Instability of the fluid interface at arbitrary perturbation amplitudes. Displacement in the Hele–Shaw cell

Abstract

The problem of the morphological stability of the fluid–fluid interface moving in the Hele–Shaw cell is considered (one fluid displaces another one). Fluids are assumed to be immiscible and incompressible. Harmonic perturbations of the interface have arbitrary amplitudes. The numerical solution reveals that with an increase in the perturbation amplitude the critical size of instability decreases to a certain value previously independently predicted theoretically using calculations of the entropy production. A comparison of these obtained values is conducted and the limitations of the theoretical predictions are clarified. Possibility of coexistence of a large number of different forms of interfaces in the case of close viscosities of the displaced and displacing fluids is discovered for the first time.