Modeling of Surface Forces between Micron-Sized Objects in Dry Condition

A. Hariri, J. Zu, R. Mrad
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引用次数: 5

Abstract

Capillary, van der Walls (vdW) and electrostatic forces, which usually termed as surface forces, can significantly affect the behavior and performance of Micro Electro Mechanical Systems (MEMS) containing surfaces that can contact each other. Here, we are concerned with vdW force, which is the dominant surface force between conducting surfaces in the dry condition. In this study, we first review existing roughness models described by stochastic processes of Gaussian and Fractal type. Then, the vdW force is formulated using two methods by considering the first and second order probability density function (pdf) of the height distribution of rough surfaces. The resulting formulae are functions of the correlation ( ñ) between successive sampling points. By analyzing these formulae based on the correlation and other parameters, the upper and lower bound of vdW force are identified and a numericalbased closed-form formula for the upper bound is derived. Finally, various situations are discussed based on the developed equations and data from a surface micro machining process.
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微米级物体在干燥条件下的表面力建模
毛细管力、范德华力(vdW)和静电力通常被称为表面力,它们可以显著影响包含可以相互接触的表面的微机电系统(MEMS)的行为和性能。在这里,我们关注的是vdW力,它是干燥条件下导电表面之间的主要表面力。在本研究中,我们首先回顾了由高斯型和分形型随机过程描述的现有粗糙度模型。然后,考虑粗糙表面高度分布的一阶和二阶概率密度函数(pdf),采用两种方法推导了vdW力。所得公式是连续采样点之间相关性的函数(ñ)。基于相关关系和其他参数对这些公式进行分析,确定了vdW力的上界和下界,并推导了上界的数值封闭形式公式。最后,根据所建立的方程和表面微加工过程的数据,讨论了各种情况。
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