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：

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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。