Coarsening rates for the dynamics of slipping droplets

TL;DR

This paper develops reduced ODE models from lubrication equations to analyze droplet coarsening dynamics on slippery substrates, deriving explicit coarsening laws and identifying thresholds for different decay regimes.

Contribution

It introduces a novel reduced model for droplet coarsening with large slip, providing explicit coarsening laws and thresholds for decay regimes.

Findings

Explicit coarsening law derived and confirmed numerically.

Existence of a threshold for decay regimes identified.

Collision/absorption model solved explicitly in the infinite slip limit.

Abstract

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.