Viscous drag, driving forces, and their reduction to Darcy's law

Abstract

On the basis of the conservation of momentum for pore water flow, a new relation between drag and driving forces is developed for flow within a saturated aquifer. Such a relation inherently includes inertial terms of both the solid phase and the fluid phase that play an important role under dynamic conditions (e.g., earthquakes) and under some transient conditions (e.g., aquifer pumping). For laminar flow of a fluid relative to the skeletal frame a new relation is reached by simplification from the more general case. The Darcy-Gersevanov law and Darcy's law are found to be special cases that result from further simplifications.