Sedimentation of hard sphere suspensions at low Reynolds number using a lattice -Boltzmann method
Particle motion in a settling suspension is directly influenced by hydrodynamic interactions, such that the particle velocities will exhibit a random component, characterized by a hydrodynamically induced diffusion. Statistically, this means that the particles tend to be uniformly distributed within the bulk. Theoretical predictions for the sedimentation velocity in homogeneous suspensions are in good agreement with experiments. On the other hand, a calculation of the particle velocity fluctuations, based on the same assumptions, is in conflict with experimental results. Our main objective was to understand this discrepancy.
Numerical simulations have shown that dynamics within the bulk are not independent of the size of the container, even when the boundaries are located far away from the observation window. We hypothesized that density fluctuations in the bulk drain away to the suspension-sediment and suspension-supernatent interfaces. This generates a continual decay in velocity fluctuations, which is replenished by hydrodynamic diffusion due to short range multiparticle interactions. A balance between convective and diffusive transport of density fluctuations leads to a correlation length beyond which the velocity fluctuations are screened. Numerical results were found to support this hypothesis.
An examination of the microstructure as the suspension settled showed that it evolves toward a statistically nonrandom state, so that particles are distributed very uniformly at large length scales. We identified this result based on the observed damping of the structure factor, S( k) → k2 as k goes to zero.
Our numerical simulations show that the long-range correlations found in monodisperse suspensions are destroyed by small amounts of polydispersity, which are found in typical laboratory experiments. The variation in particle size also leads to a segregation of different sizes as the suspension settles. The net effect is a pronounced stratification of particle concentration at the supernatent front that persists into the bulk. Because of the stratification, the velocity fluctuations within the bulk do not have to convect toward the density gradients at the front; rather, the gradient is strong enough inside the bulk to create a sink for the velocity fluctuations.