Models of Flow Through Porous Media of Polar Fluids with Pressure-Dependent Viscosity

Equations governing the flow of a polar fluid, with pressure-dependent Newtonian viscosity, through a variable-porosity medium are developed. Averaged equations are obtained using intrinsic volume averaging. A drag function is introduced to account for the interactions of the fluid with the porous matrix. Darcy and Forchheimer generalized terms, which utilize friction factor description, are included in the model equations for both granular and consolidated media to account for the effects of the porous microstructure. The developed model equations are important in the study of blood and nutrient flows in body tissues and organs, and in modelling and control of flow through synthetic porous materials that replace human tissues in burn victims. Potential other applications include flow simulation of oil products in ground layers and industrial porous domains.