Variational approach to gas flows in microchannels.

Since microdevices are gaining popularity both in commercial applications and in scientific research, there exists a rapidly growing interest in improving the conventional design techniques related with these devices. Microdevices are often operated in gaseous environments and thus their performances are affected by the gas around them. The numerical simulation of all these flows cannot be performed with the Navier-Stokes equations because the smallest characteristic length of the microdevices is comparable with the mean free path of the gas molecules, therefore the Boltzmann equation must be considered. In the current paper, gas flow rates in microchannels have been rigorously evaluated by means of a variational technique which applies to the integrodifferential form of the Boltzmann equation based on the Bhatnagar, Gross and Krook model. The Maxwell scattering kernel has been used to describe the gas-wall interactions in the most general case of two surfaces with different accommodation coefficients.