We study the flow of a micropolar fluid in a thin domain with microstructure, i.e., a thin domain with thickness $$\varepsilon $$ ε which is perforated by periodically distributed solid cylinders of size $$a_\varepsilon $$ a ε . A main feature of this study is the dependence of the characteristic length of the micropolar fluid on the small parameters describing the geometry of the thin porous medium under consideration. Depending on the ratio of $$a_\varepsilon $$ a ε with respect to $$\varepsilon $$ ε , we derive three different generalized Darcy equations where the interaction between the velocity and the microrotation fields is preserved.

中文翻译：

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微极流体流过薄多孔介质的数学建模

我们研究了微极流体在具有微观结构的薄域中的流动，即厚度为 $$\varepsilon $$ ε 的薄域，它被周期性分布的大小为 $$a_\varepsilon $$ a ε 的实心圆柱体穿孔。这项研究的一个主要特点是微极流体的特征长度依赖于描述所考虑的薄多孔介质的几何形状的小参数。根据 $$a_\varepsilon $$ a ε 与 $$\varepsilon $$ ε 的比率，我们推导出三个不同的广义达西方程，其中保留了速度和微旋转场之间的相互作用。