类fakir超疏水表面的流体动力摩擦
Hydrodynamic friction of fakir-like super-hydrophobic surfaces
摘要：
位于超疏水表面上的流体液滴仅在小的隔离区域与表面接触，并且主要与周围空气接触。因此，在这种表面附近运动的流体经历非常低的摩擦，并且超疏水表面在层流状态下显示出强烈的阻力减小。在这里，我们认为理论上的超疏水表面的圆形职位（所谓的苦行僧几何）位于一个平面的矩形晶格。使用适当的空间依赖强度的点力的叠加，我们推导出有效的表面滑移长度的平面剪切流在这样的fakir表面作为一个无限系列的线性方程的解决方案。在小表面覆盖的渐近极限的支柱，该系列可以解释为黎曼和，和滑移长度可以得到解析。对于正方形格子上的帖子，我们的分析结果与以前的数值计算在很好的定量协议。
英文摘要：
A fluid droplet located on a super-hydrophobic surface makes contact with the surface only at small isolated regions, and is mostly in contact with the surrounding air. As a result, a fluid in motion near such a surface experiences very low friction, and super-hydrophobic surfaces display strong drag-reduction in the laminar regime. Here we consider theoretically a super-hydrophobic surface composed of circular posts (so called fakir geometry) located on a planar rectangular lattice. Using a superposition of point forces with suitably spatially-dependent strength, we derive the effective surface slip length for a planar shear flow on such a fakir surface as the solution to an infinite series of linear equations. In the asymptotic limit of small surface coverage by the posts, the series can be interpreted as Riemann sums, and the slip length can be obtained analytically. For posts on a square lattice, our analytical results are in excellent quantitative agreement with previous numerical computations.
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