Resistance to Laminar Flow Through Porous Media

The equations for laminar flow through porous media for the linear and nonlinear regimes, are derived from a consideration of the hydrodynamic drag forces on individual particles. The limitation of Darcy’s law with increasing Reynolds number is shown to correspond to departures from creeping or Stokian motion of the fluid around the individual particles. The derived equation is compared to that obtained from the capillary tube model which, although commonly used as the basis for Darcy’s law, provides no real indication or explanation for the observed departures from the linear regime of flow. The approach is extended to the special case of upward flow through a fluidized or suspended bed. It is shown that as the bed expansion is increased the resistance of the particles converges with that determined for a single particle in an infinite fluid.