Research Projects

This project focuses on pore-scale phase field models in a heterogeneous porous medium, using Cahn-Hilliard equations. The work is divided into three sub-problems. The first sub-problem assumes that the interface between phases is not dependent on the scaling parameter, obtaining the solution theory and homogenization. The second sub-problem assumes that both interfacial length and surface tension term depend on the scaling parameter, demonstrating the existence of solutions via fixed point arguments and homogenizing the pore-scale problem. The final sub-problem involves general scaling of the entire micro-scale model, obtaining macroscopic descriptions of the pore scale models. If time permits, numerical simulations will be performed to compare these models with known literature results.