Subsonic gas flow in a straight and uniform microchannel

Abstract

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.