In theoretical analyses of the moving contact line, an infinite force along the solid wall has been reported based off the non-integrable stress along a single interface. In this investigation we demonstrate that the stress singularity is integrable and results in a finite force at the moving contact line if the contact line is treated as a one-dimensional manifold and all three interfaces that make up the moving contact line are taken into consideration. This is due to the dipole nature of the vorticity and pressure distribution around the moving contact line. Mathematically, this finite force is determined by summing all the forces that act over an infinitesimally small cylindrical control volume that encloses the entire moving contact line. With this finite force, we propose a new dynamic Young's equation for microscopic dynamic contact angle that is a function of known parameters only, specifically the interface velocity, surface tension, and fluid viscosity. We combine our model with Cox's model for apparent dynamic contact angle and find good agreement with published dynamic contact angle measurements.

中文翻译：

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动接触线上有限力的理论模型

在移动接触线的理论分析中，基于沿单个界面的不可积应力，已经报告了沿实体壁的无限力。在这项研究中，我们证明了应力奇异性是可积分的，如果将接触线视为一维流形并考虑构成移动接触线的所有三个界面，则应力奇异性会在移动接触线上产生有限力。这是由于移动接触线周围的涡量和压力分布的偶极子性质。从数学上讲，该有限力是通过将作用在包围整个移动接触线的无限小的圆柱形控制体积上的所有力相加来确定的。有了这个有限的力，我们提出了一个新的动态 Young' s 微观动态接触角方程，它仅是已知参数的函数，特别是界面速度、表面张力和流体粘度。我们将我们的模型与 Cox 的表观动态接触角模型相结合，并发现与已发布的动态接触角测量值非常吻合。