Transient flow of a binary gas mixture through a long capillary at arbitrary rarefaction parameters

This work proposes a model to simulate transient flow of a gas mixture at arbitrary rarefaction parameters and molar fractions through a long capillary. The transient model is based on the linear relationship between the thermodynamic fluxes (mass flow rate, diffusion flux, etc.) and the thermodynamic forces (gradients of the pressure, concentration, etc.) of the gas flow in the long capillary. The coefficients between the fluxes and the forces, namely so-called kinetic coefficients, are obtained by solving the binary-species linearized and steady Boltzmann equation using the finite-difference method. The kinetic coefficients at different rarefaction parameters and molar fractions are validated by comparing them with the literature. The Chebyshev polynomial approximation method is introduced to reduce the computational consumption of kinetic coefficients. Then the transient flow through a long capillary can be efficiently and accurately predicted by this model. Based on the proposed model, the possible clogging problem during the filling process of the target gas through the capillary is further investigated. The critical pressure ratio for judging clogging is proposed as a criterion. The influences of molar fraction, rarefaction parameter, and molecular mass ratio on the critical pressure ratio were investigated. The results showed that the critical pressure ratio was positively correlated to the rarefaction parameter and negatively correlated to the molar fraction. Only at relatively low molar fractions, the effect of molecular mass ratio on the critical pressure ratio of the light species is significant.