Coarsening rates for the dynamics of slipping droplets
European Journal of Applied Mathematics, vol.25, no.1, pp.83-115, 2014 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 25 Issue: 1
- Publication Date: 2014
- Doi Number: 10.1017/s0956792513000314
- Journal Name: European Journal of Applied Mathematics
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.83-115
- Keywords: Absorption model, Asymptotic analysis, Coarsening rates, Droplet collisions, Free films, Lubrication equations, Wall slippage
- Middle East Technical University Northern Cyprus Campus Affiliated: No
Abstract
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. Copyright © Cambridge University Press 2013.