论文标题
微极流体流过薄的多孔介质的数学建模
Mathematical modeling of micropolar fluid flows through a thin porous medium
论文作者
论文摘要
我们研究了带有微观结构的薄域中微极流体的流量，即具有厚度$ \ varepsilon $的薄域，该域被定期分布的尺寸$ a_ \ a_ \ varepsilon $的固体圆柱体穿孔。这项研究的一个主要特征是微极流体的特征长度依赖于描述所考虑的薄多孔介质的几何形状的小参数。根据$ a_ \ varepsilon $相对于$ \ varepsilon $的比率，我们得出了三个不同的通用darcy方程，在这些darcy方程中，速度和微动物场之间的相互作用被保留。
We study the flow of a micropolar fluid in a thin domain with microstructure, i.e. a thin domain with thickness $\varepsilon$ which is perforated by periodically distributed solid cylinders of size $a_\varepsilon$. 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 $a_\varepsilon$ with respect to $\varepsilon$, we derive three different generalized Darcy equations where the interaction between the velocity and the microrotation fields is preserved.
