Contact line stability of ridges and drops

¹  Laboratoire de Physique Théorique de la Matière Condensée, Université Pierre et Marie Curie Tour 24, Boîte 121, 4 place Jussieu, F-75252 Paris 05, France
²  Laboratoire de Physique Statistique de l'Ecole Normale Supérieure - 24 rue Lhomond, F-75231 Paris 05, France
³  Max-Planck-Institut für Metallforschung - Heisenbergstr. 3, D-70569 Stuttgart, Germany
⁴  Institut für Theoretische und Angewandte Physik, Universität Stuttgart - Pfaffenwaldring 57, D-70569 Stuttgart, Germany
⁵  Max-Planck-Institut für Dynamik und Selbstorganisation - Bunsenstr. 10, D-37073 Göttingen, Germany

Corresponding author: rauscher@mf.mpg.de

Received: 24 July 2007
Accepted: 23 October 2007

Abstract

Within the framework of a semi-microscopic interface displacement model in the small slope approximation 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.