Analytical solutions for partially wetting two-dimensional droplets.
Analytical solutions for partially wetting two-dimensional droplets.
复制标题
部分润湿二维液滴的分析解决方案。
作者：
J. Gomba;G. Homsy
我们提出了一个新的分析解决方案的静态形状的二维液滴与周围的薄膜在固体基板上的平衡。该模型包括毛细作用和分离-结合压力占固体和液体之间的分子间力的影响。我们推导出新的液滴的形状，横截面积，半宽度，最大曲率和拐点的解析解。我们研究了液滴尺寸对表观接触角的影响。接触线区域中的液滴的形状进行比较，通过采用文献中建议的近似值获得的配置文件，并讨论了所观察到的差异。最后，我们提出的时间演化的稳定状态，以显示如何整个配置文件，包括薄膜，演变到相应的固定配置。
We present a new analytical solution for the static shape of a two-dimensional droplet in equilibrium with a surrounding thin film on a solid substrate. The modeling includes the effects of capillarity and disjoining-conjoining pressure accounting for intermolecular forces between the solid and the liquid. We derive new analytical solutions for the shape of the droplet, the cross-sectional area, the half-width, and the maximum curvature and inflection points. We study the effects of the size of the droplet on the apparent contact angle. The shape of the droplet in the contact line region is compared with profiles obtained by employing approximations suggested in the literature, and the observed differences are discussed. Finally, we present the time evolution to the steady state to show how the whole profile, including the thin film, evolves to the corresponding stationary configuration.