Viscous fingering is the formation of finger-like patterns due to instability in the interface between two fluids in a porous media. Starting with the Navier-Stokes equations (which describes the motion of viscous fluids), I will derive the simplified Darcy’s law. One application of Darcy's law is to analyze oil and gas recovery from traditional and modern fracking techniques.
I will then conclude with an experiment where viscous fingering can be seen: the Hele-Shaw cell.