Collision rate of spheroids in turbulence

Abstract

Collisions of particles are of great importance in different processes in fluid flows, like water droplets colliding in cumulus clouds forming rain, but also dust grains that eventually form a planet. As a continuation of work that was done on spherical particles I studied the collision rate of small spheroids in three qualitatively different flows, namely in the kinetic limit, where particles move ballistically, in the shear flow, where particles move uniformly, but can overtake each other, and in a smooth random flow, which is a model for the small scales in turbulence. A corresponding theoretical model that describes the two-dimensional collision rate was presented and compared to simulation results. It was found that the particle shape has a great influence on the collision rate in all cases. In general an increasing elongation leads to a higher collision rate, while the two-dimensional shear flow was found to be an exception in the sense that the collision rate approaches zero instead. Threedimensional systems were investigated by simulations but not supported by a theory.