Critical Phonema In Composit Media

在科学和技术上具有重要意义的一类复合材料是那些当某些参数在临界点附近发生变化时，其材料和微观结构特性会发生急剧转变的材料。具有极其丰富的行为的一个例子是电流变（ER）流体，其是高复介电常数的可极化颗粒的胶体悬浮液，其典型尺寸范围从微米到毫米级，在低复介电常数的粘性流体（例如油）中。将强电场施加到这样的悬浮液上，在几毫秒内产生从油性浆料到固体状状态的戏剧性转变，悬浮液的粘度增加了许多数量级。对于不导电的介质球，这种转变的特征是形成链，这些链聚集成平行于场的列。对于金属球，形成具有分形特征的网状结构。最近，研究者介绍了一种将统计力学的方法应用于复合介质中宏观问题的方法，其长度尺度比传统统计力学领域中的大得多。在该奖项支持的研究中，研究人员将进一步发展这些方法，并将其应用于研究电流变液的临界特性，特别是那些具有较大球体的电流变液，其中热效应可以忽略不计，并且经典应用的摩擦力学产生的信息很少。材料，如电流变（ER）流体，表现出某种类型的显着过渡行为出现在整个科学和工程，并且在许多技术应用中是重要的。其他例子包括海冰、多孔介质（如砂岩和土壤）、用于智能设备和用于电磁应用的导电膜的颗粒复合材料，以及由于断裂而导致的材料失效。电流变液中的流体/固体转变是这些材料表现出的临界行为类型的一个特别有趣的例子。电流变液的流变特性的快速电控潜力吸引了人们对它的极大关注，其应用包括离合器、泵、制动器和减震器。然而，从理论的角度来看，还有很多关于材料行为和性质的转变附近的理解。在拟议的工作中，研究人员将开发数学方法来理解电流变液的转变，以及其他表现出临界行为的复合材料。

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.