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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.
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Cercignani et al. (2004) studied this question.
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