| he application of the multiphase theory to porous media flows has shown that Darcy's law, which relates the pressure force to the interfacial drag force, is restricted to "uniform-porosity" (Darcian) flows. When large porosity gradients exist in the porous medium, the flow is non-Darcian. Flow of oil near the mouth of an oil well bore hole, ground water flow, deep bed filtration, and cake filtration are some technologically-significant examples of non-Darcian flows.;To date, it has been tacitly assumed--without any theoretical or experimental verification--that Darcy's law applies locally to porous media flows with large porosity gradients. However, preliminary studies with the multiphase theory indicate that such an assumption may be too simplistic and that the local pressure gradient could depend on the fluid deformation gradient (or, in effect, the porosity gradient).;The objectives of this work are twofold: First, to determine, from first principles, the balance equations and constitutive equations for porous media flows with large porosity gradients. Second, to determine the material parameters in these constitutive equations using a "multiphase viscometer.";The large porosity gradients necessary to achieve non-Darcian flows were obtained by stacking wire cloths of different mesh sizes and wire diameters inside the "multiphase viscometer." Steady flow experiments were performed using Newtonian fluids (ethylene glycol/water) and a power law fluid (1% CMC in water) with beds having uniform, linear, parabolic, and non-parabolic porosity profiles.;The most important result is that Darcy's law applies locally to porous media flows with large porosity gradients. That is, the multiphase viscosity ;For Newtonian fluids, the resistance function... |
