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Analysis of the Roughness Regimes for Micropolar Fluids via Homogenization
Bulletin of the Malaysian Mathematical Sciences Society ( IF 1.0 ) Pub Date : 2020-09-25 , DOI: 10.1007/s40840-020-01027-1
Francisco J. Suárez-Grau

We study the asymptotic behavior of micropolar fluid flows in a thin domain of thickness \(\eta _\varepsilon \) with a periodic oscillating boundary with wavelength \(\varepsilon \). We consider the limit when \(\varepsilon \) tends to zero and, depending on the limit of the ratio of \(\eta _\varepsilon /\varepsilon \), we prove the existence of three different regimes. In each regime, we derive a generalized Reynolds equation taking into account the microstructure of the roughness.



中文翻译:

通过均质作用分析微极性流体的粗糙度状况

我们研究了厚度为\(\ eta _ \ varepsilon \)的薄域中的微极性流体流动的渐近行为,该区域的周期性振荡边界为波长\(\ varepsilon \)。我们考虑\(\ varepsilon \)趋于零时的极限,并且根据\(\ eta _ \ varepsilon / \ varepsilon \)的比率极限,我们证明了三种不同形式的存在。在每种情况下,我们都考虑了粗糙度的微观结构,得出了一个广义的雷诺方程。

更新日期:2020-09-25
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