Late stage kinetics for various wicking and spreading problems

Abstract

The kinetics of spreading of a liquid drop in a wedge or V-shaped groove, in a network of such grooves, and on a hydrophilic strip, is re-examined. The length of a droplet of volume Omega spreading in a wedge after a time t is predicted to scale as Omega^(1/5) * t^(2/5), and the height profile is predicted to be a parabola in the distance along the wedge. If the droplet is spreading radially in a sparse network of V-shaped grooves on a surface, the radius is predicted to scale as Omega^(1/6) * t^(1/3), provided the liquid is completely contained within the grooves. A number of other results are also obtained.