Yin Hanyu, Sibley David N, Thiele Uwe, Archer Andrew J
Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom.
Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm Klemm Str. 9, 48149 Münster, Germany.
Phys Rev E. 2017 Feb;95(2-1):023104. doi: 10.1103/PhysRevE.95.023104. Epub 2017 Feb 6.
We present a study of the spreading of liquid droplets on a solid substrate at very small scales. We focus on the regime where effective wetting energy (binding potential) and surface tension effects significantly influence steady and spreading droplets. In particular, we focus on strong packing and layering effects in the liquid near the substrate due to underlying density oscillations in the fluid caused by attractive substrate-liquid interactions. We show that such phenomena can be described by a thin-film (or long-wave or lubrication) model including an oscillatory Derjaguin (or disjoining or conjoining) pressure and explore the effects it has on steady droplet shapes and the spreading dynamics of droplets on both an adsorption (or precursor) layer and completely dry substrates. At the molecular scale, commonly used two-term binding potentials with a single preferred minimum controlling the adsorption layer height are inadequate to capture the rich behavior caused by the near-wall layered molecular packing. The adsorption layer is often submonolayer in thickness, i.e., the dynamics along the layer consists of single-particle hopping, leading to a diffusive dynamics, rather than the collective hydrodynamic motion implicit in standard thin-film models. We therefore modify the model in such a way that for thicker films the standard hydrodynamic theory is realized, but for very thin layers a diffusion equation is recovered.
我们展示了一项关于非常小尺度下液滴在固体基底上扩散的研究。我们关注有效润湿能（结合势）和表面张力效应显著影响稳定且正在扩散的液滴的状态。特别地，我们关注由于基底 - 液体间吸引相互作用导致的流体中潜在密度振荡，在基底附近液体中产生的强堆积和分层效应。我们表明，这种现象可以用一个薄膜（或长波或润滑）模型来描述，该模型包括一个振荡的Derjaguin（或分离或结合）压力，并探讨其对稳定液滴形状以及液滴在吸附（或前驱体）层和完全干燥基底上的扩散动力学的影响。在分子尺度上，常用的具有单一优选最小值来控制吸附层高度的双项结合势，不足以捕捉由近壁分层分子堆积引起的丰富行为。吸附层厚度通常为亚单层，即沿该层的动力学由单粒子跳跃组成，导致扩散动力学，而不是标准薄膜模型中隐含的集体流体动力学运动。因此，我们对模型进行修改，使得对于较厚的膜能实现标准流体动力学理论，但对于非常薄的层能恢复扩散方程。
