Numerical analysis of thermal-slip and diffusion-slip flows of a binary mixture of hard-sphere molecular gases

Abstract

Articles you may be interested inNumerical analysis of the Poiseuille flow and the thermal transpiration of a rarefied gas through a pipe with a rectangular cross section based on the linearized Boltzmann equation for a hard sphere molecular gas J. Vac. Sci. Technol. A 28, 603 (2010); 10.1116/1.3449056 Temperature, pressure, and concentration jumps for a binary mixture of vapors on a plane condensed phase: Numerical analysis of the linearized Boltzmann equation Phys. Fluids 18, 067102 (2006); 10.1063/1.2206220 Evaporation and condensation of a binary mixture of vapors on a plane condensed phase: Numerical analysis of the linearized Boltzmann equation Phys. Fluids 17, 047105 (2005); 10.1063/1.1882252 Numerical analysis of the shear flow of a binary mixture of hard-sphere gases over a plane wall Diffusion slip for a binary mixture of hard-sphere molecular gases: Numerical analysis based on the linearized Boltzmann equation AIP Conf.The thermal-slip ͑thermal-creep͒ and the diffusion-slip problems for a binary mixture of gases are investigated on the basis of the linearized Boltzmann equation for hard-sphere molecules with the diffuse reflection boundary condition. The problems are analyzed numerically by the finite-difference method incorporated with the numerical kernel method, which was first proposed by Sone, Ohwada, and Aoki ͓Phys. Fluids A 1, 363 ͑1989͔͒ for a single-component gas. As a result, the behavior of the mixture is clarified accurately not only at the level of the macroscopic variables but also at the level of the velocity distribution function. In addition, accurate formulas of the thermal-slip and the diffusion-slip coefficients for arbitrary values of the concentration of a component gas are constructed by the use of the Chebyshev polynomial approximation.

Modelling of multi-component gas flows in capillaries and porous solids

“…(9) and (22) for the continuum and free-molecule mass or mole fraction gradients, and Eqs. (13) and (20) for the pressure gradients, have a high degree of symmetry. Choosing a suitable interpolation method is then much more obvious.…”

“…(5) is itself open to criticism. Over the years, there have been attempts to improve on the situation through direct molecular dynamics simulations, e.g., Mo and Rosenberger [18], and by solving model versions of the Boltzmann equation in the near-wall region, e.g., Kanki et al [19], Takata et al [20] and Sharipov and Kalempa [21]. Most of this work is mathematically complex and difficult to assess, and sometimes involves restrictive modelling assumptions.…”

Assessment and development of the gas kinetic boundary condition for the Boltzmann equation

“…Although there exist accurate numerical methods to calculate these coefficients (i.e. see Loyalka (1989), Siewert (2003), and Takata et al (2003) for the Boltzmann equation with the HS potential, and Sharipov (2003a) for the Shakhov kinetic model equation), we adopt the method used in Struchtrup (2013) to obtain analytical expressions for these coefficients, which have errors of about 10% or so. With these approximate expressions, it becomes much easier for us to choose the appropriate parameters in the BC, without running the numerical simulation over all the parameter regions.…”

Comparative study between computational and experimental results for binary rarefied gas flows through long microchannels

“…It has been shown that for flows with small Mach numbers (such as the ones investigated here) and the Knudsen number varying from the free molecular through the transition up to the hydrodynamic regimes, linearized kinetic theory is the most efficient approach providing reliable results with modest computational effort. The discrete velocity method has been successfully developed for solving such kinetic equations, simulating flows through long channels of various cross sections for both single component gases (Sharipov 1999;Aoki 2001;Valougeorgis and Naris 2003;Breyiannis et al 2008) and gaseous mixtures (Sharipov and Kalempa 2002;Takata et al 2003;Naris et al 2004Naris et al , 2005Kosuge and Takata 2008). In addition, in the case of one-dimensional flows the semi-analytical discrete ordinate method has been developed to solve kinetic equations associated with gaseous mixtures in a very elegant and computationally efficient manner (Siewert and Valougeorgis 2004).…”