Asymptotic modelling of flows in microchannel by using Navier–Stokes or Burnett equations and comparison with DSMC simulations

The modelling of isothermal gas flows driven by pressure drops, in coplanar microchannels is investigated. The goal is to construct an asymptotic model deduced from Navier–Stokes or Burnett equations for this type of flow, assuming slip boundary conditions along the walls. The dimensionless balance equations are written, taking into account a geometrical parameter introduced in this study. The application of the Principle of Least Degeneracy produces models with small Mach numbers and small or moderate Knudsen numbers and allows the development of asymptotic models. The first and second approximations associated with the Navier–Stokes or Burnett equations are presented and discussed. Navier–Stokes and Burnett second approximations reduce the mass flow rates.Additionally, first asymptotic solutions as against Direct Simulation Monte Carlo (DSMC) simulations show overall satisfactory agreements.

► Asymptotic modelling of microchannel flows.
► DSMC simulations of micro-channels flows.
► Burnett equations of coplanar micro-channel flows.