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Coarsening rates for the dynamics of slipping droplets
We derive reduced finite dimensional 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 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
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