This work utilizes the direct simulation Monte Carlo (DSMC) calculations and examines the influence of rarefication on the mixing length and effective diffusion coefficient in a two-species mixing problem. There have been efforts in past rarefied mixing flow studies to bridge between the mixing evolution rate and Knudsen number. A careful review of those efforts shows that the past derived relations did not determine the weights of Reynolds (or Peclet) number in the rarefaction influences. Although they indicated that an increase in Knudsen would decrease the mixing length, such reductions were primarily due to the Reynolds (or Peclet) reduction. Therefore, those studies could not explicitly appraise the contribution of rarefaction in the total mass diffusion magnitude. This work focuses specifically on the role of rarefaction in the total diffusive mass transfer magnitude in rarefied gas mixing problems. It excludes the contributions of momentum and heat to the mass diffusion via imposing suitable velocity, pressure, and temperature fields in the mixer domain. The results show that there will be some decreases in the diffusive mass fluxes and some increases in the mixing length as Knudsen increases. Using the Fick’s law, the effective diffusion coefficient is then calculated in the mixer zone. The results show that this coefficient may vary considerably throughout the mixer zone due to the local rarefaction level variation. The results of all investigated cases indicate that the trends of their effective diffusion coefficient variations approach to a limiting value as the rarefaction level decreases.
Mixing and mass transfer in ladle refining process.
