Sedimentation of non-Brownian spheres at high volume fractions

We performed direct numerical simulations of non-Brownian sedimenting particles, using a smooth profile method over a wide range of volume fractions from 0.01 to 0.5. We found that hydrodynamic velocity fluctuations scale as phi(1/2), both parallel and perpendicular to gravity at low volume fractions (phi <= 0.04) due to anisotropic microstructure and decay with further increase in phi because of many body hydrodynamic interactions. Unlike velocity fluctuations, vertical relaxation times scale as phi(-1/2) for the full range of volume fractions, whereas horizontal relaxation times decrease as phi(-1/2) at low volume fractions, remain unchanged and then decrease sharply at high volume fractions. Similarly, horizontal and vertical diffusion coefficients increase as phi(1/2) at low volume fractions. Moreover, vertical diffusion decays with further increase in phi, whereas horizontal diffusion remains unchanged and then decreases. The microstructure analysis of the suspension showed that at low volume fractions the anisotropic microstructure determines the transport properties and at phi > 0.12 many body interactions govern the system properties, whereas a cross-over exists in between these two regimes.