Fluid flow through porous and nanoporous media within the prisme of extended thermodynamics: emphasis on the notion of permeability

The study of fluid flows through porous and nanoporous media is important in many natural and industrial situations. One relevant parameter is the permeability of the porous material. An original approach is proposed within the prism of Extended Irreversible Thermodynamics. More specifically, the system fluid–solid matrix is modelled by a two-component mixture and the permeability is obtained after calculating the seepage velocity and comparison with Darcy’s law. An explicit analytical expression of the permeability coefficient is proposed and discussed. The analysis is restricted to one-dimensional situations and incompressible fluids. The validity of the model is checked by calculating the flow rate through cylindrical nano pores: comparison with experimental data shows a good agreement.