  Smectic liquid crystal films a few molecular layers thick that are freely
suspended in air are used as a model system to study the coalescence of fluids
in two dimensions. High-speed video microscopy is used to observe the
coalescence of islands, which are thicker, disk-shaped regions of the film, in
a process driven by the line tension associated with edge dislocations along
the island boundaries and limited by viscous dissipation in the liquid crystal
and in the surrounding air. The early time growth of the bridge connecting the
merging islands reveals much slower dynamics than predicted by Hopper's
classical hydrodynamic model of coalescence of two infinitely long, fluid
cylinders in vacuum, a discrepancy proposed to be due to significant
dissipation in the background film and in the air that is not included in
Hopper's theory. At late times, the elliptical merged island relaxes
exponentially to a circular shape, at rates that are described quantitatively
by a model originally developed for the evolution of fluid domains in Langmuir
films.
