Coarsening rates for the dynamics of slipping droplets
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Submission date: 04. Jul. 2012
published in: European journal of applied mathematics, 25 (2014), p. 83-115
DOI number (of the published article): 10.1017/S0956792513000314
MSC-Numbers: 35B36, 35G20, 35Q35
PACS-Numbers: 68.15.+e, 83.50.Rp, 02.30.Jr
Keywords and phrases: coarsening rates, collision and absorbtion, lubrication equations, slippage, free films
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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.