The evolution of interfacial topology during coarsening

Quantitative characterization of coarsening is achieved through topological measurements such as the genus, the number of handles, and the number of independent bodies (liquid droplets). Topological analysis was performed on experimentally derived, three-dimensional reconstructions of dendritic microstructures. Measured topological quantities were reported on a per volume basis and scaled by the length scale of the system to remove effects of the changing length scale during coarsening. The scaled genus decreased with coarsening time due to the simplification of the topology of the microstructure, while the number of liquid droplets increased with coarsening time. These results were supplemented with calculations of the interfacial velocity determined using phase-field simulations that employ the experimental three-dimensional reconstructions as the initial condition. Through these calculations it is shown that liquid droplets form through capillary-driven instabilities of interconnected liquid channels, while liquid tubes are created through topological singularities occurring on large planar-like walls of liquid.