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

• Published in: Micromachines (Basel) Vol. 15; no. 10; p. 1263
• Main Authors: Anheuer, Daniel, Schwarz, Johannes, Debera, Patrick, Heinrich, Klaus, Kutter, Christoph, Richter, Martin
• Format: Journal Article
• Language: English
• Published: Switzerland MDPI AG 16.10.2024; MDPI
• Subjects: Air overpressure; Analysis; Boundary conditions; Computer industry; Continuum modeling; Decay; Deviation; Diffusion rate; Exact solutions; experimental characterization; Flap valves; Flow velocity; Fluid flow; Gas flow; Gases; Geometry; Knudsen flow; Leakage; Mass flow; Mean free path; Measurement; Measurement methods; microvalve; Natural gas; Navier-Stokes equations; pressure decay; Reproducibility; Self diffusion; Sensors; Silicon; Silicon wafers; simulation; Valves; Wall slip; United States; Germany; OpenFOAM; pressure decay; silicon; simulation; flap valves; experimental characterization; microvalve; measurement; leakage
• ISSN: 2072-666X; 2072-666X
• DOI: 10.3390/mi15101263

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 cm /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 cm /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 > 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.