Sun Chengzhen, Zhou Runfeng, Zhao Zhixiang, Bai Bofeng
State Key Laboratory of Multiphase Flow in Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi 710049, China.
School of Urban Planning and Municipal Engineering, Xi'an Polytechnic University, Xi'an, Shaanxi 710048, China.
Langmuir. 2021 May 25;37(20):6158-6167. doi: 10.1021/acs.langmuir.1c00298. Epub 2021 May 10.
Water flow through two-dimensional nanopores has attracted significant attention owing to the promising water purification technology based on atomically thick membranes. However, the theoretical description of water flow in nanopores based on the classical continuum theory is very challenging owing to the pronounced entrance/exit effects. Here, we extend the classical Hagen-Poiseuille equation for describing the relationship between flow rate and pressure loss in laminar tube flow to two-dimensional nanopores. A totally theoretical model is established by appropriately considering the velocity slip on pore surfaces both in the friction pressure loss and entrance/exit pressure loss. Based on molecular dynamics simulations of water flow through graphene nanopores, it is shown that the model can not only well predict the overall flow rate but also give a good estimation of the velocity profiles. As the pore radius and length increase, the model can reduce to the equations applicable to the fluid flow in infinitely/finitely long nanotubes, thin orifices, and macroscale tubes, showing an accurate prediction of the existing experimental and simulation data of the water flow through nanotubes and nanopores in the literature. Namely, the presented model is a unified model that can uniformly describe the fluid flow from nanoscales to macroscales by modifying the classical continuum theory.
由于基于原子级厚度膜的水净化技术前景广阔，二维纳米孔中的水流引起了广泛关注。然而，基于经典连续介质理论对纳米孔中水流进行理论描述极具挑战性，因为存在明显的进出口效应。在此，我们将描述层流管流中流速与压力损失关系的经典哈根 - 泊肃叶方程扩展到二维纳米孔。通过在摩擦压力损失和进出口压力损失中适当考虑孔隙表面的速度滑移，建立了一个完全理论化的模型。基于水分子通过石墨烯纳米孔流动的分子动力学模拟，结果表明该模型不仅能很好地预测总体流速，还能对速度分布给出良好估计。随着孔隙半径和长度增加，该模型可简化为适用于无限/有限长纳米管、细孔口和宏观尺度管道中流体流动的方程，准确预测了文献中关于水分子通过纳米管和纳米孔流动的现有实验和模拟数据。也就是说，所提出的模型是一个统一模型，通过修正经典连续介质理论，能够统一描述从纳米尺度到宏观尺度的流体流动。
