从三流体交界到杨氏定律：本构与刚性支撑极限下的润湿

中文摘要 AI 辅助

杨氏定律描述刚性固体上的润湿，而纽曼平衡描述三流体交界处的力平衡，两者对应不同的允许运动。我们通过有序连续介质构造将二者联系起来。一个仿射粘弹性第三相，在固定模量且无松弛极限下，首先获得永久变形记忆。独立指定的材料-表面定律区分了表面自由能与机械表面应力。在可变形支撑上，固体材料的位移与润湿-干燥分界的迁移分别给出独立的平衡条件。在固定的宏观观测距离下，锚固支撑的刚性化抑制了位移，但可逆迁移仍可能发生。存留的变分给出杨氏定律；受约束的力学则作为反作用力承载法向以及一般情况下的切向毛细载荷。两个互补的结果证实了这一简化。一个具有圆形液体界面的夹紧有限应变模型，给出了约化能量的均匀收敛以及全局几乎极小化子对空间杨氏角的恢复。另一个独立的二次半空间模型给出了平稳迁移导数的收敛和非零极限牵引分布。这些结果解释了局部的类纽曼脊如何能与相对于远处壁面测量的杨氏角共存，同时区分了几何收敛与迁移及反作用力控制。

英文摘要

Young's law on a rigid solid and the Neumann balance at a three-fluid junction describe different admissible motions. We connect them through an ordered continuum construction. An affine viscoelastic third phase first acquires permanent deformation memory in the no-relaxation limit at fixed modulus. Independently specified material-surface laws distinguish surface free energy from mechanical surface stress. On the deformable support, displacement of solid material and migration of the wet-dry partition give separate equilibrium conditions. Stiffening an anchored support suppresses displacement at a fixed macroscopic observation distance but leaves reversible migration possible. The surviving variation gives Young's law; the constrained mechanics remains as a reaction carrying normal and, in general, tangential capillary loads. Two complementary results substantiate this reduction. A clamped finite-strain model with circular liquid interfaces yields uniform convergence of reduced energies and recovery of the spatial Young angle for global almost minimisers. A separate quadratic half-space model gives convergence of stationary migration derivatives and a nonzero limiting traction distribution. The results explain how a local Neumann-like ridge can coexist with a Young angle measured against the distant wall, while distinguishing geometric convergence from the control of migration and reaction forces.

发表机构

• Technische Universität Darmstadt（达姆施塔特工业大学）

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