Viscous Fingering in a Reacting System

This project involves using spectral methods (numerical methods that use fourier transforms) to solve an instablity that occurs in porous media flows. This instability occurs when a fluid of low viscosity is flowing behind a fluid of high viscosity. In this case this difference is caused by different concentrations of chemical species. In the instability then, the solution of low viscosity invades the solution of high viscosity in long, finger-like structures. When no chemistry is involved, this flow is of interest in extracting petroleum from underground. However, when the chemical species reacts, more complicated patterns are formed. These include droplets of one solution that move into and through the other solution, and a moving chemical wave that propogates faster than the fluid velocity. The goal of this project is to develop and test a more complex chemistry model and observe what happens.