Critical Phonema In Composit Media

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A scientifically and technologically important class ofcomposite materials are those which exhibit a sharp transition in theirmaterial and microstructural properties as some parameter isvaried near a critical point. One example with extremely richbehavior is an electrorheological (ER) fluid, which is a colloidal suspension of polarizable particles of high complexdielectric constant, with typical sizes ranging from micron tomillimeter scales, in a viscous fluid of low complex dielectricconstant such as oil. The application of a strong electric field to such a suspension produces within milliseconds a dramatictransition from an oily slurry to a solid-like state with anincrease in the viscosity of the suspension by many orders ofmagnitude. For non-conducting dielectric spheres, the transition is characterized by the formation of chains which aggregate intocolumns parallel to the field. For metal spheres, net-likestructures with fractal characteristics form. Recently theinvestigator has introduced a way of applying the methods ofstatistical mechanics to macroscopic problems in compositemedia, for length scales much larger than the in the traditionaldomain of statistical mechanics. In the research supported by this award, the investigator will develop these methods further and beginapplying them to study the critical properties of ER fluids,particularly those with larger spheres where thermal effectsare negligible, and classical application of statisticalmechanics yields little information.Materials such as electrorheological (ER) fluids which exhibit some type of marked transitional behavior appear throughout science and engineering, and are important in many technological applications. Other examples include sea ice, porous media such as sandstones and soils, particulate composites used insmart devices and in conducting films for electromagnetic applications, and material failure due to fracture. The fluid/solid transition in ER fluids is a particularly interesting example of the type of critical behavior exhibited by these materials. The potential for rapidelectrical control of rheological properties has attractedconsiderable attention to ER fluids, with applications includingclutches, pumps, brakes and shock absorbers. From a theoreticalstandpoint, however, there remains much to be understood about the material behavior and properties near the transition. In theproposed work the investigator will develop mathematical methodsfor understanding the transition in ER fluids, as well as othercomposite materials exhibiting critical behavior.