Kobryn Alexander E, Kovalenko Andriy
National Institute for Nanotechnology, National Research Council of Canada, 11421 Saskatchewan Drive, Edmonton, Alberta T6G2M9, Canada.
J Chem Phys. 2008 Oct 7;129(13):134701. doi: 10.1063/1.2972978.
Motivated by the fundamental questions raised by the most recent experimental achievements in nanofluidics, we propose the first-ever derivation and calculation of the hydrodynamic slip length from the first principles of statistical mechanics, namely, a combination of linear response theory and equilibrium molecular theory of solvation. The slip length derived is related to the fluid organization near the solid surface, as governed by the solid-liquid interaction. In the wide range of shear rates and surface-liquid interactions, the slip length is expressed in terms of the Green-Kubo-Nakano relations as a function of the anisotropic inhomogeneous time-correlation function of density fluctuations of the liquid in contact with the surface. The time dependence of the correlation function is factored out by treating it in the hydrodynamic limit. The spatially inhomogeneous two-body correlation function is represented in the Kirkwood-type approximation as a product of the three-dimensional density distributions of interaction sites of the liquid near the surface and the site-site pair correlations of the bulk liquid. The presented treatment generalizes the phenomenological definition of the friction coefficient (as well as the slip length) to a tensor quantity, which reflects an anisotropic nature of an ordered crystalline or nanopatterned surface. This enables theoretical prediction of friction forces acting aslant to the liquid flow direction for such surfaces. We derive generic analytical expressions for the liquid-surface friction coefficient (and slip length) for an arbitrary surface-liquid interaction potential. We further illustrate it by numerical calculations for a laminar flow of nine different molecular liquids, including water, at ambient conditions in contact with the (100) face-centered cubic cell surface of gold, copper, and nickel modeled by using optimized potential for liquid simulation models for liquids and the Steele potential for crystalline surfaces. The obtained values for slip length range from few to hundreds of nanometers and microns and are consistent with experimental measurements.
受纳米流体学最新实验成果所引发的基本问题的驱动，我们从统计力学的第一原理出发，即线性响应理论与溶剂化平衡分子理论相结合，首次推导并计算了流体动力滑移长度。所推导的滑移长度与固体表面附近的流体组织有关，这由固液相互作用决定。在广泛的剪切速率和表面 - 液体相互作用范围内，滑移长度根据格林 - 久保 - 中野关系表示为与表面接触的液体密度涨落的各向异性非均匀时间关联函数的函数。通过在流体动力学极限下处理关联函数，消除了其时间依赖性。空间非均匀的两体关联函数在柯克伍德型近似中表示为表面附近液体相互作用位点的三维密度分布与本体液体位点 - 位点对关联的乘积。所提出的处理方法将摩擦系数（以及滑移长度）的唯象定义推广为张量量，这反映了有序晶体或纳米图案表面的各向异性性质。这使得能够对作用于这种表面且与液体流动方向倾斜的摩擦力进行理论预测。我们推导了任意表面 - 液体相互作用势下液体 - 表面摩擦系数（和滑移长度）的通用解析表达式。我们通过对九种不同分子液体（包括水）在环境条件下与金、铜和镍的（100）面心立方晶胞表面层流的数值计算进一步说明了这一点，其中使用了针对液体的优化液体模拟模型势和针对晶体表面的斯蒂尔势。所获得的滑移长度值范围从几纳米到数百纳米及微米，并且与实验测量结果一致。
