Department of Chemical Engineering, McGill University , Montreal, Quebec H3A 0C5, Canada.
Langmuir. 2013 Nov 19;29(46):14168-77. doi: 10.1021/la403088r. Epub 2013 Nov 4.
Surface curvature affects the shape, stability, and apparent contact angle of sessile and pendant drops. Here, we develop an approximate analytical solution for non-axisymmetric perturbations to small spherical drops on a flat substrate, assuming a fixed contact angle and fixed drop volume. The analytical model is validated using numerical solutions of the Laplace equation from the Surface Evolver software. We investigate the effects of surface curvature on drop shape, pressure, and surface energy, ascertaining the energy-gradient force that drives lateral drop migration. By balancing this force with the viscous resistance/drag force, in the lubrication approximation, we predict velocities of the order of 0.1 mm s(-1) for 1 mm diameter drops of water with a 30° contact angle on a substrate with a curvature gradient of 0.01 mm(-2), achieved, for example, on a harmonic surface with a wavelength of 4 cm and an amplitude of 4 mm.
表面曲率会影响固着和悬滴的形状、稳定性和表观接触角。在这里，我们针对小的球形液滴在平面基底上的非轴对称微扰，假设固定接触角和固定液滴体积，开发了一个近似解析解。通过使用 Surface Evolver 软件的拉普拉斯方程的数值解来验证分析模型。我们研究了表面曲率对液滴形状、压力和表面能的影响，确定了驱动侧向液滴迁移的能量梯度力。通过在润滑近似中平衡该力与粘性阻力/曳力，我们预测对于在曲率梯度为 0.01 mm(-2)的基底上直径为 1mm、接触角为 30°的水液滴，其速度约为 0.1mm/s，这可以通过例如在波长为 4cm、振幅为 4mm 的谐表面上实现。
