Ensembles of interacting drops that slide down an inclined plate show adramatically different coarsening behavior as compared to drops on a horizontalplate: As drops of different size slide at different velocities, frequentcollisions result in fast coalescence. However, above a certain size individualsliding drops are unstable and break up into smaller drops. Therefore, thelong-time dynamics of a large drop ensemble is governed by a balance of mergingand splitting. We employ a long-wave film height evolution equation anddetermine the dynamics of the drop size distribution towards a stationary statefrom direct numerical simulations on large domains. The main features of thedistribution are then related to the bifurcation diagram of individual dropsobtained by numerical path continuation. The gained knowledge allows us todevelop a Smoluchowski-type statistical model for the ensemble dynamics thatwell compares to full direct simulations.
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