### Abstract

We derive reduced ODE models starting from one dimensional lubrication equations describing coarsening dynamics of droplets in nanometric polymer film interacting on a hydrophobically coated solid substrate in the presence of large slippage at the liquid/solid interface. In the limiting case of the infinite slip length corresponding in applications to free films a collision/absorption model then arises and is solved explicitly. The exact coarsening law is derived for it analytically and confirmed numerically. Existence of a threshold for the decay of initial distributions of droplet distances at infinity at which the coarsening rates switch from algebraic to exponential ones is shown.

### Related Links

- http://www.mis.mpg.de/de/publications/preprints/2012/2012-38.html - preprint of the article