软固体上的接触角：从杨氏定律到诺依曼定律
Contact angles on a soft solid: from Young's law to Neumann's law
摘要：
由于固体在毛细力的作用下发生弹性变形，因此液滴在软基底上形成的接触角不遵守经典的杨氏关系。固体的有限弹性也使得接触角不同于诺依曼定律预测的接触角，诺依曼定律适用于液滴漂浮在另一种液体上时。在这里，我们推导出一个弹性毛细模型的接触角在一个软固体，通过耦合的平均场模型的分子相互作用的弹性。我们证明，消失的弹性模量的限制产生诺依曼定律或其轻微的变化，这取决于在固体表面层的力的传输。当由表面张力与弹性模量之比$γ/E$定义的长度尺度达到几个分子尺寸时，出现接触角从刚性极限（杨氏）到柔性极限（诺依曼）的变化。
英文摘要：
The contact angle that a liquid drop makes on a soft substrate does not obey the classical Young's relation, since the solid is deformed elastically by the action of the capillary forces. The finite elasticity of the solid also renders the contact angles different from that predicted by Neumann's law, which applies when the drop is floating on another liquid. Here we derive an elasto-capillary model for contact angles on a soft solid, by coupling a mean-field model for the molecular interactions to elasticity. We demonstrate that the limit of vanishing elastic modulus yields Neumann's law or a slight variation thereof, depending on the force transmission in the solid surface layer. The change in contact angle from the rigid limit (Young) to the soft limit (Neumann) appears when the length scale defined by the ratio of surface tension to elastic modulus $γ/E$ reaches a few molecular sizes.
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