The analytic equations of mass flow rate for gas flow in microchannels or microtubes developed in the 1990s have been widely validated by experimental results for slow-speed flow, but the applicability for high-speed flow might be constrained. A new model for analyzing the modified Navier–Stokes equations of the gas flow in 2D microchannels and microtubes is proposed in this study, named the simplified quasi-2D (SQ2D) model. The applicability of the SQ2D model can be in the range from slow-speed flow to high-speed flow with no-slip boundary conditions or high-order slip boundary conditions. The flows in 2D microchannels and microtubes, with hydraulic diameters sized from 5 µ m to 100 µ m and various hydraulic-diameter-to-length ratios, were analyzed by the SQ2D model under different pressure conditions. The mass flow rates calculated by the SQ2D model meet the data computed by the computational fluid dynamics-based method better than the analytic equations in the hig...

中文翻译：

---

用于微通道和微管中气体流动的简化准二维模型

1990年代开发的微通道或微管中的气体质量流率解析方程已被慢速流的实验结果广泛验证，但高速流的适用性可能受到限制。本研究提出了一种用于分析二维微通道和微管中气体流动的改进的Navier-Stokes方程的新模型，称为简化准2D（SQ2D）模型。SQ2D模型的适用范围可以从低速流到具有无滑移边界条件或高阶滑移边界条件的高速流。通过SQ2D模型在不同压力条件下分析了水力直径为5 µm至100 µm且水力直径与长度之比不同的2D微通道和微管中的流动。