Complex Flows In Porous Media

多孔材料中的流体流动在自然、工业和生物环境中普遍存在。 这些范围从相对简单的流动，通过均匀的和良好的特性的均匀介质中的非常复杂的流动，在强烈的非均匀介质，或在反应和/或可变形的多孔介质中的流体的热化学和流动的动力学可以显着改变的介质，这反过来又进一步复杂的流动的属性。 三个这样复杂的流动构成了这一建议的科学基础。 第一个是材料科学应用，在三元合金凝固过程中产生。 在这里，多孔介质由树枝状晶体组成，树枝状晶体根据间隙流体的局部热力学条件固化或熔化。 在这种反应性多孔介质中，流体流动和凝固过程是紧密耦合的。 第二个项目是为了响应环境科学家在开发非均匀多孔介质中地下水污染物的去除或遏制策略方面的兴趣。 所提出的工作地址重力驱动的空间非均匀多孔介质中的流动，使用渐近均匀化方法，以确定有效的介质属性，其特征在于一个相对复杂的多孔介质由一个简单得多的描述。 第三个项目涉及流体流过多孔介质，其多孔基质可因流体流过而变形。这种流动出现在土壤、人体组织、器官和肿瘤中，以及工业应用中，如注塑、过滤和喷墨打印。 拟议的工作试图扩展喷墨打印技术的数学建模工具，并将这些想法连接到其他应用领域。 拟议的研究是一个跨学科的性质，通过使用应用数学技术直接解决材料加工，环境科学和工业印刷技术的问题。 直接受本研究影响的应用包括工业合金加工、去除或遏制地下水污染物和相关环境危害的策略，以及喷墨打印等工业应用过程中产生的流动。 这项工作可能会间接影响地球物理流动的理解，发生在地球的核心或在海冰的形成和融化，其他工业应用，如注塑成型和过滤，以及生物应用，涉及组织，器官和肿瘤中的流体运输在人体。 PI在乔治梅森大学提出的工作将涉及与田纳西大学、北卡罗来纳州大学以及联合王国和国家标准与技术研究所的研究人员的合作。

Fluid flows in porous materials are ubiquitous in natural, industrial and biological settings. These range from relatively simple flows through homogeneous media with uniform and well-characterized properties to very complex flows in strongly heterogeneous media, or in reactive and/or deformable porous media in which the thermochemistry of the fluid and the dynamics of the flow can significantly alter the properties of the media which in turn then further complicate the flow. Three such complex flows form the scientific basis for this proposal. The first, a materialsscience application, arises during the solidification of a ternary alloy. Here the porous medium is made up of dendritic crystals that solidify or melt depending on local thermodynamic conditions of the interstitial fluid. The fluid flow and solidification processes are tightly coupled in this reactive porous medium. The second project arises in response to interest by environmental scientists in developing strategies for the removal or containment of groundwater contaminants in nonhomogeneous porous media. The proposed work addresses gravity-driven flow through spatially nonuniform porous media using asymptotic homogenization methods in order to identify effective media properties which characterize a relatively complex porous media by a much simpler description. The third project involves fluid flowthrough a porous medium whose porous matrix can be deformed by the fluid moving through it. Such flows appear in soils, in tissues, organs and tumors in the human body and in industrial applications such as injection molding, filtration and inkjet printing. The proposed work attempts to extend mathematical modeling tools for inkjet printing technology and to connect these ideas to other application areas. The proposed research is of an interdisciplinary nature that throughthe use of applied mathematical techniques addresses directly problems in materials processing, environmental science and industrial printing technologies. Applications impacted directly by this research include industrial alloy processing, strategies for the removal or containment of groundwater contaminants and related environmental hazards, and flows arising during industrial applications such as inkjet printing. This work may indirectly impact the understanding of geophysical flows that occur in the earth's core or during the formation and melting of sea ice, other industrial applications such as injection molding and filtration, and biological applications involving the transport of fluid in tissues, organs and tumors in the human body. The work proposed by the PI at George Mason University will involve collaboration with researchers at the University of Tennessee, the University of North Carolina as well as with researchers in the United Kingdom and at the National Institute of Standards and Technology.