A two-dimensional similarity solution for capillary driven flows

This work describes a two-dimensional similarity solution of a viscous capillary flow in a thin film. The solution describes two confronted contact Lines which are being gradually welded by a point that advances at constant velocity along the common contact line. The liquid has a partial wetting contact angle cr with respect to the substrate. It is found that the capillary number is proportional to the cube of the contact angle, the proportionality factor being found with high accuracy. An important result is that the curvature diverges at the welding point, thus showing that a singular point may exist in a capillary driven flow. Also, the solution is immune to the contact line paradox, since the energy dissipation rate is bounded. (C) 1999 Published by Elsevier Science B.V. All rights reserved.