Chen Shuyu, Wang Han, Qian Tiezheng, Sheng Ping
Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China.
CAEP Software Center for High Performance Numerical Simulation, Beijing, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Oct;92(4):043007. doi: 10.1103/PhysRevE.92.043007. Epub 2015 Oct 7.
The lack of a first-principles derivation has made the hydrodynamic boundary condition a classical issue for the past century. The fact that the fluid can have interfacial structures adds additional complications and ambiguities to the problem. Here we report the use of molecular dynamics to identify from equilibrium thermal fluctuations the hydrodynamic modes in a fluid confined by solid walls, thereby extending the application of the fluctuation-dissipation theorem to yield not only the accurate location of the hydrodynamic boundary at the molecular scale, but also the relevant parameter value(s) for the description of the macroscopic boundary condition. We present molecular dynamics results on two examples to illustrate the application of this approach-one on the hydrophilic case and one on the hydrophobic case. It is shown that the use of the orthogonality condition of the modes can uniquely locate the hydrodynamic boundary to be inside the fluid in both cases, separated from the molecular solid-liquid interface by a small distance Δ that is a few molecules in size. The eigenvalue equation of the hydrodynamic modes directly yields the slip length, which is about equal to Δ in the hydrophilic case but is larger than Δ in the hydrophobic case. From the decay time we also obtain the bulk viscosity which is in good agreement with the value obtained from dynamic simulations. To complete the picture, we derive the Green-Kubo relation for a finite fluid system and show that the boundary fluctuations decouple from the bulk only in the infinite-fluid-channel limit; and in that limit we recover the interfacial fluctuation-dissipation theorem first presented by Bocquet and Barrat. The coupling between the bulk and the boundary fluctuations provides both the justification and the reason for the effectiveness of the present approach, which promises broad utility for probing the hydrodynamic boundary conditions relevant to structured or elastic interfaces, as well as two-phase immiscible flows.
在过去的一个世纪里，由于缺乏第一性原理推导，流体动力学边界条件一直是一个经典问题。流体能够具有界面结构这一事实给该问题增添了额外的复杂性和模糊性。在此，我们报告利用分子动力学从平衡热涨落中识别受固体壁限制的流体中的流体动力学模式，从而扩展涨落 - 耗散定理的应用，不仅能在分子尺度上精确确定流体动力学边界的位置，还能得到描述宏观边界条件的相关参数值。我们给出了两个例子的分子动力学结果，以说明这种方法的应用——一个是亲水性情况，另一个是疏水性情况。结果表明，在这两种情况下，利用模式的正交性条件都能唯一地确定流体动力学边界位于流体内部，与分子固 - 液界面相隔一小段距离Δ，其大小为几个分子。流体动力学模式的本征值方程直接给出滑移长度，在亲水性情况下，滑移长度约等于Δ，但在疏水性情况下大于Δ。从衰减时间我们还得到了体黏度，它与动态模拟得到的值吻合良好。为完善这一图景，我们推导了有限流体系统的格林 - 库博关系，并表明边界涨落仅在无限流体通道极限下才与主体解耦；在该极限下，我们恢复了博凯和巴拉特首次提出的界面涨落 - 耗散定理。主体涨落与边界涨落之间的耦合既为当前方法的有效性提供了依据，也说明了其原因，该方法有望广泛应用于探测与结构化或弹性界面以及两相不混溶流相关的流体动力学边界条件。
