Immiscible, Viscoelastic (Rivlin - Ericksen) Liquid-Liquid Displacements in Permeable Media

Slow, immiscible, viscoelastic (Rivlin - Ericksen) liquid-liquid displacement in a permeable medium is considered. The necessary and sufficient criteria for stability are that the displacing fluid is denser, less mobile and the ratio of medium permeability to viscoelasticity of the displacing fluid is less than the ratio of medium permeability to the viscoelasticity of the displaced fluid. The instability criteria and critical wave length are found to be the same as those for ordinary viscous liquid-liquid displacements in permeable media.