Computational investigation of the clustering of droplets in widening pipe geometries

Experimentally, periodically released droplets in systems of widening pipes show clustering. This is surprising, as purely hydrodynamic interactions are repulsive so that agglomeration should be prevented. In the main part of this paper, we investigate the clustering of droplets under the influence of phenomenological hydrostatic forces and some hypothetical attraction. In two appendices, we explain why a direct numerical simulation for this system is rather more difficult (and probably not possible with current methods) than the “simple” geometry would suggest.