Media viscous fingering

When the mobility ratio is greater than one, the front between the displaced and displacing fluids is unstable if the porous medium is sufficiently wide (> 10 cm) to allow the formation and propagation of viscous fingers. The lower viscosity fluid channels or "fingers" through the displaced fluid, leaving much of it uncontacted. (See... 

The third problem is known as the Saffinan-Taylor instability of a fluid interface for motion of a pair of fluids with different viscosities in a porous medium. It is this instability that leads to the well-known and important phenomenon of viscous fingering. In this case, we first discuss Darcy s law for motion of a single-phase fluid in a porous medium, and then we discuss the instability that occurs because of the displacement of one fluid by another when there is a discontinuity in the viscosity and permeability across an interface. The analysis presented ignores surface-tension effects and is thus valid strictly for miscible displacement. ... 

Lutsko, J.F., Boon, J.P., and Somers, J.A., Lattice gas automata simulations of viscous fingering in a porous medium, in T.M.M. Verheggen Numerical Methods for the Simulation of Multi-Phase and Complex Flow, Springer-Verlag, Berlin, 124-135, 1992. 

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