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.