Relaxation of a dewetting contact line. Part 1. A full-scale hydrodynamic calculation
Relaxation of a dewetting contact line. Part 1. A full-scale hydrodynamic calculation
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DOI：
10.1017/s0022112007005216
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发表时间：
2007-05
影响因子：
3.7
通讯作者：
J. Snoeijer;B. Andreotti;G. Delon;M. Fermigier
中科院分区：
文献类型：
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作者：
J. Snoeijer;B. Andreotti;G. Delon;M. Fermigier
从理论上研究了在所谓的“Landau-Levich”几何中去湿接触线的松弛，其中垂直固体板从部分润湿液体的浴中取出。该研究是在润滑理论的框架内进行的，其中流体动力学在所有长度尺度（从分子到宏观）上都得到了解决。我们调查的未扰动的接触线，这原来是更复杂的比预期的简化的“准静态”理论的基础上的表观接触角的分叉图。线性稳定性分析表明，低于临界毛细数夹带，Cac，接触线是线性稳定的所有波数。在远离临界点处，色散关系具有渐近性态|Q|并且与准静态方法相比很好。然而，接近Cac时，一种不同的机制接管了，分散性从|Q|更常见的是q2。这些发现意味着接触线不能使用速度和表观接触角之间的普遍关系来描述，但必须明确对待粘性效应。
The relaxation of a dewetting contact line is investigated theoretically in the so-called ‘Landau–Levich’ geometry in which a vertical solid plate is withdrawn from a bath of partially wetting liquid. The study is performed in the framework of lubrication theory, in which the hydrodynamics is resolved at all length scales (from molecular to macroscopic). We investigate the bifurcation diagram for unperturbed contact lines, which turns out to be more complex than expected from simplified ‘quasi-static’ theories based upon an apparent contact angle. Linear stability analysis reveals that below the critical capillary number of entrainment, Cac, the contact line is linearly stable at all wavenumbers. Away from the critical point, the dispersion relation has an asymptotic behaviour σ∝|q| and compares well to a quasi-static approach. Approaching Cac, however, a different mechanism takes over and the dispersion evolves from ∼|q| to the more common ∼q2. These findings imply that contact lines cannot be described using a universal relation between speed and apparent contact angle, but viscous effects have to be treated explicitly.