Beading instability and spreading kinetics in grooves with convex curved sides

TL;DR

This paper investigates the coarsening and spreading behavior of liquid droplets in grooves with convex curved sides, revealing a specific growth law for droplet size over time based on viscous hydrodynamics.

Contribution

It introduces a new model for droplet coarsening in convex grooves, deriving a t^(1/7) growth law and analyzing spreading kinetics, expanding understanding beyond traditional wedge geometries.

Findings

Droplet size grows as t^(1/7) over time.

Droplet line density decreases as t^(-3/7).

Spreading kinetics of isolated drops are discussed.

Abstract

The coarsening kinetics for the beading instability for liquid contained in a groove with convex curved sides (for example between a pair of parallel touching cylinders) is considered as an open channel flow problem. In contrast to a V-shaped wedge or U-shaped microchannel, it is argued that droplet coarsening takes place by viscous hydrodynamic transport through a stable column of liquid that coexists with the droplets in the groove at a slightly positive Laplace pressure. With some simplifying assumptions, this leads to a t^(1/7) growth law for the characteristic droplet size as a function of time, and a t^(-3/7) law for the decrease in the droplet line density. Some remarks are also made on the spreading kinetics of an isolated drop deposited in such a groove.