Modeling and Simulation of a Surface Micromachined Knudsen Pump

This paper presents a simulation model for a silicon micromachined Knudsen pump that combines analytical and numerical methods. It involves numerical modeling of the thermal response, followed by an analytical estimate of the pumping using Kennard’s model. The loss of performance resulting from gas diffusion though walls of the pump is specifically addressed. The results are subsequently validated against the previously reported experimental measurements of a single-stage Knudsen pump. This device, which has a total footprint of less than 1500 x 2000 μm, has multiple narrow channels connecting two cavities, one of which is heated. This cavity is further connected through a wide channel to a third cavity, which remains at ambient. The simulation model for this device predicts a vacuum pressure of 0.47 atm. at an input power of 97.6 mW, which deviates less than 20% from the experimentally observed data. Finally, the paper extends the concept of single stage pumping to a multi-stage pump. While Kennard’s model is used for modeling the first stage, the simulation for subsequent stages, which are characterized by a relatively high Knudsen number, uses an empirically corrected correlation by Knudsen.