Flows of rarefied gaseous mixtures with a low mole fraction. Separation phenomenon

An approach to a model of rarefied gaseous mixtures with a low mole fraction of one species based on the linearized Boltzmann equation is proposed. As an example, the separation phenomenon in a binary gaseous mixture flowing through a long tube into a vacuum is considered by assuming an arbitrary pressure at the tube’s entrance. In this situation, the regime of gas flow along the tube can vary from hydrodynamic to free molecular. The calculations were carried out for a mixture of Helium–Xenon considering two limits, first when the mole fraction of Helium is low and second when the mole fraction of Xenon is low. As a result, flow rates of each species and their density distributions along the tube are calculated in a wide range of gas rarefaction in the tube inlet. The advantages of the present methodology in comparison to that developed previously for an arbitrary mole fraction are pointed out.

► The separation phenomenon in a binary gas mixture is numerically investigated.
► A kinetic model to the linearized Boltzmann equation is employed.
► The whole range of gas rarefaction is considered.
► Simplifications are done due to the low concentration of one species.