Subsonic gas flow in a straight and uniform microchannel

微通道 机械 马赫数 层流 打滑(空气动力学) 努森数 材料科学 压缩性 等温流动 边值问题 可压缩流 物理 流量(数学) 热力学 明渠流量 量子力学
作者
Yitshak Zohar,Sylvanus Yuk Kwan Lee,Wing Yin Lee,Linan Jiang,Penger Tong
出处
期刊:Journal of Fluid Mechanics [Cambridge University Press]
卷期号:472: 125-151 被引量:131
标识
DOI:10.1017/s0022112002002203
摘要

A nonlinear equation based on the hydrodynamic equations is solved analytically using perturbation expansions to calculate the flow field of a steady isothermal, compressible and laminar gas flow in either a circular or a planar microchannel. The solution takes into account slip-flow effects explicitly by utilizing the classical velocity-slip boundary condition, assuming the gas properties are known. Consistent expansions provide not only the cross-stream but also the streamwise evolution of the various flow parameters of interest, such as pressure, density and Mach number. The slip-flow effect enters the solution explicitly as a zero-order correction comparable to, though smaller than, the compressible effect. The theoretical calculations are verified in an experimental study of pressure-driven gas flow in a long microchannel of sub-micron height. Standard micromachining techniques were utilized to fabricate the microchannel, with integral pressure microsensors based on the piezoresistivity principle of operation. The integrated microsystem allows accurate measurements of mass flow rates and pressure distributions along the microchannel. Nitrogen, helium and argon were used as the working fluids forced through the microchannel. The experimental results support the theoretical calculations in finding that acceleration and non-parabolic velocity profile effects were found to be negligible. A detailed error analysis is also carried out in an attempt to expose the challenges in conducting accurate measurements in microsystems.
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