Wu Haibin, Moyle Nichole, Jagota Anand, Hui Chung-Yuen
Department of Mechanical and Aerospace Engineering, Field of Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853, USA.
Soft Matter. 2020 Mar 21;16(11):2760-2773. doi: 10.1039/c9sm02447f. Epub 2020 Feb 26.
Lubricated sliding on soft elastic substrates occurs in a variety of natural and technological settings. It very often occurs in the iso-viscous elasto-hydrodynamic lubrication (EHL) regime (e.g., soft solid, low pressure). In this regime, for sliding of a smooth sphere on a soft solid, a "Hertz-like" effective contact region forms. Much of the fluid is squeezed out of the contact region although enough is retained to keep the solid surfaces fully separated. This is accompanied by complex deformation of the soft solid. The behavior of such soft lubricated contacts is controlled by a single dimensionless parameter 1/β that can be interpreted as a normalized sliding velocity. Solving this fundamental soft-lubrication problem poses significant computational difficulty for large β, which is the limit relevant for soft solids. As a consequence, little is known about the structure of the flow field under soft lubrication in the intake and outlet regions. Here we present a new solution of this soft lubrication problem focusing on the "Hertz" limit. We develop a formulation in polar coordinates that handles difficult computational issues much better than previous methods. We study how hydrodynamic pressure, film thickness and hydrodynamic friction vary with β. Scaling laws for these relationships are given in closed form for a range of β not previously accessible theoretically but that is typical in applications. The computational method presented here can be used to study other soft lubrication problems.
在各种自然和技术环境中都会出现软弹性基底上的润滑滑动。它经常发生在等粘性弹性流体动力润滑（EHL） regime（例如，软固体，低压）中。在这种 regime 下，对于光滑球体在软固体上的滑动，会形成一个“类赫兹”有效接触区域。尽管有足够的流体被保留以保持固体表面完全分离，但大部分流体还是被挤出了接触区域。这伴随着软固体的复杂变形。这种软润滑接触的行为由一个单一的无量纲参数 1/β 控制，该参数可解释为归一化滑动速度。对于大 β（这是与软固体相关的极限），解决这个基本的软润滑问题会带来巨大的计算困难。因此，对于软润滑下入口和出口区域的流场结构知之甚少。在这里，我们提出了这个软润滑问题的一种新解决方案，重点关注“赫兹”极限。我们开发了一种极坐标下的公式，它比以前的方法能更好地处理困难的计算问题。我们研究了流体动力压力、膜厚和流体动力摩擦如何随 β 变化。对于一系列以前在理论上无法获得但在应用中很典型的 β，这些关系的缩放定律以封闭形式给出。这里提出的计算方法可用于研究其他软润滑问题。
