Gaseous slip flow analysis of a micromachined flow sensor for ultra small flow applications

Abstract

The velocity slip of a fluid at a wall is one of the most typical phenomena in microscale gas flows. This paper presents a flow analysis considering the velocity slip in a capacitive micro gas flow sensor based on pressure difference measurements along a microchannel. The tangential momentum accommodation coefficient (TMAC) measurements of a particular channel wall in planar microchannels will be presented while the previous micro gas flow studies have been based on the same TMACs on both walls. The sensors consist of a pair of capacitive pressure sensors, inlet/outlet and a microchannel. The main microchannel is 128.0 µm wide, 4.64 µm deep and 5680 µm long, and operated under nearly atmospheric conditions where the outlet Knudsen number is 0.0137. The sensor was fabricated using silicon wet etching, ultrasonic drilling, deep reactive ion etching (DRIE) and anodic bonding. The capacitance change of the sensor and the mass flow rate of nitrogen were measured as the inlet-to-outlet pressure ratio was varied from 1.00 to 1.24. The measured maximum mass flow rate was 3.86 × 10 −10 kg s −1 (0.019 sccm) at the highest pressure ratio tested. As the pressure difference increased, both the capacitance of the differential pressure sensor and the flow rate through the main microchannel increased. The laminar friction constant f · Re, an important consideration in sensor design, varied from the incompressible no-slip case and the mass sensitivity and resolution of this sensor were discussed. Using the current slip flow formulae, a microchannel with much smaller mass flow rates can be designed at the same pressure ratios.

Molecular Momentum Transport at Fluid-Solid Interfaces in MEMS/NEMS: A Review

“…[ 141 ], Hsieh et al . [ 142 ], Jang and Wereley [ 143 , 144 ] reported on the effects of surface roughness on the average TMAC in silica and glass microchannels. Jang and Wereley [ 144 ] further derived the relation between the averaged TMAC and the TMAC for different wall species.…”

Revisited analysis of gas convection and heat transfer in micro channels: Influence of viscous stress power at wall on Nusselt number

“…Gas micro-ows, possibly with heat transfer, can be found in : micro heat exchangers for the cooling of electronic components or in chemistry [6,7], micro pumps and turbines, including the thermal transpiration-driven Knudsen pumps for vacuum pumping applications [810], micro-systems for the species separation in gas mixtures such as the method of gas separation by membranes [11], micro gas analyzers such as micro mass spectrometers and micro-chromatographs [12,13], supersonic gas ows in micro-nozzles to control the nano-satellite attitude or the boundary layers in aerodynamics [1418], articial lungs [19,20], pressure, ow rate and temperature micro-sensors in gas ows [21,22], etc. This paper investigates the theoretical models available to simulate and analyze the slightly rareed gas micro-ows with heat transfer, when Kn 0.1.…”

Gaseous slip flow of a rectangular microchannel with non-uniform slip boundary conditions

“…Studies of very small gas flow in microchannels have been essential in a large number of applications such as ultra sensitive gas flow sensors, gas chromatography, microchemical gas reactors, low-pressure semiconductor manufacturing machines, microscale heat exchangers, and micro gas regulators (Sagi et al 2004;Jang and Wereley 2007;Gross et al 2004;Shin and Besser 2006;Cho et al 1992;Debray et al 2005). The characteristic length scale of the gas flow in a microchannel is usually in the range of microns or tens of microns, and the mean free path of most common gases is approximately 60 nm at atmospheric conditions (Karniadakis et al 2005).…”