Post-Tanner stages of droplet spreading: the energy balance approach revisited

TL;DR

This paper revisits the energy balance approach to droplet spreading, incorporating line tension effects to explain various late-stage behaviors such as pancake formation and accelerated spreading, reconciling previous conflicting observations.

Contribution

It introduces a revised energy balance model that includes line tension, explaining different late-stage spreading behaviors of droplets on substrates.

Findings

Positive line tension leads to pancake-like shapes.

Negative line tension causes accelerated spreading.

The model unifies different late-stage spreading regimes.

Abstract

The spreading of a circular liquid drop on a solid substrate can be described by the time evolution of its base radius R(t). In complete wetting the quasistationary regime (far away from initial and final transients) typically obeys the so-called Tanner law, with R t^alpha_T, alpha_T=1/10. Late-time spreading may differ significantly from the Tanner law: in some cases the drop does not thin down to a molecular film and instead reaches an equilibrium pancake-like shape; in other situations, as revealed by recent experiments with spontaneously spreading nematic crystals, the growth of the base radius accelerates after the Tanner stage. Here we demonstrate that these two seemingly conflicting trends can be reconciled within a suitably revisited energy balance approach, by taking into account the line tension contribution to the driving force of spreading: a positive line tension is responsible for the formation of pancake-like structures, whereas a negative line tension tends to lengthen the contact line and induces an accelerated spreading (a transition to a faster power law for R(t) than in the Tanner stage).