Fluid Flows in Reactive, Heterogeneous and Deformable Porous Media

多孔材料中的流体流动在许多自然、工业和生物环境中都很常见。这些范围从相对简单的流动通过具有均匀和良好特征的均匀介质到非常复杂的流动在强非均质介质中，或在反应性和/或可变形的多孔介质中，流体的热化学和流动动力学可以显著改变介质的性质，从而进一步复杂化流动。这种复杂流动的三种类型构成了这一建议的科学基础：(1)在三元合金凝固过程中发生的流体流动，其中存在由细尺度树枝状晶体组成的反应性多孔基体；(2)在非均质多孔介质中重力驱动的流动；(3)流体流过可变形多孔材料。多孔材料中的流体流动是材料科学、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感兴趣和重要的问题。在这个建议中发展的数学模型是由各种问题驱动的，并应用于各种问题，包括涡轮叶片的工业加工、地下水中的污染物输送、生物组织中的流体输送和喷墨打印。本项目将资助本科生和研究生研究人员。

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.