Gaseous slip flow in long microchannels

TLDR

The study investigates gaseous flow with slight rarefaction in long microchannels through analytic and experimental methods. The authors perform a two‑dimensional Navier‑Stokes analysis with first‑order slip boundary conditions, use perturbation expansion and ideal gas EOS to derive a zeroth‑order solution that matches experiments, and fabricate wafer‑bonded microchannels with controlled surfaces for accurate mass‑flow measurement. Slip velocity alters pressure distribution, causing wall‑normal mass migration, and experimental helium mass‑flow measurements in long microchannels agree well with the analytic predictions.

Abstract

An analytic and experimental investigation into gaseous flow with slight rarefaction through long microchannels is undertaken. A two-dimensional (2-D) analysis of the Navier-Stokes equations with a first-order slip-velocity boundary condition demonstrates that both compressibility and rarefied effects are present in long microchannels. By undertaking a perturbation expansion in /spl epsiv/, the height-to-length ratio of the channel, and using the ideal gas equation of state, it is shown that the zeroth-order analytic solution for the streamwise mass flow corresponds well with the experimental results. Also, the effect of slip upon the pressure distribution is derived, and it is obtained that this slip velocity leads directly to a wall-normal migration of mass. The fabrication of wafer-bonded microchannels that possess well-controlled surface structure is described, and a means for accurately measuring the mass how through the channels is presented. Experimental results obtained with this mass-flow measurement technique for streamwise helium mass flow through microchannels 52.25-/spl mu/m wide, 1.33-/spl mu/m deep, and 7500-/spl mu/m long for a pressure range of 1.6-4.2 atmospheres (outlet pressures at atmospheric) are presented and shown to compare favorably with the analysis.