Comparison of relaxation phenomena in binary gas-mixtures of Maxwell molecules and hard spheres

The strategy for computing the Boltzmann collision integrals for gaseous mixtures is presented and bestowed to compute the fully non-linear Boltzmann collision integrals for hard sphere gas-mixtures. The Boltzmann collision integrals associated with the first 26 moments of each constituent in a gas-mixture are presented. Moreover, the Boltzmann collision integrals are exploited to study the relaxation phenomena of diffusion velocities, stresses and heat fluxes in binary gas-mixtures of Maxwell molecules and hard spheres.

[1]  F. Sharipov,et al.  Benchmark problems for mixtures of rarefied gases. I. Couette flow , 2013 .

[2]  T. G. Cowling,et al.  The mathematical theory of non-uniform gases , 1939 .

[3]  Raphael Aronson,et al.  Theory and application of the Boltzmann equation , 1976 .

[4]  T. F. Morse,et al.  Kinetic Model Equations for a Gas Mixture , 1964 .

[5]  T. Ruggeri,et al.  Heat conduction in multi-temperature mixtures of fluids: the role of the average temperature , 2009 .

[6]  J. Broadwell,et al.  Study of rarefied shear flow by the discrete velocity method , 1964, Journal of Fluid Mechanics.

[7]  B. Perthame,et al.  A Consistent BGK-Type Model for Gas Mixtures , 2002 .

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

[9]  J. Kestin,et al.  Equilibrium and transport properties of the noble gases and their mixtures at low density , 1984 .

[10]  C. Lee,et al.  Kinetic Theory of Shock Tube Problems for Binary Mixtures , 1971 .

[11]  P. Brancher,et al.  Topology and dynamics of the A-pillar vortex , 2013 .

[12]  Manuel Torrilhon,et al.  Higher order moment equations for rarefied gas mixtures , 2015, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[13]  G. M. Kremer,et al.  An Introduction to the Boltzmann Equation and Transport Processes in Gases , 2010 .

[14]  V. Garzó,et al.  A kinetic model for a multicomponent gas , 1989 .

[15]  H. Struchtrup Macroscopic transport equations for rarefied gas flows , 2005 .

[16]  H. Struchtrup,et al.  Regularization of Grad’s 13 moment equations: Derivation and linear analysis , 2003 .

[17]  Henning Struchtrup,et al.  Capturing non-equilibrium phenomena in rarefied polyatomic gases: A high-order macroscopic model , 2014 .

[18]  B. Hamel Kinetic Model for Binary Gas Mixtures , 1965 .

[19]  V. Gupta,et al.  Automated Boltzmann Collision Integrals for Moment Equations , 2012 .

[20]  H. Grad Note on N‐dimensional hermite polynomials , 1949 .

[21]  G. A. Tirskii,et al.  The use of the moment method to derive the gas and plasma transport equations with transport coefficients in higher-order approximations☆ , 2003 .

[22]  Manuel Torrilhon,et al.  Regularized 13-moment equations: shock structure calculations and comparison to Burnett models , 2004, Journal of Fluid Mechanics.

[23]  P. Bhatnagar,et al.  A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems , 1954 .

[24]  I. Graur,et al.  Two-fluid computational model for a binary gas mixture , 2001 .

[25]  A. Bobylev,et al.  The Chapman-Enskog and Grad methods for solving the Boltzmann equation , 1982 .

[26]  Li-Shi Luo,et al.  Lattice Boltzmann model for binary mixtures. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  G. Bird Molecular Gas Dynamics and the Direct Simulation of Gas Flows , 1994 .

[28]  Stéphane Brull,et al.  Derivation of a BGK model for mixtures , 2012 .

[29]  V. Zhdanov Transport Processes in Multicomponent Plasma , 2002 .

[30]  Manuel Torrilhon,et al.  A robust numerical method for the R13 equations of rarefied gas dynamics: Application to lid driven cavity , 2013, J. Comput. Phys..

[31]  A BGK Model for Gas Mixtures , 2014 .

[32]  Manuel Torrilhon,et al.  Couette and Poiseuille microflows : Analytical solutions for regularized 13-moment equations , 2009 .

[33]  L. Sirovich Kinetic Modeling of Gas Mixtures , 2011 .