  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.
