Boundary conditions for the Boltzmann equation from gas-surface interaction kinetic models.

Boundary conditions for the Boltzmann equation are investigated on the basis of a kinetic model for gas-surface interactions. The model takes into account gas and physisorbed molecules interacting with a surface potential and colliding with phonons. The potential field is generated by fixed crystal molecules, and the interaction with phonons represents the fluctuating part of the surface. The interaction layer is assumed to be thinner than the mean free path of the gas and physisorbed molecules, and the phonons are assumed to be at equilibrium. The asymptotic kinetic equation for the inner physisorbate layer is derived and used to investigate gas distribution boundary conditions. To be more specific, a model of the boundary condition for the Boltzmann equation is derived on the basis of an approximate iterative solution of the kinetic equation for the physisorbate layer, and the quality of the model is assessed by detailed numerical simulations, which also clarify the behavior of the molecules in the layer.

Two-temperature Navier-Stokes equations for a polyatomic gas derived from kinetic theory.

A polyatomic gas with slow relaxation of the internal modes is considered, and the Navier-Stokes equations with two temperatures, the translational and internal temperatures, are derived for such a gas on the basis of the ellipsoidal-statistical (ES) model of the Boltzmann equation for a polyatomic gas, proposed by Andries et al. [Eur. J. Mech. B, Fluids 19, 813 (2000)10.1016/S0997-7546(00)01103-1], by the Chapman-Enskog procedure. Then, the derived equations are applied to numerically investigate the structure of a plane shock wave in CO_{2} gas, which is known to have slowly relaxing internal modes. The results show good agreement with those obtained by the direct numerical analysis of the ES model for moderately strong shock waves. In particular, the results perfectly reproduce the double-layer structure of the shock profiles consisting of a thin front layer with rapid change and a thick rear layer with slow relaxation of the internal modes.

Cylindrical Couette flow of a rarefied gas: Effect of a boundary condition on the inverted velocity profile.

The cylindrical Couette flow of a rarefied gas between a rotating inner cylinder and a stationary outer cylinder is investigated under the following two kinds of kinetic boundary conditions. One is the modified Maxwell-type boundary condition proposed by Dadzie and Méolans [J. Math. Phys. 45, 1804 (2004)] and the other is the Cercignani-Lampis condition, both of which have separate accommodation coefficients associated with the molecular velocity component normal to the boundary and with the tangential component. An asymptotic analysis of the Boltzmann equation for small Knudsen numbers and a numerical analysis of the Bhatnagar-Gross-Krook model equation for a wide range of the Knudsen number are performed to clarify the effect of each accommodation coefficient as well as of the boundary condition itself on the behavior of the gas, especially on the flow-velocity profile. As a result, the velocity-slip and temperature-jump conditions corresponding to the above kinetic boundary conditions are derived, which are necessary for the fluid-dynamic description of the problem for small Knudsen numbers. The parameter range for the onset of the velocity inversion phenomenon, which is related mainly to the decrease in the tangential momentum accommodation, is also obtained.