The planar Couette flow for gaseous mixture He–Ar is calculated by the direct simulation Monte Carlo method based on ab initio potential over the whole range of the gas rarefaction for several values of the mole fraction and for two values of the wall speed. The smaller value of the speed corresponds to the limit when the nonlinear terms are negligible, while the larger value describes a nonlinear flow. The shear stress, velocity gradient, temperature, and mole fraction profiles are presented. The reported results can be used as benchmark data to test model kinetic equations for gaseous mixtures. To study the influence of the intermolecular potential, the same simulations are carried out for the hard sphere molecular model. A relative deviation of the results based on this model from those based on the ab initio potential are analyzed. It is pointed out that the difference between the shear stresses of the two potentials for the linearized solution is within 1%, while it reaches 6% for the nonlinear cases.
Received 23 November 2012Accepted 17 January 2013Published online 15 February 2013
The calculations were carried out in LCPAD (UFPR). The authors thank the Brazilian agencies CNPq and CAPES for support of their research.
Article outline: I. INTRODUCTION II. STATEMENT OF THE PROBLEM III. HYDRODYNAMIC LIMIT IV. FREE-MOLECULAR REGIME V. TRANSITIONAL REGIME VI. RESULTS AND DISCUSSIONS A. Shear stress B. Velocity gradient C. Temperature D. Mole fraction VII. CONCLUSIONS
4.S. Varoutis, D. Valougeorgis, and F. Sharipov, “Simulation of gas flow through tubes of finite length over the whole range of rarefaction for various pressure drop ratios,” J. Vac. Sci. Technol. A.27, 1377–1391 (2009).
11.J. Kestin, K. Knierim, E. A. Mason, B. Najafi, S. T. Ro, and M. Waldman, “Equilibrium and transport properties of the noble gases and their mixture at low densities,” J. Phys. Chem. Ref. Data13, 229–303 (1984).
15.E. Bich, R. Hellmann, and E. Vogel, “Ab initio potential energy curve for the neon atom pair and thermophysical properties for the dilute neon gas. II. Thermophysical properties for low-density neon,” Mol. Phys.106, 813–825 (2008).
16.E. Bich, R. Hellmann, and E. Vogel, “Ab initio potential energy curve for the helium atom pair and thermophysical properties of the dilute helium gas. II. Thermophysical standard values for low-density helium,” Mol. Phys.105, 3035–3049 (2007).
17.T. P. Haley and S. M. Cybulski, “Ground state potential energy curves for He-Kr, Ne-Kr, Ar-Kr, and Kr2: Coupled-cluster calculations and comparison with experiment,” J. Chem. Phys.119, 5487–5496 (2003).
19.E. Vogel, B. Jaeger, R. Hellmann, and E. Bich, “Ab initio pair potential energy curve for the argon atom pair and thermophysical properties for the dilute argon gas. II. Thermophysical properties for low-density argon,” Mol. Phys.108, 3335–3352 (2010).
31.G. A. Bird, M. A. Gallis, J. R. Torczynski, and D. J. Rader, “Accuracy and efficiency of the sophisticated direct simulation Monte Carlo algorithm for simulating noncontinuum gas flows,” Phys. Fluids21, 017103 (2009).
33.S. K. Loyalka, N. Petrellis, and T. S. Storvik, “Some exact numerical results for the BGK model: Couette, Poiseuille and thermal creep flow between parallel plates,” Z. Angew. Math. Phys.30, 514–521 (1979).
43.E. L. Tipton, R. V. Tompson, and S. K. Loyalka, “Chapman-Enskog solutions to arbitrary order in Sonine polynomials III: Diffusion, thermal diffusion, and thermal conductivity in a binary, rigid-sphere, gas mixture,” Eur. J. Mech. B/Fluids28, 353–386 (2009).
49.E. L. Tipton, R. V. Tompson, and S. K. Loyalka, “Chapman-Enskog solutions to arbitrary order in Sonine polynomials II: Viscosity in a binary, rigid-sphere, gas mixture,” Eur. J. Mech. B/Fluids28, 335–352 (2009).