On the representative elementary volume of the Ergun's law

Several expressions can be used to predict the pressure drop caused by a vi scous incompressible fluid flow through a granular media. These laws are em piricals and are obtained at macroscopic scale. One of these, Ergun's law, is currently used in a local form to modelling t he momentum transfer between fluid and solid. There is not a real justifica tion. In these study, the direct simulation of Navier-Stokes Equation is us ed to calculate pressure drop caused by viscous incompressible fluid flow t hrough a granular media. Some simulations realised for different volume of granular media allow to Sind a representative elementary volume and prove t he local character of the Ergun's law.