Dynamics of stable viscous displacement in porous media

Immiscible displacement of one fluid by another fluid in porous media has important applications in a wide range of different technologies. Most often mentioned is hydrology and and oil recovery. From a theoretical point of view, the displacement process is very complex and hard to describe in detail. Especially, much attention has been paid to the rich variety of displacement structures that is observed. The displacement structures are found to depend strongly on the fluid properties like viscosity, interfacial tension, fluid flow rate, and wettability [1–4]. In drainage displacement the primary process is the displacement of a wetting fluid by a nonwetting fluid in porous media. Consider a two-dimensional horizontal displacement of a less viscous fluid by a more viscous fluid. At high injection rates the front that develops between the invading and defending fluid, is known to stabilize [3]. In contrast, at extremely low injection rate the invading fluid generates a growing cluster similar to the