Prolongation of two phases in the model of fluid displacement through a capillary

The problem of a piston-like displacement of a fluid by another in a capillary is examined. It is suggested that each fluid is prolonged into the domain occupied by the other fluid. This enables the replacement of the two-phase flow problem by a transient single-phase flow problem, with discontinuity in velocity and pressure on a film interface. The problems related to the triple point are solved by introducing a limit fluid near the pore wall. The demonstration of the Washburn equation contributes to the physical justification of our model. To cite this article: Y. Lucas et al., C. R. Mecanique 334 (2006).