Phase Transitions in Composite Media

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GoldenDMS-1009704 The investigator and his colleagues conduct fundamentalmathematical and numerical studies of phase transitions incomposite materials, with applications to electrorheological (ER)fluids and sea ice, which share similar microstructural features. They develop a statistical mechanics framework in which suchtransitions can be studied, and explore random matrixcharacterizations of composite microstructures and theirevolution. One central problem to be addressed is the existenceof a critical electric field necessary to induce the fluid/solidtransition in ER fluids. They anticipate that this phenomenongoes beyond classical phase transitions in statistical mechanics,representing a new type of transitional mechanism that depends ona competition between geometrical entropy and electrical energy. They also study the fluid transport and related microstructuraltransition in sea ice, which plays a key role in Earth's climatesystem. Such microstructures can be identified with randommatrices, and the investigators study the evolution ofmicrostructural features with such techniques. Composite materials arise throughout the physical andbiological sciences and across most types of engineering. One ofthe key features of these types of problems is the criticaldependence of the effective material properties on the parameterscharacterizing the system. For example, an electrorheological(ER) fluid is a suspension of particles in a viscous fluid suchas oil. If an applied electric field exceeds a critical valuethen the particles form chains and the suspension undergoes afluid/solid transition within milliseconds. This electricallyinduced transition has been used in applications including nextgeneration clutches, brakes, micro-fluidic valves, and humanprosthetics. Another example is sea ice, a composite of pure icewith brine inclusions, which plays a key role in Earth's climatesystem. If the temperature exceeds a critical value, then fluidcan flow through the ice. This transition mediates a broad rangeof processes in the polar ice packs that are fundamental tomaking better predictions of climate change. The investigatorand colleagues conduct fundamental mathematical and numericalstudies of these transitions in ER fluids and sea ice. Theybring to bear sophisticated techniques of theoretical statisticalphysics to better understand the behavior of these types ofmaterials. Through these studies, the investigator anticipatesthe development of applications to other high-tech composites andto other areas critical to our understanding of polar climatechange. The project is cofunded by the Division of Mathematical Sciencesand the Division of Materials Research.