Nabeth Jeremy, Chigullapalli Sruti, Alexeenko Alina A
School of Aeronautics and Astronautics, Purdue University, West Lafayette, Indiana 47907, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jun;83(6 Pt 2):066306. doi: 10.1103/PhysRevE.83.066306. Epub 2011 Jun 10.
At the microscale, even moderate temperature differences leading to thermal nonequilibrium can result in significant Knudsen forces generated by the energy exchange between gas molecules and solids immersed in a gas. Experimental measurements of the microscale Knudsen force have been reported by Passian et al., Phys. Rev. Lett. 90, 124503 (2003) using heated microcantilevers of atomic force microscope probes. The present study investigates the mechanism and magnitude of Knudsen forces in detail based on numerical solution of the Boltzmann kinetic equation with the ellipsoidal statistical Bhatnagar-Gross-Krook approximation for the collisional relaxation process. A direct comparison between the numerical simulations and experimental measurements is presented. We show that, assuming a fully diffuse interaction of gas molecules with the surfaces of the heated cantilever, simulations agree with measurements for different operating pressures in argon and nitrogen ambients. For the helium ambient the simulations agree with measurements only when an incomplete accommodation is used. A closed-form model for the nondimensional Knudsen force coefficient on a heated microbeam is obtained that can be used for quantifying such forces in analysis and design of microsystems under a wide range of geometrical, thermal, and pressure conditions.
在微观尺度下，即使是导致热非平衡的适度温差，也会因气体分子与浸没在气体中的固体之间的能量交换而产生显著的克努森力。帕西安等人在《物理评论快报》90, 124503 (2003)中报道了使用原子力显微镜探针的加热微悬臂梁对微观尺度克努森力的实验测量。本研究基于玻尔兹曼动力学方程的数值解，并采用碰撞弛豫过程的椭球统计布特纳格尔-格罗斯-克鲁克近似，详细研究了克努森力的机制和大小。给出了数值模拟与实验测量的直接比较。我们表明，假设气体分子与加热悬臂梁表面完全漫反射相互作用，模拟结果与氩气和氮气环境中不同工作压力下的测量结果一致。对于氦气环境，只有当采用不完全适应时，模拟结果才与测量结果一致。得到了加热微梁上无量纲克努森力系数的封闭形式模型，可用于在广泛的几何、热和压力条件下，对微系统分析和设计中的此类力进行量化。
