Beyond Tanner's Law: Crossover between Spreading Regimes of a Viscous Droplet on an Identical Film

TL;DR

This paper investigates how polymer microdroplets level on thin films, revealing a crossover from Tanner's law to a different regime, with a theoretical model explaining the transition based on thin film hydrodynamics.

Contribution

It introduces a comprehensive theoretical model that captures the crossover between spreading regimes of viscous droplets on films of varying thickness.

Findings

Identifies a crossover in spreading behavior from Tanner's law to a different regime.

Develops a quantitative model based on thin film hydrodynamics.

Shows that leveling time depends on molecular properties, droplet size, and film thickness.

Abstract

We present results on the leveling of polymer microdroplets on thin films prepared from the same material. In particular, we explore the crossover from a droplet spreading on an infinitesimally thin film (Tanner's law regime) to that of a droplet leveling on a film thicker than the droplet itself. In both regimes, the droplet's excess surface area decreases towards the equilibrium configuration of a flat liquid film, but with a different power law in time. Additionally, the characteristic leveling time depends on molecular properties, the size of the droplet, and the thickness of the underlying film. Flow within the film makes this system fundamentally different from a droplet spreading on a solid surface. We thus develop a theoretical model based on thin film hydrodynamics that quantitatively describes the observed crossover between the two leveling regimes.