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The coarsening kinetics for the beading instability for liquid contained in agroove with convex curved sides (for example between a pair of paralleltouching cylinders) is considered as an open channel flow problem. In contrastto a V-shaped wedge or U-shaped microchannel, it is argued that dropletcoarsening takes place by viscous hydrodynamic transport through a stablecolumn of liquid that coexists with the droplets in the groove at a slightlypositive Laplace pressure. With some simplifying assumptions, this leads to at^(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 remarksare also made on the spreading kinetics of an isolated drop deposited in such agroove.

Beading instability and spreading kinetics in grooves with convex curved sides