Oscillatory motion of a viscous fluid in a porous medium

An oscillatory flow of an incompressible fluid in a saturated porous medium in the presence of a solid inclusion has been theoretically studied. Unsteady filtration has been described by the Brinkman–Forchheimer equation, where inertial effects and terms with acceleration characteristic of high filtration rates and the presence of pulsations are taken into account. The convective part of the acceleration is responsible for nonlinear effects near macroinhomogeneities. These effects can play a noticeable role in unsteady flows in the porous medium, as is shown for the problem of a solid ball streamed by an oscillatory flow having a given velocity at infinity. The results indicate that a secondary averaged flow appears in the case of high frequencies and cannot be described by Darcy’s or Forchheimer’s filtration laws.