Sedimentation of a non-Brownian dilute monodisperse suspension

We present a numerical simulation study of the homogeneous sedimentation of non-Brownian dilute suspensions of hard spheres. Attention is focused on the question if the steady sedimentation state is attainable in computer simulations of model systems with periodic boundary conditions. The low Reynolds number regime is considered, being the fluid flow induced by the motion of the suspended particles described by the stationary Stokes equation. The simulations were carried out using a fast version of the HYDROMULTIPOLE algorithm, which makes possible the analysis of the long-time dynamics of systems of hundreds of particles. The description of the hydrodynamic interactions between particles includes lubrication correction and higher-order multipole moments accounting for all long-range (non-integrable) contributions. The algorithm for numerical integration of the equations of motion incorporates an alternative scheme to displace the spheres in close relative motion, when short-range lubrication effects dominate. The evolution of suspensions with particle volume fraction φ = 0.05 has been simulated, starting from two different initial configurations. The stationary state, which is independent of the initial condition, has been reached. The sedimentation velocity and the short-range structure of the configurational distribution of the particles in the steady state agree with the predictions of the theory recently developed by Cichocki and Sadlej [Europhys. Lett. 72, 936 (2005)]. (authors)