Abstract

Solid-liquid mixtures produced following dendritic solidification are morphologically complex with spatially varying mean and Gaussian interfacial curvature. The morphology and topology of these mixtures set the properties of these systems, such as the permeability of the mush. The structure of the mush is determined by coarsening, a process wherein regions of interface with large curvature grow at the expense of regions of interface with small curvature. To understand the manner in which these systems evolve during coarsening, we have employed in-situ three-dimensional x-ray tomography and phase-field simulations. The evolution of the interface shape distribution, the probability of finding a patch of interface with a certain mean and Gaussian curvature, is determined. The experiments also show the importance of topological singularities, such as the pinching of tubes of liquid, in the coarsening process. We find that the experimentally determined temporal power law governing the pinching process agrees with theory. We will also discuss the evolution of the genus, or Euler characteristic, of the interfaces during coarsening.