Three-dimensional lubrication model of a contact line corner singularity

¹ Laboratoire de Physique et de Mécanique des Milieux Hétérogènes and Fédération de Recherche Matière et Système Complexes (UMR 7636 and FR 2438 of CNRS), ESPCI 10 rue Vauquelin, 75005 Paris, France
² Division of Engineering and Applied Sciences, Harvard University Cambridge MA 02138, USA

Received: 26 June 2003
Accepted: 24 November 2003

Abstract

Drops sliding along inclined planes in situations of partial wetting develop a “corner” at the back of the drop, similar to contact line shapes observed on plates withdrawn from a bath. We discuss, in the framework of lubrication theory, the 3D structure of this corner singularity: similarity solutions exist such that the interface adopts the shape of a cone, with well-defined relationships linking its two characteristic angles. Near both contact lines forming the corner, the solution reduces to the well-known lubrication solution for a single contact line, with an effective capillary number involving the normal component of the contact line velocity.