Phase Transitions in Composite Media

University Of Utah, Salt Lake City UT

Investigators

Abstract

Golden DMS-1009704 The investigator and his colleagues conduct fundamental mathematical and numerical studies of phase transitions in composite materials, with applications to electrorheological (ER) fluids and sea ice, which share similar microstructural features. They develop a statistical mechanics framework in which such transitions can be studied, and explore random matrix characterizations of composite microstructures and their evolution. One central problem to be addressed is the existence of a critical electric field necessary to induce the fluid/solid transition in ER fluids. They anticipate that this phenomenon goes beyond classical phase transitions in statistical mechanics, representing a new type of transitional mechanism that depends on a competition between geometrical entropy and electrical energy. They also study the fluid transport and related microstructural transition in sea ice, which plays a key role in Earth's climate system. Such microstructures can be identified with random matrices, and the investigators study the evolution of microstructural features with such techniques. Composite materials arise throughout the physical and biological sciences and across most types of engineering. One of the key features of these types of problems is the critical dependence of the effective material properties on the parameters characterizing the system. For example, an electrorheological (ER) fluid is a suspension of particles in a viscous fluid such as oil. If an applied electric field exceeds a critical value then the particles form chains and the suspension undergoes a fluid/solid transition within milliseconds. This electrically induced transition has been used in applications including next generation clutches, brakes, micro-fluidic valves, and human prosthetics. Another example is sea ice, a composite of pure ice with brine inclusions, which plays a key role in Earth's climate system. If the temperature exceeds a critical value, then fluid can flow through the ice. This transition mediates a broad range of processes in the polar ice packs that are fundamental to making better predictions of climate change. The investigator and colleagues conduct fundamental mathematical and numerical studies of these transitions in ER fluids and sea ice. They bring to bear sophisticated techniques of theoretical statistical physics to better understand the behavior of these types of materials. Through these studies, the investigator anticipates the development of applications to other high-tech composites and to other areas critical to our understanding of polar climate change. The project is cofunded by the Division of Mathematical Sciences and the Division of Materials Research.