Modeling a microfluidic system using Knudsen's empirical equation for flow in the transition regime

Knudsen's model for gas flow in the transition regime is successfully applied to a micromachined flow path of varying cross-sectional area where the type of flow changes from the viscous to the molecular regime as the gas flows through the device. The gas flow model was originally developed to aid in the design of an integrated microflow controller [J. K. Robertson, Ph.D. thesis, University of Michigan, 1996, and J. K. Robertson and K. D. Wise, Proc. IEEE Micro Electro Mechanical Systems 7 (1994)] and to diagnose problems encountered with the microvalves during testing of the device. The main how channel was rectangular in shape similar to 12.8 mum high, 400 mum wide and 2694 mum long. The model was fit to the data by adjusting a single parameter. The model successfully predicted the conductance of the channel for differential pressures greater than 500 Torr-where the gas entered the flow path in the viscous regime and exited in the molecular regime-and less than 11 Torr-where the gas entered the flow path in the transition regime and exited in the molecular regime. The model is computationally simple, can be easily set up on a spreadsheet, and should be useful for the rapid modeling of other micromachined flow paths. (C) 2001 American Vacuum Society.