The Darcy-Forchheimer Law for Modelling Fluid Flow in Biological Tissues

The motion of the interstitial fluid of a biological tissue is studied by employing the Darcy-Forchheimer law, a correction to standard Darcy's law. The tissue is modelled as a saturated biphasic medium comprising the fluid and a deformable matrix. The reason for undertaking this study is that a description of the tissue's dynamics based on the Darcy-Forchheimer law might be more complete than the one based on Darcy's law, since the former provides a better macroscopic representation of the microscopic fluid-solid interactions. Through numerical simulations, we analyse the influence of the Forchheimer's correction.