Averaged equations in a Hele-Shaw cell: Hierarchy of models

In contrast to the classical Darcy law, Navier–Stokes–Darcy model of a flow in a Hele‐Shaw cell includes small inertial and viscous forces in the plane of a cell. The displacement of viscous fluid by a less viscous one from a Hele‐Shaw cell is studied numerically using these models. A distinguishing feature is the special microgravity conditions of displacement.Miscibility of fluids together with the high speed of displacement (Peclet number tends to infinity) provides the absence of surface tension on the one hand and minimal manifestation of molecular diffusion on the other. Simulations based on the Darcy law and on the Navier–Stokes–Darcy model have been compared. The Navier–Stokes–Darcy model clearly exhibits a better consistency with the experimental data.