软涂层在流体介导载荷作用下的弹性流体动力学研究
Elastohydrodynamics of a soft coating under fluid-mediated loading by a spherical probe
摘要：
物体在有流体介入的软壁附近的运动是弹性流体动力学中的一个典型问题，在生物学和摩擦学的学科中都有发现。特别是，在扫描探针显微镜的上下文中，经常遇到的一个球体朝向一个软基板与介入流体的运动。虽然已经对这种设置进行了基础理论研究，但它们侧重于具体应用，从而进行了适当的简化。在这里，我们提出了一个多功能的半分析框架，用于研究轴对称加载的刚性球体附近的软弹性基板上涂覆的刚性平台介导的电解质水溶液的弹性流体动力学。三种加载模式被认为是接近，衰退和振荡。该框架结合了大的振荡频率和振幅，压力和衬底变形之间的双向耦合，以及DLVO力的存在。从计算使用的框架，我们获得的DLVO力的影响，基板厚度，基板材料的可压缩性（量化泊松比）和高振荡频率的SPM等遇到的不同的物理设置的见解。我们列出了一些关键的观察。较厚且更可压缩的基底允许较大的变形，即实际上较软。DLVO力的存在导致力的放大高达两个数量级，并且对于低频下的振荡负载和低速下的接近/后退负载，基板变形高达一个数量级。对于高频振荡载荷，DLVO力不会明显影响系统的力和挠度行为。在展示了我们的框架的多功能性和实用性之后，我们希望它能够发展成为解决软润滑问题的多样化和有用的工具。
英文摘要：
Motion of an object near a soft wall with intervening fluid is a canonical problem in elastohydrodynamics, finding presence in subjects spanning biology to tribology. Particularly, motion of a sphere towards a soft substrate with intervening fluid is often encountered in the context of scanning probe microscopy. While there have been fundamental theoretical studies on this setup, they have focussed on specific applications and thus enforced suitable simplifications. Here we present a versatile semi-analytical framework for studying the elastohydrodynamics of axisymmetric loading of a rigid sphere near a soft elastic substrate coated on a rigid platform mediated by an aqueous electrolytic solution. Three loading modes are considered - approach, recession and oscillatory. The framework incorporates - large oscillation frequency and amplitude, two-way coupling between pressure and substrate deformation, and presence of DLVO forces. From computations using the framework, we gain insights on the effects of DLVO forces, substrate thickness, substrate material compressibility (quantified by Poisson's ratio) and high oscillation frequency for different physical setups encountered in SPM and the likes. We list some key observations. A substrate that is thicker and more compressible allows for larger deformation, i.e. is effectively softer. Presence of DLVO forces lead to magnification in force of upto two orders of magnitude and in substrate deformation of upto an order of magnitude for oscillatory loading at low frequencies and approach/recession loading at low speed. For oscillatory loading at high frequencies, DLVO forces do not appreciably affect the force and deflection behaviour of the system. Having demonstrated the versatility and utility of our framework, we expect it to evolve into a diverse and useful tool for solving problems of soft-lubrication.
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