ON THE FLUID-PHASE MOMENTUM BALANCE LAWS AND MOMENTUM JUMP CONDITION FOR POROUS-MEDIA FLOW

The global momentum balance for the fluid phase in a solid-fluid mixture such as a porous medium, the local momentum balance, and the momentum jump condition, are considered. It is shown that many sets, each consisting of a global balance, a local balance, and a jump condition, are consistent with experiment. These sets differ only through the expression for the fluid-phase stress tensor. To obtain any consistent set, a buoyancy force which, contrary to the term often referred to as such, is a straightforward generalization of Archimedes' principle, must be included. Each local momentum balance corresponds to a differential form of Darcy's law. Arguments supporting the expression for the fluid-phase stress tensor leading to the common differential form of Darcy's law and the continuity-of-pressure jump condition, are given. Difficulties encountered in earlier derivations of the differential form of Darcy's law are avoided, and an apparent inconsistency concerning the momentum jump condition is removed.