Particles in fluids

For finite Reynolds numbers the interaction of moving fluids with particles is still only understood phenomenologically. We will present various numerical studies. First we will introduce a numerical technique to simulate granular motion in a fluid. Particle trajectories are calculated by Newton's law and collisions are described by soft-sphere potentials. The fluid flow is calculated solving the Navier-Stokes equation. The momentum transfer is directly calculated from the stress tensor around particles. This scheme is validated calculating the drag coefficient, finding the limitations on the Reynolds number in mesh size and computer time. Then we discuss sedimentation of two particles and reproduce the "Draft, Kiss and Tumbled" effect showing that we can reproduce hydrodynamic interactions on the scale of the particle. The terminal velocity of particles is in good agreement with experiments and we recover the Richardson and Zaki law. We also will use the Lattice Boltzmann Method and the solver "Fluent" which elucidates this issue from different points of view. We show that the distribution of particle velocities inside a sheared fluid can be obtained over many orders of magnitude. We also consider the case of fixed particles, i.e. a porous medium and present the distribution of channel openings and fluxes. These distributions show a scaling law in the density of particles and for the fluxes follow an unexpected stretched exponential behaviour. The next issue will be filtering, i.e. the release of massive tracer particles within this fluid. Interestingly a critical Stokes number below which no particles are captured and which is characterized by a critical exponent of 1/2. Finally we will also show data on saltation, i.e. the fact that the motion of particles on a surface which are dragged by the fluid performs jumps. This is the classical aeolian transport mechanism responsible for dune formation. The empirical relations between flux and wind velocity are reproduced. Finally we also briefly discuss quicksand and its collapse.