Coarsening rates for the dynamics of slipping droplets

Kitavtsev G.

European Journal of Applied Mathematics, vol.25, no.1, pp.83-115, 2014 (SCI-Expanded) identifier identifier

  • 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.