Abstract Pseudo-plastic fluids exhibit a non-linear stress-strain relationship which can provoke large, localized viscosity gradients. For the flow of such fluids in porous media the consequence is a strong variability of the effective permeability with porosity, angle of the macroscopic pressure gradient, and rheological parameters of the fluid. Such a variability is investigated on the basis of adjoint homogenization theory for a Carreau fluid in an idealized porous medium geometry, highlighting differences with respect to the Newtonian case. It is shown in particular that the more we depart from Newtonian conditions, the more the (often used) hypothesis of an effective viscosity in Darcy’s law is a poor approximation, for the effective permeability tensor becomes strongly anisotropic.

中文翻译：

---

剪切稀化流体通过多孔介质的流动

摘要 假塑性流体表现出非线性应力-应变关系，可引起较大的局部粘度梯度。对于这种流体在多孔介质中的流动，其结果是有效渗透率随孔隙率、宏观压力梯度的角度和流体的流变参数发生强烈变化。这种可变性是在理想化多孔介质几何形状中 Carreau 流体的伴随均质化理论的基础上进行研究的，突出了与牛顿情况的差异。特别表明，我们越远离牛顿条件，达西定律中有效粘度的（经常使用的）假设就越是糟糕的近似，因为有效渗透率张量变得强烈各向异性。