the angular diffusion coefficient D R ( ) decrease with . Also in this case D C ( ) is determined by inverse compressibility and increases rapidly close to freezing. This is in contrast to the case of flexible chainlike molecules in the lattice-gas limit, where D C ( ) first increases and then decreases as a function of the density due to the interplay between compressibility and mobility.

We study the steady-state dynamics of sedimenting non-Brownian particles in confined geometries with full hydrodynamic interactions at small but finite Reynolds numbers. We employ extensive computer simulations using a method where a continuum liquid phase is coupled through Stokesian friction to a discrete particle phase. In particular, we consider a sedimentation box which is otherwise periodic except that it is confined by two parallel walls parallel to gravity with a spacing L x . By systematically varying L x we explore the change in dynamics from a quasi-two-dimensional (2D) case to a three-dimensional case. We find that in such confined geometries there is a depletion of particle number density at the walls for small volume fractions, while for large volume fractions there is an excess number of particles at the walls. For the average sedimentation velocity, we find that the Richardson-Zaki law is well obeyed but the decrease of the velocity for dilute systems is slower for smaller values of L x . We study the anisotropy of the velocity fluctuations and find that in the direction of gravity there is excellent agreement with the predicted scaling with respect to L x . We also find that the behavior of the corresponding diffusion coefficients as a function of L x is qualitatively different in the direction parallel to gravity and perpendicular to it. In the quasi-2D limit where particles block each other, the velocity fluctuations behave differently from the other confined systems.

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