Coarsening of dewetting thin ?lms subject to gravity

Thin films of viscous fluids coating hydrophobic substrates are unstable to dewetting instabilities, and long-time evolution leads to the formation of an array of near-equilibrium droplets connected by ultra-thin fluid layers. In the absence of gravity, previous use of lubrication theory has shown that coarsening dynamics will ensue -- the system will evolve by successively eliminating small drops to yield fewer larger drops. While gravity is expected to only have an influence on thicker films, we show that it has a significant influence on the coarsening dynamics of the problem, dramatically slowing the rate of coarsening for large drops. Small drops may be relatively unaffected, but as coarsening progresses, these aggregate into larger drops whose shape and dynamics are different.