On a hydrodynamic permeability of a system of coaxial partly porous cylinders with superhydrophobic surfaces

The paper considers a Stokes-Brinkman's system with varying viscosity that describes the continuous flow of viscous incompressible liquid along an ensemble of partially porous cylindrical particles using the cell approach. The analytical solution for the considered system was derived and analyzed for a particular case of Brinkman's viscosity which illustrates the presence of superhydrophobic surfaces in a porous system. Some numerical validation of the derived results are done and the hydrodynamic permeability of the porous system was calculated and analyzed depending on geometrical and physicochemical parameters. Our analysis of the problem shows that the bigger the impermeable core the less the coefficient of hydrodynamic permeability what agrees with the physical process of the filtration. In addition, the bigger the specific permeability of porous layer the greater the hydrodynamic permeability of the porous medium.