# Beading instability and spreading kinetics in grooves with convex curved sides

Source: [Beading instability and spreading kinetics in grooves with convex curved sides](<https://www.sota2.com/research/paper/68fa32cb1e209131ce88ad09>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:53:46.852Z

Authors: Patrick B Warren

Published: 2015-01-21T16:34:14.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1501.05220>)

[PDF](<https://arxiv.org/pdf/1501.05220.pdf>)