Quantifying phase mixing and separation behaviors across length and time scales

Phase mixing and separation phenomena abound in a multiplicity of diverse material systems including composites, alloys, granular media, complex fluids, and biological tissues. While characterizing phase mixing is critical to understanding material microstructure formation, manufacturing methods, and physical properties, previous mixing metrics are only valid for special systems and fail to detect changes in mixing with respect to length scale, not to mention time scales. To improve upon the current state-of-the-art, we introduce and study a broadly applicable mixing metric that leverages the hyperuniformity concept, demonstrating that it provides the first unifying framework for systematically ranking and classifying mixing in materials across length and time scales. This task is accomplished by applying our metric to a diverse set of real and simulated material microstructures with varying degrees of order/disorder as well as distinct phase geometries and topologies. Our metric provides physically intuitive rankings of mixing in these example systems and is highly-sensitive to their salient dynamical features, including phase coarsening, separation, and transitions. We expect that our mixing metric can also be used to inform the design and discovery of materials with prescribed length- and time-dependent phase mixing or separation behaviors.