Air Leakages at Microvalves: Pressure Decay Measurements and Extended Continuum Modelling of Knudsen Flows

Abstract

To improve the performance of valves in relation to the leakage rate, a comprehensive evaluation of the valve characteristics and behavior during pressure exposure is important. Often, these low gas flow rates below 0.1 cm3/min cannot be accurately measured with conventional flow sensors. This paper presents a small and low-cost test rig for measuring gas leakage rates accurately, even far below 0.1 cm3/min, with the pressure decay method. These leakage flows are substantiated with a flow model, where we demonstrate the feasibility of modeling those gas flows with an extended Navier–Stokes framework to obtain more accurate theoretical predictions. As expected, the comparison to the experimental results proves that the classical Navier–Stokes system is unsuitable for modeling Knudsen flows. Hence, self-diffusion of gas, a wall-slip boundary condition, and an effective mean free path model were introduced in a physically evident manner. In terms of the calculated mass flow, while self-diffusion and slip boundary conditions explain deviations from the classical Navier–Stokes equation for Knudsen numbers already smaller than 1, the effective mean free path model has an effect, especially when Kn > 1. For simplified conditions, an analytical solution was presented and compared to the results of an OpenFOAM CFD-solver for flow rates through more complex gap-flow geometries of the flap valve. Hereby, acceptable deviations between 10% and 20% were observed. A comparison with measurement results was carried out. The reproducibility of the measurement method was verified by comparing multiple measurements of one silicon microvalve sample to a state-of-the-art flow sensor. Three geometrically similar passive silicon microvalves were measured with air overpressure decreasing from 15 kPa relative to atmospheric pressure. Maximum gas volume flowing in a blocking direction of 1–26 µL/min with high reproducibility and marginal noise were observed.