A comparative study between computational and experimental results for pressure-driven binary gas flows through long microchannels is performed. The theoretical formulation is based on the McCormack kinetic model and the computational results are valid in the whole range of the Knudsen number. Diffusion effects are taken into consideration. The experimental work is based on the Constant Volume Method, and the results are in the slip and transition regime. Using both approaches, the molar flow rates of the He-Ar gas mixture flowing through a rectangular microchannel are estimated for a wide range of pressure drops between the upstream and downstream reservoirs and several mixture concentrations varying from pure He to pure Ar. In all cases, a very good agreement is found, within the margins of the introduced modeling and measurement uncertainties. In addition, computational results for the pressure and concentration distributions along the channel are provided. As far as the authors are aware of, this is the first detailed and complete comparative study between theory and experiment for gaseous flows through long microchannels in the case of binary mixtures.

A slip-flow boundary condition has been developed in the lattice Boltzmann model combining an interpolation method and a simple slip boundary condition for straight walls placed at arbitrary distance from the last fluid node. An analytical expression has been derived to connect the model parameters with the slip velocity for Couette and Poiseuille flows in the nearly continuum limit. The proposed interpolation method ensures that the slip velocity is independent of the wall position in first order of the Knudsen number. Computer simulations have been carried out to validate the model. The Couette and Poiseuille flows agree with the analytical results to machine order. Numerical simulation of a moving square demonstrates the accuracy of the model for walls moving in both the tangential and normal directions.

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The flow of binary gas mixtures through long micro-channels with triangular and trapezoidal cross sections is investigated in the whole range of the Knudsen number. The flow is driven by pressure and concentration gradients. The McCormack kinetic model is utilized to simulate the rarefied flow of the gas mixture, and the kinetic equations are solved by an upgraded discrete velocity algorithm. The kinetic dimensionless flow rates are tabulated for selected noble gas mixtures flowing through micro-channels etched by KOH in silicon (triangular and trapezoidal channels with acute angle of 54.74°). Furthermore, the complete procedure to obtain the mass flow rate for a gas mixture flowing through a channel, based on the dimensionless kinetic results, which are valid in each cross section of the channel, is presented. The study includes the effect of the separation phenomenon. It is shown that gas separation may change significantly the estimated mass flow rate. The presented methodology can be used for engineering purposes and for the accurate comparison with experimental results.

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