Three-dimensional lubrication model of a contact line corner singularityL. Limat1 and H. A. Stone2
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 in final form 24 November 2003)
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of partial wetting develop a "corner" at the back of the drop, similar to contact line shapes observed on plates withdrawn from a bath.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.
68.08.Bc - Wetting.
47.15.Gf - Low-Reynolds-number (creeping) flows.
68.15.+e - Liquid thin films.
© EDP Sciences 2004