A note on the stability of an immiscible liquid layer in a porous medium

The Saffman—Taylor instability of a liquid layer is studied by the standard first-order perturbation method. The viscosity and density of the layer and the bounding fluids are assumed to be constant. Interfacial tension is taken into account. An expression for the rate of growth of perturbations at the interface is determined. Results obtained by previous analyses are shown to be particular cases of this solution. The reduction in the rate of growth of the perturbations due to the presence of the liquid layer is demonstrated.