Fluid Flows in Reactive, Heterogeneous and Deformable Porous Media

流体在多孔材料中的流动在许多自然、工业和生物环境中都很常见。这些流动的范围从通过具有均匀和良好特性的均匀介质的相对简单的流动到在强烈非均质介质中的非常复杂的流动，或者在活性和/或可变形的多孔介质中的流动，在这些介质中，流体的热化学和流动的动力学可以显著改变介质的性质，从而使流动进一步复杂化。三种类型的复杂流动构成了这一提议的科学基础：(1)三元合金凝固过程中的流体流动，其中存在由细小的树枝状晶体组成的反应性多孔基质；(2)重力驱动的非均匀多孔介质中的流动；(3)流体在可变形的多孔材料中的流动。发生在多孔材料中的流体流动引起了材料科学、环境科学、生物医学科学和应用数学等广泛领域的科学家和工程师的兴趣和重视。这项建议中开发的数学模型受到各种问题的启发并应用于各种问题，包括涡轮叶片的工业处理、地下水流动中的污染物传输、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.