粗糙疏水表面有效滑移的均匀化计算
Computation of the effective slip of rough hydrophobic surfaces via homogenization
摘要：
本文定量分析了粗糙疏水表面对粘性牛顿流体的影响。我们使用的模型介绍了Ybert和合著者，其中粗糙的表面被替换为一个平面交替小面积的滑移和无滑移。我们调查的平均滑移产生的边界，这取决于这些领域之间的比例。这个问题减少到一个非本地系统的均匀化，涉及的Dirichlet诺依曼映射的斯托克斯算子，在一个域与小孔。考虑到Allaire的工作，我们计算了各种类型的粗糙度（riblets，补丁）的平均滑移精确的比例律。数值计算完成并证实了分析。
英文摘要：
We present a quantitative analysis of the effect of rough hydrophobic surfaces on viscous newtonian flows. We use a model introduced by Ybert and coauthors in which the rough surface is replaced by a flat plane with alternating small areas of slip and no-slip. We investigate the averaged slip generated at the boundary, depending on the ratio between these areas. This problem reduces to the homogenization of a non-local system, involving the Dirichlet to Neumann map of the Stokes operator, in a domain with small holes. Pondering on works by Allaire, we compute accurate scaling laws of the averaged slip for various types of roughness (riblets, patches). Numerical computations complete and confirm the analysis.
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