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Dewetting with conical tail formation: how to include a line friction of microscopic origin, and possibly evaporation?
The European Physical Journal Special Topics ( IF 2.8 ) Pub Date : 2020-09-14 , DOI: 10.1140/epjst/e2020-900244-1
Laurent Limat

Most studies of dewetting fronts in 3D with a “corner formation”, as happens behind a drop sliding down an incline are based on a generalisation of Voinov theory, with (at least implicitly) a slip length at small scale. I here first examine what happens, if instead of considering a free slip at small scale, one admits a non-zero additional line friction of microscopic origin. Concerning the selection of cone angles, I show that most features of the model are unchanged, except that the “slip length” must be replaced in the equations with an “effective” cut off that can become apparently unphysically small. I suggest that these results could explain problematical cut-offs in the hydrodynamical modelling observed recently by Winkels et al. on water drops [K.G. Winkels, I.R. Peters, J. Snoeijer, F. Evangelista, M. Riepen, A. Daerr, L. Limat, Eur. Phys. J. Special Topics 192, 195 (2011)]. The sole difficulty with this interpretation is the law ruling the radius of curvature of the corner tip at small scale, which remains unsatisfactory. I suggest that evaporation of the liquid should also be considered at these very small scales and propose a preliminary “toy model” to take this effect into account. The orders of magnitude are better recovered without changing the structure of the equations developed initially for “classical” wetting dynamics with silicon oil drops.



中文翻译:

带有锥形尾部形成的去湿:如何包括微观起源的线摩擦以及可能的蒸发?

大多数在3D中以“角形成”对前沿进行去湿的研究(例如,沿倾斜向下滑动的液滴后面的现象)都是基于Voinov理论的一般化,其滑移长度(至少是隐含的)是小规模的。我首先在这里研究发生的情况,如果不是考虑小范围的自由滑移,而是承认微观起源的非零附加线摩擦。关于锥角的选择,我表明模型的大多数特征都没有改变,只是必须在方程式中用“有效”截断代替“滑移长度”,该截断显然会变得很小。我认为这些结果可以解释Winkels等人最近观察到的流体动力学模型中的问题性临界值。水滴[KG Winkels,IR Peters,J。Snoeijer,F。Evangelista,M。Riepen,A。Daerr,L。Limat,Eur。物理192,195(2011)]。这种解释的唯一困难是在小比例尺上确定角尖的曲率半径的法则,这仍然不能令人满意。我建议也应该在很小的范围内考虑液体的蒸发,并提出一个初步的“玩具模型”来考虑这种影响。在不改变最初为硅油滴“经典”润湿动力学而开发的方程式结构的情况下,可以更好地恢复数量级。

更新日期:2020-09-16
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