McHale Glen, Gao Nan, Wells Gary G, Barrio-Zhang Hernán, Ledesma-Aguilar Rodrigo
Institute for Multiscale Thermofluids, School of Engineering, The University of Edinburgh, Edinburgh EH9 3FB, U.K.
Department of Mechanical Engineering, University of Birmingham, Birmingham B15 2TT, U.K.
Langmuir. 2022 Apr 12;38(14):4425-4433. doi: 10.1021/acs.langmuir.2c00178. Epub 2022 Mar 30.
The empirical laws of dry friction between two solid bodies date back to the work of Amontons in 1699 and are pre-dated by the work of Leonardo da Vinci. Fundamental to those laws are the concepts of static and kinetic coefficients of friction relating the pinning and sliding friction forces along a surface to the normal load force. For liquids on solid surfaces, contact lines also experience pinning and the language of friction is used when droplets are in motion. However, it is only recently that the concept of coefficients of friction has been defined in this context and that droplet friction has been discussed as having a static and a kinetic regime. Here, we use surface free energy considerations to show that the frictional force per unit length of a contact line is directly proportional to the normal component of the surface tension force. We define coefficients of friction for both contact lines and droplets and provide a droplet analogy of Amontons' first and second laws but with the normal load force of a solid replaced by the normal surface tension force of a liquid. In the static regime, the coefficient of static friction, defined by the maximum pinning force of a droplet, is proportional to the contact angle hysteresis, whereas in the kinetic regime, the coefficient of kinetic friction is proportional to the difference in dynamic advancing and receding contact angles. We show the consistency between the droplet form of Amontons' first and second laws and an equation derived by Furmidge. We use these liquid-solid Amontons' laws to describe literature data and report friction coefficients for various liquid-solid systems. The conceptual framework reported here should provide insight into the design of superhydrophobic, slippery liquid-infused porous surfaces (SLIPS) and other surfaces designed to control droplet motion.
两个固体之间干摩擦的经验定律可追溯到1699年阿蒙顿的工作，并且早于列奥纳多·达·芬奇的工作。这些定律的基础是静摩擦系数和动摩擦系数的概念，它们将沿表面的钉扎摩擦力和滑动摩擦力与法向载荷力联系起来。对于固体表面上的液体，接触线也会经历钉扎，并且当液滴运动时会使用摩擦的术语。然而，直到最近才在这种情况下定义了摩擦系数的概念，并且液滴摩擦被讨论为具有静态和动态两种状态。在这里，我们利用表面自由能的考虑来表明，接触线每单位长度的摩擦力与表面张力的法向分量成正比。我们定义了接触线和液滴的摩擦系数，并给出了阿蒙顿第一定律和第二定律的液滴类比，但用液体的法向表面张力代替了固体的法向载荷力。在静态状态下，由液滴的最大钉扎力定义的静摩擦系数与接触角滞后成正比，而在动态状态下，动摩擦系数与动态前进接触角和后退接触角的差值成正比。我们展示了阿蒙顿第一定律和第二定律的液滴形式与弗米吉推导的一个方程之间的一致性。我们使用这些液固阿蒙顿定律来描述文献数据，并报告各种液固系统的摩擦系数。这里报道的概念框架应该为超疏水、注入滑液的多孔表面（SLIPS）以及其他旨在控制液滴运动的表面的设计提供见解。
