A semi-analytical method to estimate the effective slip length of spreading spherical-cap shaped droplets using Cox theory
A semi-analytical method to estimate the effective slip length of spreading spherical-cap shaped droplets using Cox theory
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DOI：
10.1088/1873-7005/aaaef6
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发表时间：
2018-03
影响因子：
1.5
通讯作者：
M. Wörner;Xuan Cai;H. Alla;P. Yue
中科院分区：
文献类型：
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作者：
M. Wörner;Xuan Cai;H. Alla;P. Yue
关于动态铺展的Cox-Voinov定律将表观接触角（θ）和平衡接触角的立方值之间的差与瞬时接触线速度（U）相关联。将铺展结果与该流体动力学润湿理论进行比较需要整个过程中θ和U的准确数据。我们考虑的情况下，重力可以忽略不计，因此，扩展液滴的形状可以密切近似的球冠。使用几何依赖关系，我们将一般的考克斯定律的传播半径的时间演变的半解析关系。数值计算表明，当气体粘度小于液滴粘度的约1%时，扩展曲线变得与气体粘度无关。由于惯性可能会使假设无效的初始阶段的蔓延，一个定量的标准时，球帽假设是合理的，来自利用相场模拟的部分润湿液滴的蔓延。所发展的理论使我们能够比较球帽形液滴的实验/计算铺展曲线与考克斯理论，而不需要θ和U的瞬时数据。此外，考克斯理论的拟合使我们能够估计的有效滑移长度。这是潜在的有用的滑动长度和参数之间的关系，在移动接触线的数值方法建立。
The Cox–Voinov law on dynamic spreading relates the difference between the cubic values of the apparent contact angle (θ) and the equilibrium contact angle to the instantaneous contact line speed (U). Comparing spreading results with this hydrodynamic wetting theory requires accurate data of θ and U during the entire process. We consider the case when gravitational forces are negligible, so that the shape of the spreading drop can be closely approximated by a spherical cap. Using geometrical dependencies, we transform the general Cox law in a semi-analytical relation for the temporal evolution of the spreading radius. Evaluating this relation numerically shows that the spreading curve becomes independent from the gas viscosity when the latter is less than about 1% of the drop viscosity. Since inertia may invalidate the made assumptions in the initial stage of spreading, a quantitative criterion for the time when the spherical-cap assumption is reasonable is derived utilizing phase-field simulations on the spreading of partially wetting droplets. The developed theory allows us to compare experimental/computational spreading curves for spherical-cap shaped droplets with Cox theory without the need for instantaneous data of θ and U. Furthermore, the fitting of Cox theory enables us to estimate the effective slip length. This is potentially useful for establishing relationships between slip length and parameters in numerical methods for moving contact lines.