The viscous-slip, diffusion-slip, and thermal-creep problems for a binary mixture of rigid spheres described by the linearized Boltzmann equation

Abstract An analytical version of the discrete-ordinates method (the ADO method) is used with recently established analytical expressions for the rigid-sphere scattering kernels to develop concise and particularly accurate solutions to the viscous-slip, the diffusion-slip, and the half-space thermal-creep problems for a binary gas mixture described by the linearized Boltzmann equation. In addition to a computation of the viscous-slip, the diffusion-slip, and the thermal-slip coefficients, for the case of Maxwell boundary conditions for each of the two species, the velocity, heat-flow, and shear-stress profiles are established for each species of particles. Numerical results are reported for two binary mixtures (Ne–Ar and He–Xe) with various molar concentrations.

[1]  Brian T. Smith,et al.  Matrix Eigensystem Routines — EISPACK Guide , 1974, Lecture Notes in Computer Science.

[2]  C. E. Siewert,et al.  A discrete-ordinates solution for a non-grey model with complete frequency redistribution , 1999 .

[3]  S. Loyalka.  Velocity Slip Coefficient and the Diffusion Slip Velocity for a Multicomponent Gas Mixture , 1971 .

[4]  H. Kramers,et al.  On the slip of a diffusing gas mixture along a wall , 1943 .

[5]  Felix Sharipov,et al.  Velocity slip and temperature jump coefficients for gaseous mixtures. IV. Temperature jump coefficient , 2005 .

[6]  S. Takata,et al.  Numerical analysis of the shear flow of a binary mixture of hard-sphere gases over a plane wall , 2004 .

[7]  Shugo Yasuda,et al.  Numerical analysis of thermal-slip and diffusion-slip flows of a binary mixture of hard-sphere molecular gases , 2003 .

[8]  F. J. McCormack.  Construction of linearized kinetic models for gaseous mixtures and molecular gases , 1973 .

[9]  C. Cercignani.  The Boltzmann equation and its applications , 1988 .

[10]  C. Siewert.  On computing the thermal-slip coefficient from Kramers’ problem , 2004 .

[11]  T. Ghosh,et al.  Measurements of thermal creep in binary gas mixtures , 1999 .

[12]  R. Tompson,et al.  Boundary slip phenomena in a binary gas mixture , 2002 .

[13]  C. Siewert,et al.  Some solutions (linear in the spatial variables) and generalized Chapman–Enskog functions basic to the linearized Boltzmann equations for a binary mixture of rigid spheres , 2007 .

[14]  C. Siewert,et al.  Concise and accurate solutions to half-space binary-gas flow problems defined by the McCormack model and specular-diffuse wall conditions , 2004 .

[15]  F. Sharipov,et al.  Velocity slip and temperature jump coefficients for gaseous mixtures. I. Viscous slip coefficient , 2004 .

[16]  A formulation of the linearized Boltzmann equations for a binary mixture of rigid spheres , 2005 .

[17]  M. M. R. Williams,et al.  Mathematical methods in particle transport theory , 1971 .

[18]  C. E. Siewert,et al.  The linearized Boltzmann equation: Concise and accurate solutions to basic flow problems , 2003 .

[19]  Sudarshan K. Loyalka,et al.  Temperature jump and thermal creep slip: Rigid sphere gas , 1989 .

[20]  J. Ferziger,et al.  Mathematical theory of transport processes in gases , 1972 .

[21]  Kazuo Aoki,et al.  Numerical analysis of the shear and thermal creep flows of a rarefied gas over a plane wall on the basis of the linearized Boltzmann equation for hard‐sphere molecules , 1989 .

[22]  C. Siewert,et al.  The McCormack model: channel flow of a binary gas mixture driven by temperature, pressure and density gradients , 2004 .

[23]  C. E. Siewert,et al.  Viscous-slip, thermal-slip, and temperature-jump coefficients as defined by the linearized Boltzmann equation and the Cercignani–Lampis boundary condition , 2003 .

[24]  Y. Onishi.  On the behavior of a slightly rarefied gas mixture over plane boundaries , 1986 .

[25]  F. Sharipov.  Heat transfer in the Knudsen layer. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Jack Dongarra,et al.  LINPACK Users' Guide , 1987 .

[27]  B. S. Garbow,et al.  Matrix Eigensystem Routines — EISPACK Guide , 1974, Lecture Notes in Computer Science.

[28]  R. H. Fowler.  The Mathematical Theory of Non-Uniform Gases , 1939, Nature.

[29]  M. M. R. Williams,et al.  A review of the rarefied gas dynamics theory associated with some classical problems in flow and heat transfer , 2001 .

[30]  Model equations in rarefied gas dynamics: Viscous-slip and thermal-slip coefficients , 2002 .

[31]  C. Pekeris,et al.  SOLUTION OF THE BOLTZMANN-HILBERT INTEGRAL EQUATION. , 1955, Proceedings of the National Academy of Sciences of the United States of America.

[32]  S. K. Loyalka,et al.  The Kramers problem: Velocity slip and defect for a hard sphere gas with arbitrary accommodation , 1990 .

[33]  C. E. Siewert,et al.  Unified solutions to classical flow problems based on the BGK model , 2001 .

[34]  C. E. Siewert,et al.  The temperature-jump problem based on the linearized Boltzmann equation for a binary mixture of rigid spheres , 2007 .

[35]  R. Tompson,et al.  Viscosity and velocity slip coefficients for gas mixtures: Measurements with a spinning rotor gauge , 1999 .