### Coarsening Dynamics of Two-Phase Mixtures

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John Gibbs, Northwestern University
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The presence of interfaces within a system increases the total energy of the system. This results in coarsening, a phenomenon in which the structure of the system evolves over time in a way that minimizes the total interfacial area, and therefore the total energy of the system. Coarsening in a system of spherical particles in a matrix has been well studied, both analytically and experimentally, and has been shown to result in an increase in the average particle size and a decrease in the total number of particles; thus, the total volume of the spheres remains constant but their surface area decreases. In contrast to this simple, well-known behavior of spherical particles, the coarsening behavior for systems with more intricate interfacial shapes is complex and relatively unknown. To study the effect of morphological complexity of the interfaces on the dynamics of coarsening, time-resolved, 3-D measurements of the structure are made using X-ray computed tomography. This allows for in-situ measurement of the interfacial locations, which can be used to compute the shape and velocity of individual interfaces. Two-phase mixtures of liquid and solid aluminum are used for these experiments because the nearly isotropic interfacial energy of this system makes it easy to generalize the findings to many other two-phase mixtures. Trends in the distribution and evolution of interfacial shapes and velocities are compared across different ratios of volume fraction of solid to liquid, highlighting different regimes of coarsening behavior, and comparisons between different times are made to show the self-similarity of the structures. Trends in the distribution of velocities for a given interfacial shape will be shown. Despite the complexities of diffusion that are required for interfacial motion, these distributions appear to be Gaussian with a predictable mean and standard deviation.

**Abstract Author(s): **John W. Gibbs, Peter W. Voorhees