Macroscopic model for unsteady generalized Newtonian fluid flow in homogeneous porous media

A macroscopic model for unsteady incompressible isothermal non-Newtonian flow in homogeneous porous media, taking into account inertial and slip effects at solid–fluid interfaces, is derived this work. The development carried out considering a general Newton’s law of viscosity the fluid phase. Using classical volume averaging method, seepage velocity shown to be solenoidal. momentum equation Laplace domain, employing simplified version which calls upon Green’s formulas adjoint problems function pairs pressure. In takes form Darcy’s corrected by term that accounts initial condition. Once transformed back time provides depends on two terms. first one under convolution between pressure gradient derivative an apparent permeability tensor. second memory effect conditions. These effective quantities are determined from solution single closure problem naturally results derivations. consistent with Newtonian case simplifies steady versions some models. validated pore-scale simulations performed 2D structures, Carreau fluid. impact inertia dynamics coefficients highlighted.