Momentum transfer within a porous medium. II. Stress boundary condition

In this paper, we derive a boundary condition at the interface between a free fluid and a porous medium stating that the stress is transferred both to the fluid within the porous medium and to the solid skeleton. A zero stress jump is obtained so that the total stress is preserved at the interface. The boundary condition is obtained with the volume averaging method following the approach of Ochoa-Tapia and Whitaker [“Momentum transfer at the boundary between a porous medium and a homogeneous fluid—I. Theoretical development,” Int. J. Heat Mass Transfer 38(14), 2635–2646 (1995)], but starting from the momentum balances written on the fluid and on the solid of the porous region, the latter was derived in part I of this paper. In the same way, also the boundary condition at the interface between a porous medium and a homogeneous solid is obtained. Both boundary conditions describe the equilibrium of forces at the interface, where part of the stress is carried by the solid skeleton and part by the fluid within the porous medium. With the derived boundary conditions, together with the stress transfer equation within the solid skeleton, it is now possible to satisfy the overall force equilibrium on a shear cell partially filled with a porous medium.