Stability of One-Dimensional Vertical Flow Through a Porous Domain Under Pumping of a Finite Volume of Impurity

The problem of stability of one-dimensional filtration flow in a rectangular domain of porous medium is solved. The flow occurs when a portion of impurity is transported through the region against gravity. It is shown that the instability has an absolute character. A Rayleigh-Taylor instability is observed at the backward front of the concentration pulse. In this case, the observation time is always less than the passage time of the pulse through the domain. A theoretical model is proposed to describe this phenomenon taking into account immobilization and clogging. The influence of the problem parameters on the characteristic time of instability onset is investigated. Comparison of computational results with experimental data has shown the appropriateness of the chosen model. The ways of increasing this time are analyzed. It is shown that only one way to increase the instability time is to significantly reduce the buoyancy force impact. The latter force can be diminish by alteration of the gravity force.