AI 中文总结
该研究建立模态框架，通过本征函数分解探究纳米通道流动中密度变化对重力驱动流动的影响，明确密度与加速度的模式耦合作用，为相关流动的理解与预测提供系统方法。
AI 中文摘要
我们应用一种模态框架来研究密度变化对纳米尺度重力驱动流动的影响。通过对密度场和加速度场进行本征函数分解，每个剪切-压力模式被分离为均匀贡献项和非均匀贡献项，非均匀贡献项由密度和外加加速度的傅里叶振幅决定。这种分解为识别密度变化与外部驱动如何耦合并调控流动行为提供了直接手段。我们首先重新研究泊肃叶流动，结果表明，当通道高度大于特征分子间距离时，均匀贡献项主导长波长（小波矢）响应，这与先前的模拟结果一致。相比之下，对于正弦驱动流动，加速度模式的选择性激发可产生相反的行为，即非均匀贡献项主导长波长响应。结果表明，密度变化的影响取决于具体的流动，具体取决于加速度场和密度场之间的详细模式耦合。本文提出的框架为理解和预测依赖于外加加速度的流动提供了直接且系统的方法。
英文摘要
We apply a modal framework for investigating the effect of density variations on gravity-type driven flows at the nanoscale. Using eigenfunction decomposition of the density and acceleration fields, each shear-pressure mode is separated into a homogeneous contribution and an inhomogeneous contribution determined by the Fourier amplitudes of the density and applied acceleration. This decomposition provides a direct means of identifying how density variations and external forcing couple and govern the flow behavior. We first revisit the Poiseuille flow and show that for channel heights larger than the characteristic intermolecular distance the homogeneous contribution dominates the long wave length (small wave vector) response, consistent with previous simulation results. In contrast, for sinusoidally driven flow, selective excitation of acceleration modes can produce the opposite behavior, with the inhomogeneous contribution dominating the long wave length response. The results show that the effect of the density variations depends on the specific flow; specifically the detailed mode coupling between the acceleration and density fields. The framework presented here provides a direct systematic approach for understanding and predicting the flow depending on the applied acceleration.
Comments6 pages, 4 figures
