  Ensembles of interacting drops that slide down an inclined plate show a
dramatically different coarsening behavior as compared to drops on a horizontal
plate: As drops of different size slide at different velocities, frequent
collisions result in fast coalescence. However, above a certain size individual
sliding drops are unstable and break up into smaller drops. Therefore, the
long-time dynamics of a large drop ensemble is governed by a balance of merging
and splitting. We employ a long-wave film height evolution equation and
determine the dynamics of the drop size distribution towards a stationary state
from direct numerical simulations on large domains. The main features of the
distribution are then related to the bifurcation diagram of individual drops
obtained by numerical path continuation. The gained knowledge allows us to
develop a Smoluchowski-type statistical model for the ensemble dynamics that
well compares to full direct simulations.
