Velocity fluctuations and hydrodynamic diffusion in finite-Reynolds-number sedimenting suspensions

The velocity variance and the hydrodynamic diffusivity for a finite-Reynolds-number settling suspension are determined from lattice-Boltzmann simulations of many particles in cubic cells with periodic boundary conditions. The velocity variance is found to grow logarithmically with the size of the computational domain in contrast to the algebraic growth found in comparable Stokes-flow simulations. The growth rate and size of the velocity variance are found to be smaller than the theoretical prediction for a random suspension owing to a deficit in particle pair probability distribution in the wake of a test particle that screens the velocity disturbance felt by other particles. The particle velocity variance is smaller than the fluid velocity variance because a particle does not follow fluid motions on length scales comparable to or smaller than its own size. The hydrodynamic diffusivity of particles is proportional to the product of the root-mean-square velocity and the size of the computational domain. (C) 2008 American Institute of Physics.