Complex Porous Media Flows in Materials, Environmental and Biological Applications

该项目涉及对非均质、反应性和/或可变形多孔材料中复杂流动的研究。首先，三元合金的凝固过程中会形成一层多孔的糊状层，由被流体包围的枝晶晶体组成。在这个糊状层中，流体的运动与固体的生长或溶解相结合。流体运动的动力学和固体材料的演变之间的新的相互作用将被检查。其次，流体在非均质多孔材料中的流动，如地质地下系统，将使用均质化技术进行检测。第三，探索多孔隐形眼镜佩戴者泪膜的数学模型。这些模型将隐形眼镜上方和下方的泪液膜的薄流体膜模型与通过隐形眼镜的流体流动和蒸发结合起来。本研究探讨了流体通过多孔材料的运动，这些材料存在于广泛的自然、工业、环境和生物医学环境中。数学模型被用来描述这些复杂的系统。计算工具被用来探测这些模型的特征。模拟和分析的结果相结合，提供新的见解，拓宽我们对物理和生物现象的理解。三个主要关注领域的动机是：(1)在合金铸造过程中观察到的材料科学现象，(2)污染地下水系统的修复，以及(3)干眼症，特别是多孔隐形眼镜佩戴者可能受到的影响。这些广泛的主题是通过多孔材料流体运动的共同存在联系在一起的。该项目将涉及本科生和研究生，他们将通过研究接受跨学科培训。

This project involves an investigation of complex flows in heterogenous, reactive and/or deformable porous materials. First, the solidification of a ternary alloy involves the formation of a porous mushy layer made up of dendritic crystals surrounded by fluid. In this mushy layer the motion of fluid is coupled to the growth or dissolution of the solid. Novel interactions between the dynamics of the fluid motion and the evolution of the solid material will be examined. Second, fluid flows in heterogeneous porous materials, such as geological subsurface systems, will be examined using homogenization techniques. Third, mathematical models of tear films for wearers of porous contact lenses will be explored. These models couple thin fluid film models of the tear films above and below the contact lens to fluid flow and evaporation through the contact lens.This research explores the motion of fluid through porous materials that are present in a broad range of natural, industrial, environmental and biomedical settings. Mathematical models are used to describe these complex systems. Computational tools are used to probe features of these models. Results of simulations and analyses are combined to provide new insights and broaden our understanding of physical and biological phenomena. Three main focus areas are motivated by (1) phenomena occurring in materials science observed during the casting of alloys, (2) the remediation of contaminated ground water systems, and (3) dry eye conditions and specifically how wearers of porous contact lenses may be affected. These broad topics are linked by the common presence of fluid motion through porous materials. This project will involve undergraduate and graduate students that will receive interdisciplinary training through research.