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.
