Generalized Navier-Stokes-Darcy model

Generalized Navier-Stokes-Darcy (GNSD) model is proposed to describe a viscous fluid displacement from a Hele-Shaw cell by a less viscous one. The key difference from conventional models is the presence of phase permeabilities in the equations of motions. In the absence of viscous differential and inertial terms, the proposed model is reduced to generalized Darcy's law for a Hele-Shaw cell. The law has been applied for linear stability analysis of a plane interface between two viscous fluids. An absolute instability of the interface-a classical result of Saffman and Taylor for short waves-is also valid under generalized Darcy's law. On the other hand, long wave disturbances can be absolutely stable-a new result, which does not follow from other models.