The lattice-Boltzmann method has been refined to take account of near-contact interactions between spherical particles. First, we describe a comprehensive solution to the technical problems that arise when two discretized surfaces come into contact. Second, we describe how to incorporate lubrication forces and torques into lattice-Boltzmann simulations, and test our method by calculating the forces and torques between a spherical particle and a plane wall. Third, we describe an efficient update of the particle velocities, taking into account the possibility that some of the differential equations are stiff.

Lattice-Boltzmann simulations have been used to investigate low-Reynolds-number settling of monodisperse and polydisperse suspensions. We confirm the discovery that particle velocity fluctuations are strongly suppressed by no-slip walls at the top and bottom of the system, even in regions distant from the boundaries. We also show that a monodisperse suspension develops a strongly anisotropic long-range microstructure during the settling process, with vanishing density fluctuations in the horizontal plane. We find no numerical evidence that the particle concentration in the bulk is stratified; diffusive spreading of the suspension-supernatant interface is suppressed by hindered settling, as would be expected in moderately concentrated suspensions. Long-range correlations in particle density fluctuations are destroyed by polydispersity in particle size, and in this case density fluctuations are finite at all length scales and in all directions. However, in polydisperse suspensions there is significant stratification, due to differential settling rather than interface diffusion, which provides an alternative mechanism for screening the hydrodynamic interactions. It is possible that this is the dominant mechanism for hydrodynamic screening in several laboratory experiments.

We report direct observations of the structure factor in a settling suspension, using numerical simulations based on a lattice-Boltzmann model of the fluid. We find that the horizontal density fluctuations in bounded suspensions are strongly suppressed by the settling process, vanishing as k(2) at long wavelengths. Our measurements of the structure factor confirm the qualitative predictions of one of several competing theories, although this theory does not yet explain why container walls are so important. Our results contradict the idea that a settling suspension is inevitably stratified by hydrodynamic dispersion at the suspension-supernatent interface.

Molecular simulations are carried out to determine the elastic stability limits of polyethylene and n-alkane crystals under external stresses. For polyethylene, the instability that occurs at the lowest critical stress corresponds to planes of polymer chains perpendicular to the a-axis being shifted along the c-axis (which is the chain axis); this simulation result concurs with the previous experimental result that (100)[001] crystallographic slip is the dominant plastic deformation mechanism in polyethylene crystals. For n-alkane crystals, the stability of the crystal with respect to isotropic tensile stress is greater for n-alkanes with even numbers of carbon atoms, due to more favorable packing at the chain ends. This odd-even effect in the elastic stability is related to the well-known odd-even effect in the melting temperatures of n-alkane crystals.