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Coarsening rates for the dynamics of slipping droplets

Published online by Cambridge University Press:  04 September 2013

GEORGY KITAVTSEV
GEORGY KITAVTSEV*
Affiliation:
Max-Planck Institute for Mathematics in the Sciences, Inselstraße 22, 04103 Leipzig, Germany email: georgy.kitavtsev@mis.mpg.de
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Abstract

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Reduced ordinary differential equation (ODE) models arising from a high-order lubrication system and 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 are analysed. 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.

Keywords

Coarsening ratesWall slippageDroplet collisionsAbsorption modelLubrication equationsFree filmsAsymptotic analysis
Type
Papers
Information
European Journal of Applied Mathematics , Volume 25 , Issue 1 , February 2014 , pp. 83 - 115
Copyright
Copyright © Cambridge University Press 2013 

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