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 to describe the evolution of fluid domains in Langmuir films.
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