Late stage kinetics for various wicking and spreading problems

TL;DR

This paper re-examines the late-stage kinetics of liquid spreading in various geometries, deriving scaling laws for droplet length and radius in wedges, networks, and strips, with predictions validated by theoretical analysis.

Contribution

It introduces new scaling laws for droplet spreading in wedge and network geometries, extending understanding of late-stage wetting dynamics.

Findings

Droplet length in a wedge scales as Omega^(1/5) * t^(2/5).

Radial spreading in a network scales as Omega^(1/6) * t^(1/3).

Height profile in a wedge is parabolic.

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.