Effect of Medium Dispersivity on the Viscous Fingering Instability in Porous Media

Flow processes that involve the displacement of a viscous fluid by a less viscous one often lead to a hydrodynamic instability known as viscous fingering. In this study the viscous fingering instability for anisotropic dispersive flows will be addressed. In order to understand the physics of the flow displacement, the basic equations of conservation of mass and momentum are solved for a two-dimensional porous medium. The linear stability of the flow is analyzed first. The flow is then modeled numerically using a highly accurate spectral method based on the Hartley transformation. The streamfunction and concentration fields are tracked using an iteration process for two dimensional flows in every time-step. In this study, different types of anisotropic dispersions are considered and their effects on finger patterns are examined. We will present physical discussion of how medium dispersivity affects hydrodynamics and could result in interesting instability schemes.