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Thisstudydescribesatheoreticalanalysisoffree-molecular flowsbetweentwoplates,bothequippedwithvacuum pumps, with an aim to investigate the facility effects of large chambers equipped with distributed cyrogenic vacuum pumps. Three free-molecular models are proposed to study the unsteady flow behavior, and to calculate the average number density and average velocity of the rarefied background gas molecules between the two plates. The first model is based on mass conservation and predicts that the unsteady evolution is a multiple time scale process. The second model is a classical steady kinetic model, whereas the third model is the most advanced kinetic model that includes chamber wall effects. In the last two models, a detailed balance of flux along different flow directions and reflection relations lead to exact solutions. All three models include the chamber facility effects, especially pump size and pump sticking coefficient. Simulations with the direct simulation Monte Carlo method are performed and the results are compared with the analytical results. The analytical results from these models can be used to estimate the average background pressure and velocity in large vacuum chambers equipped with multiple pumps for experiments and simulations.

Free Molecular Flows Between Two Plates Equipped with Pumps