Moving contact lines at non-zero capillary number
Moving contact lines at non-zero capillary number
复制标题
以非零毛细管数移动接触线
DOI：
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发表时间：
1986
影响因子：
3.7
通讯作者：
Kalvis M. Jansons
中科院分区：
文献类型：
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作者：
Kalvis M. Jansons
考虑在小毛细管数[Copf ]的限制下具有一维周期性粗糙度的固体表面上的流体-流体界面的不稳定运动。我们表明，界面的宏观行为可以描述，在[Copf ]的领导秩序，在定义良好的连续量，即使复杂的流体运动在附近的接触线不能。关键是接触角滞后使得有可能隔离接触线处的粘性应力奇异性，因为对于充分缓慢移动的流体-流体界面，接触线的所有移动发生在比宏观时间尺度短得多的时间内。宏观描述的有效“滑移长度”与速度有关，等于a[Copf ]−1，其中a是固体表面粗糙度的波长。最后，我们考虑表面的二维随机粗糙度，并认为他们也将表现出速度依赖的“滑移长度”，虽然速度的依赖性将在这种情况下更强。这些结果结合早期的工作（Jansons 1985）解释了为什么观察到的“滑移长度”可以比粗糙度大得多，以及为什么“粘滑”的程度随着速度的增加而减小。
Consider the unsteady motion of a fluid–fluid interface over and attached to a solid surface with one-dimensional periodic roughness in the limit of small capillary number [Copf ]. We show that the macroscopic behaviour of the interface can be described, to leading order in [Copf ], in terms of well-defined continuum quantities, even though the complicated fluid motion in the neighbourhood of the contact line cannot. The key is that contact-angle hysteresis makes it possible to isolate the viscous stress singularity at the contact line, since for a sufficiently slowly moving fluid—fluid interface all the movement of the contact line occurs in a time much shorter than the macroscopic timescale. The effective ‘slip length’ for the macroscopic description is shown to be velocity dependent and equal to a[Copf ]−1, where a is the wavelength of the roughness on the solid surface. Finally, we consider surfaces with two-dimensional random roughness, and argue that they too would exhibit velocity dependent ‘slip lengths’, though the velocity dependence would be stronger in this case. These results combined with earlier work (Jansons 1985) explain why observed ‘slip lengths’ can be much larger than roughness dimensions, and why the degree of ‘stick-slip’ decreases with increasing speed.