Soft Wetting Ridge Rotation in Sessile Droplets and Capillary Bridges

We investigate the
deformation of soft solid layers in the presence
of sessile droplets or capillary bridges. Unlike models that assume
Young’s law governs the contact angle, we incorporate the surface
tension balance at the contact line to analyze the rotation of the
wetting ridge and the corresponding change in the contact angle. Our
findings reveal that the rotation direction of the wetting ridge aligns
with the sign of the Laplace pressure. Interestingly, although a softer
solid layer typically decreases the contact angle for sessile droplets,
a negative Laplace pressure in a hydrophilic capillary bridge pulls
the solid–liquid interface, leading to an increased contact
angle. A hydrophilic capillary bridge would be expected to move from
thicker regions of a soft layer to thinner areas, exhibiting behavior
opposite that of a sessile droplet. The interplay between soft layer
deformation and contact angle modulation provides valuable insights
into controlling droplet motion through elastocapillarity.

本研究探讨了存在座滴（sessile droplet）或毛细桥（capillary bridge）时软固体层的变形行为。不同于假设接触角由杨氏定律（Young’s law）支配的现有模型，我们引入接触线处的表面张力平衡，用以分析润湿脊（wetting ridge）的旋转过程与接触角的相应变化。研究结果显示，润湿脊的旋转方向与拉普拉斯压强（Laplace pressure）的符号一致。值得注意的是，尽管更软的固体层通常会降低座滴的接触角，但亲水（hydrophilic）毛细桥内的负拉普拉斯压强会牵拉固液界面（solid-liquid interface），最终使接触角增大。亲水毛细桥会从软固体层的较厚区域向较薄区域迁移，其运动行为与座滴完全相反。软层变形与接触角调控之间的相互作用，为通过弹性毛细（elastocapillarity）效应调控液滴运动提供了极具价值的理论参考。