Contact line stability of ridges and drops

TL;DR

This paper investigates the stability of liquid ridges and drops on substrates, revealing that drops are stable while ridges tend to break up into droplets due to long-wavelength instabilities, challenging previous capillary model predictions.

Contribution

It introduces a semi-microscopic model analyzing contact line stability, showing that short-wavelength instabilities are spurious and only long-wavelength Rayleigh-Plateau instability affects ridges.

Findings

Drops are generally stable under perturbations.

Ridges undergo Rayleigh-Plateau instability leading to breakup.

Short-wavelength instabilities predicted by capillary models are invalid.

Abstract

Within the framework of a semi-microscopic interface displacement model we analyze the linear stability of sessile ridges and drops of a non-volatile liquid on a homogeneous, partially wet substrate, for both signs and arbitrary amplitudes of the three-phase contact line tension. Focusing on perturbations which correspond to deformations of the three-phase contact line, we find that drops are generally stable while ridges are subject only to the long-wavelength Rayleigh-Plateau instability leading to a breakup into droplets, in contrast to the predictions of capillary models which take line tension into account. We argue that the short-wavelength instabilities predicted within the framework of the latter macroscopic capillary theory occur outside its range of validity and thus are spurious.