论文标题
基于几何的模型，用于涂在硅晶片上的滴剂和可膨胀的聚合物刷膜上
A geometry-based model for spreading drops applied to drops on a silicon wafer and a swellable polymer brush film
论文作者
论文摘要
我们研究了在滴度接近球形帽的状态下扩散的动力学。后一个简化适用于高度粘性滴的晚期（粘性）阶段，直径低于毛细管长度。此外，它适用于在膨胀的聚合物刷上的滴剂扩散，在膨胀的聚合物刷上，与底物的复杂相互作用导致了非常缓慢的扩散动力学。如果毛细管数是接触角的函数，则球形盖几何形状允许扩展闭合的普通微分方程（ODE），因为经验接触角模型是这种情况。后一种方法是由De Gennes（现代物理学的评论，1985年）引入的，该方法针对小接触角。在目前的工作中，我们将方法推广到任意接触角。该方法应用于在硅晶片上扩散水甘油滴并在PNIPAM涂层硅晶片上扩散水滴的实验数据。发现在部分润湿的情况下，ode模型能够描述扩散动力学。此外，如果接触角和毛细管数之间的关系是通用的，则该模型可以预测球形盖形液滴的扩散动力学。
We investigate the dynamics of spreading in a regime where the shape of the drop is close to a spherical cap. The latter simplification is applicable in the late (viscous) stage of spreading for highly viscous drops with a diameter below the capillary length. Moreover, it applies to the spreading of a drop on a swellable polymer brush, where the complex interaction with the substrate leads to a very slow spreading dynamics. The spherical cap geometry allows to derive a closed ordinary differential equation (ODE) for the spreading if the capillary number is a function of the contact angle as it is the case for empirical contact angle models. The latter approach has been introduced by de Gennes (Reviews of Modern Physics, 1985) for small contact angles. In the present work, we generalize the method to arbitrary contact angles. The method is applied to experimental data of spreading water-glycerol drops on a silicon wafer and spreading water drops on a PNIPAm coated silicon wafer. It is found that the ODE-model is able to describe the spreading kinetics in the case of partial wetting. Moreover, the model can predict the spreading dynamics of spherical cap-shaped droplets if the relationship between the contact angle and the capillary number is universal.
