Fluid Flows in Reactive, Heterogeneous and Deformable Porous Media

多孔材料中的流体流动在许多自然、工业和生物环境中是常见的。 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。三种类型的这种复杂的流动构成了这一建议的科学基础：（1）在三元合金凝固期间发生的流体流动，其中存在由细尺度树枝状晶体构成的反应性多孔基质，（2）在非均质多孔介质中的重力驱动流动，以及（3）流体在可变形多孔材料中的流动，多孔材料中的流体流动对于研究多孔材料的科学家和工程师来说是非常重要的。广泛的领域，包括材料科学，环境科学，生物医学科学和应用数学。 在这个建议中开发的数学模型的动机和应用程序的各种问题，包括工业加工的涡轮机叶片，污染物在地下水流中的传输，在生物组织中的流体传输，和喷墨打印。 本科生和研究生研究人员将在该项目下得到支持。

Fluid flows in porous materials are familiar in many 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 types of such complex flows form the scientific basis for this proposal: (1) fluid flows that occur during the solidification of ternary alloys, where a reactive porous matrix made up of fine-scale dendritic crystals is present, (2) gravity-driven flows in heterogeneous porous media, and (3) fluid flows through deformable porous materials.Fluid flows occurring in porous materials are of interest and importance to scientists and engineers in a broad range of fields that include materials science, environmental science, biomedical science and applied mathematics. The mathematical models developed in this proposal are motivated by and have application to a variety of problems including industrial processing of turbine blades, contaminant transport in groundwater flows, fluid transport in biological tissues, and inkjet printing. Undergraduate and graduate students researchers will be supported under this project.