弹性毛细血管脊的奇异性
On the singular nature of the elastocapillary ridge
摘要：
软界面的功能对于生物学和表面科学中的许多应用至关重要。最近的研究已经使用液滴来探测弹性体网络的表面力学。实验表明一个复杂的表面弹性，也被称为沙特尔沃思效应，其中表面张力是不恒定的，但取决于基板变形。然而，由于奇异的弹性形变，在液滴拉动网络的点处引起的，解释仍然有争议。在这里，我们揭示了弹性毛细奇异性的性质与各种本构关系的界面能的超弹性基板。首先，我们使用目标自适应有限元模拟精细地解决了奇点附近。这证实了以前有争议的关于接触角的诺依曼定律在大弹性形变下的普遍有效性。随后，我们推导出精确解的非线性弹性力学描述的奇异性分析。这些解决方案是在完美的协议与数值，并表明，在接触线的拉伸，如以前所测量的实验，始终指向一个强大的夏特沃斯效应。最后，使用Noether定理，我们提供了一个定量的润湿滞后和Eshelby样的力量之间的联系，从而提供了一个完整的框架中存在的Shuttleworth效应的软润湿。
英文摘要：
The functionality of soft interfaces is crucial to many applications in biology and surface science. Recent studies have used liquid drops to probe the surface mechanics of elastomeric networks. Experiments suggest an intricate surface elasticity, also known as the Shuttleworth effect, where surface tension is not constant but depends on substrate deformation. However, interpretations have remained controversial due to singular elastic deformations, induced exactly at the point where the droplet pulls the network. Here we reveal the nature of the elastocapillary singularity on a hyperelastic substrate with various constitutive relations for the interfacial energy. First, we finely resolve the vicinity of the singularity using goal-adaptive finite element simulations. This confirms the universal validity, also at large elastic deformations, of the previously disputed Neumann's law for the contact angles. Subsequently, we derive exact solutions of nonlinear elasticity that describe the singularity analytically. These solutions are in perfect agreement with numerics, and show that the stretch at the contact line, as previously measured experimentally, consistently points to a strong Shuttleworth effect. Finally, using Noether's theorem we provide a quantitative link between wetting hysteresis and Eshelby-like forces, and thereby offer a complete framework for soft wetting in the presence of the Shuttleworth effect.
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