A simplified quasi-2D model for gas flow in microchannels and microtubes

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 µm to 100 µm 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 high Mach number region. The results were also compared with the numerical or experimental data from other studies, good agreements could be reached. Some particular characteristics of micro gas flow were also identified and briefly discussed with the data computed by the SQ2D model.