Self-similar flow and contact line geometry at the rear of cornered drops

Partially wetting drops sliding down an inclined plane develop a "corner singularity" at the rear, consisting of two dynamic contact lines that intersect. We analyze the three-dimensional flow in the vicinity of this singularity by exploring similarity solutions of the lubrication equations. These predict a self-similar structure of the velocity field, in which the fluid velocity does not depend on the distance to the corner tip; this is verified experimentally by particle image velocimetry. The paper then addresses the small-scale structure of the corner, at which the singularity is regularized by a nonzero radius of curvature R of the contact line. Deriving the lubrication equation up to the lowest order in 1/R, we show that contact line curvature postpones the destabilization of receding contact lines to liquid deposition, and that 1/R increases dramatically close to the "pearling" instability. The general scenario is thus that sliding drops avoid a forced wetting transition by forming a corner of two inclined contact lines, which is regularized by a rounded section of rapidly decreasing size. (c) 2005 American Institute of Physics.