Kunert Christian, Harting Jens
Institute for Computational Physics, University of Stuttgart, Pfaffenwaldring 27, D-70569 Stuttgart, Germany.
Phys Rev Lett. 2007 Oct 26;99(17):176001. doi: 10.1103/PhysRevLett.99.176001. Epub 2007 Oct 23.
Surface roughness becomes relevant if typical length scales of the system are comparable to the variations as it is the case in microfluidic setups. Here, an apparent slip is often detected which can have its origin in the misleading assumption of perfectly smooth boundaries. We investigate the problem by means of lattice Boltzmann simulations and introduce an "effective no-slip plane" at an intermediate position between peaks and valleys of the surface. Our simulations agree with analytical results for sinusoidal boundaries, but can be extended to arbitrary geometries and experimentally obtained data. We find that the apparent slip is independent of the detailed boundary shape, but only given by the distribution of surface heights. Further, we show that slip diverges as the amplitude of the roughness increases which highlights the importance of a proper treatment of surface variations in very confined geometries.
如果系统的典型长度尺度与变化相当，如在微流体装置中那样，表面粗糙度就变得很重要。在这里，经常会检测到明显的滑移，其根源可能在于对完美光滑边界的错误假设。我们通过格子玻尔兹曼模拟来研究这个问题，并在表面的峰谷之间的中间位置引入一个“有效无滑移平面”。我们的模拟结果与正弦边界的解析结果一致，但可以扩展到任意几何形状和实验获得的数据。我们发现，明显的滑移与详细的边界形状无关，仅由表面高度的分布决定。此外，我们表明，随着粗糙度幅度的增加，滑移会发散，这突出了在非常受限的几何形状中正确处理表面变化的重要性。
