Coalescence Dynamics of Fluids in Two Dimensions: Merging of Islands in Freely-Suspended Smectic Films*

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 study the coalescence of islands, thicker, disk-shaped regions of the film bounded by edge dislocations. The early time growth of the bridge connecting the merging islands is essentially linear, while at long times the relaxation dynamics are exponential. The observations are compared with Hopper’s classical hydrodynamic model of the coalescence of two infinitely long, fluid cylinders [Journal of the American Ceramic Society 76, 2947 (1993)] and with models appropriate to quasi-two dimensional fluids developed by Mann [ Phys. Rev. E 51, 5708 (1995)] and Camley [Biophysical Journal 99, L44 (2010)] to explain their observations of domain relaxation in Langmuir films.