Brenner Howard
Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Oct;84(4 Pt 2):046309. doi: 10.1103/PhysRevE.84.046309. Epub 2011 Oct 13.
This paper offers a simple macroscopic approach to the question of the slip boundary condition to be imposed upon the tangential component of the fluid velocity at a solid boundary. Plausible reasons are advanced for believing that it is the energy equation rather than the momentum equation that determines the correct fluid-mechanical boundary condition. The scheme resulting therefrom furnishes the following general, near-equilibrium linear constitutive relation for the slip velocity of mass along a relatively flat wall bounding a single-component gas or liquid: (v(m))(slip)=-α∂lnρ/∂s|(wall), where α and ρ are, respectively, the fluid's thermometric diffusivity and mass density, while the length δs refers to distance measured along the wall in the direction in which the slip or creep occurs. This constitutive relation is shown to agree with experimental data for gases and liquids undergoing thermal creep or pressure-driven viscous creep at solid surfaces.
本文针对在固体边界处施加于流体速度切向分量的滑移边界条件问题，提出了一种简单的宏观方法。有合理理由认为，决定正确的流体力学边界条件的是能量方程而非动量方程。由此得出的方案给出了沿界定单组分气体或液体的相对平坦壁面的质量滑移速度的如下一般近平衡线性本构关系：(v(m))(滑移)=-α∂lnρ/∂s|(壁面)，其中α和ρ分别为流体的热扩散率和质量密度，而长度δs是指沿壁面在滑移或蠕动发生方向上测量的距离。该本构关系被证明与在固体表面经历热蠕变或压力驱动粘性蠕变的气体和液体的实验数据相符。
