Asymptotic Modelling of Isothermal Gaseous Flow in Microchannels by Using Burnett Equations

摘要

For the description of gas flows in microchannels, it is important to investigate asymptotic models to describe the basic physical phenomena. Our purpose is to model isothermal gaseous flows in coplanar microchannels at low Mach numbers and with low to moderate Knudsen numbers. Burnett macroscopic equations for mass and momentum are written with slip conditions for velocity on the two microchannel walls. Taking into account the small parameter equal to the ratio of the two longitudinal and transversal lengths, an asymptotic model is proposed. Several aspects of the solution are discussed, depending on the relative drop pressure and on the Knudsen number. Particularly, for Knudsen numbers between 0.05 and 0.30, the Burnett stresses reduce the magnitude of the longitunal velocity and the mass flow rate.