Collective drag and sedimentation: Comparison of simulation and experiment in two and three dimensions

We simulate systems of particles immersed in fluid at Reynolds numbers on the particle scale of 0.1 to 20. Our simulation method is based on a finite differencing multi-grid Navier-Stokes solver for the fluid and a molecular dynamics technique for the particle motion. The mismatch between the fixed rectangular grid and the spherical particle shape is taken into account by considering analytical series expansions of the pressure and velocity of the fluid in the vicinity of the particle surface. We give an expression for the force on a particle in terms of the expansion coefficients. At each time step these coefficients are determined from pressure and velocity values on the fluid grid. We demonstrate the validity of our approach by performing numerical simulations of flow through porous solid beds and of bulk sedimentation in two and three spatial dimensions. We compare our results to experimental data and analytical results. Quantitative agreement is found in situations where the volume fraction remains below approximately 0.25 both in two and three dimensions, provided that at the same time the Reynolds number remains below about 10. In contrast, e.g., to finite-element techniques the method remains fast enough to allow dynamical simulations of particle-fluid systems with several hundred spheres on workstations taking all inertial effects into account.