Beading instability and spreading kinetics in grooves with convex curved sides

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.