Zhang Hongwu, Zhang Zhongqiang, Zheng Yonggang, Ye Hongfei
State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116024, People's Republic of China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Jun;81(6 Pt 2):066303. doi: 10.1103/PhysRevE.81.066303. Epub 2010 Jun 8.
A corrected second-order slip boundary condition is proposed to solve the Navier-Stokes equations for fluid flows confined in parallel-plate nanochannels. Compared with the classical second-order slip boundary condition proposed by Beskok and Karniadakis, the corrected slip boundary condition is not only dependent on the Knudsen number and the tangential momentum accommodation coefficient, but also dependent on the relative position of the slip surface in the Knudsen layer. For the fluid flows in slip-flow regime with the Knudsen number less than 0.3, Couette cell is investigated using molecular-dynamics simulations to verify Newtonian flow behaviors by examining the constitutive relationship between shear stress and strain rate. By comparing the velocity profiles of Poiseuille flows predicted from the Navier-Stokes equations with the corrected slip boundary condition with that from molecular-dynamics simulations, it is found that the flow behaviors in our models can be effectively captured.
提出了一种修正的二阶滑移边界条件，用于求解平行板纳米通道内流体流动的纳维-斯托克斯方程。与Beskok和Karniadakis提出的经典二阶滑移边界条件相比，修正后的滑移边界条件不仅依赖于克努森数和切向动量适应系数，还依赖于滑移面在克努森层中的相对位置。对于克努森数小于0.3的滑移流态下的流体流动，通过分子动力学模拟研究了库埃特流槽，通过考察剪应力与应变率之间的本构关系来验证牛顿流动行为。通过将修正滑移边界条件下纳维-斯托克斯方程预测的泊肃叶流速度分布与分子动力学模拟得到的速度分布进行比较，发现我们模型中的流动行为能够被有效地捕捉到。
