Instability of inclined fluid-film flow with substrate filtration

Gravity-driven flows of thin fluid films with a free surface along a porous substrate occur in many important circumstances found in industry and natural settings. In this thesis a model for such flows is derived by coupling the Navier-Stokes equations governing the clear flow in the fluid film with Darcy's law for the filtration of fluid through the porous medium. A linear stability analysis is conducted and the effect of various parameters on the state of neutral stability is investigated. A simplified model is developed by reducing the dimensionality of the problem, which is then employed in order to determine the nonlinear effects on the stability of the equilibrium flow.