The goal of this project is to develop mathematical tools for the understanding and prediction of the behavior and properties of heterogeneous materials. In these studies, the length scale of the heterogeneity is generally much smaller than the size of the material. The particular problems considered here are the transport of solute and heat in porous media and the understanding of the flow within poroelastic materials due to time dependent applied loads. The particular mathematical techniques to be used include asymptotic and homogenization methods, numerical simulations and modeling.
The problems studied here are motivated by applications of scientific and technological interest. Examples where solute transport in porous media plays an important role, and thus the results of this project have an impact, include: the transport of contaminants in soils, the transport of nutrients in bones, the intrusion of salt in fresh water in soils near ocean coasts, movement of minerals (e.g. fertilizers) in soils, recovery techniques in oil reservoirs, etc. Heat transport in porous media plays an important role in the transport of reactive solutes in rocks and soils (the reactions produce heat and the transport of that heat is coupled with the fate of the solutes, nuclear waste is included here), solar receivers, building thermal insulation materials, fuel cells and drying technology. Additionally, while flow within poroelastic materials occurs in many systems such as soils and rocks, a main motivation of the project is the transport of nutrients in bones and the stresses generated by the flow within bone, which are believed to play a role in the remodeling of the bone (i.e. change of bone shape and size due to gain and loss of bone mass in different regions of the bone).
