In this paper, we study the stationary incompressible power law fluid flow in a thin porous medium. The media under consideration is a bounded perforated 3D domain confined between two parallel plates, where the distance between the plates is very small. The perforation consists in an array solid cylinders, which connect the plates in perpendicular direction, distributed periodically with diameters of small size compared to the period. For a specific choice of the thickness of the domain, we found that the homogenization of the power law Stokes system results a lower-dimensional nonlinear Brinkman type law.

中文翻译：

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薄多孔介质中非牛顿流动的低维非线性布林克曼定律

在本文中，我们研究了薄多孔介质中的稳态不可压缩幂律流体流动。所考虑的介质是限制在两个平行板之间的有界穿孔 3D 域，其中板之间的距离非常小。穿孔由阵列实心圆柱体组成，这些圆柱体在垂直方向上连接板，周期性分布，与周期相比，直径较小。对于域厚度的特定选择，我们发现幂律斯托克斯系统的均匀化导致了低维非线性 Brinkman 型定律。