Theoretical derivation of slip boundary conditions for single-species gas and binary gas mixture

H-theorem and boundary conditions for two-temperature model: Application to wave propagation and heat transfer in polyatomic gases

Polyatomic gases find numerous applications across various scientific and technological fields, necessitating a quantitative understanding of their behavior in nonequilibrium conditions. In this study, we investigate the behavior of rarefied polyatomic gases, particularly focusing on heat transfer and sound propagation phenomena. By utilizing a two-temperature model, we establish constitutive equations for internal and translational heat fluxes based on the second law of thermodynamics. A novel reduced two-temperature model is proposed, which accurately describes the system's behavior while reducing computational complexity. Additionally, we develop phenomenological boundary conditions adhering to the second law, enabling the simulation of gas-surface interactions. The phenomenological coefficients in the constitutive equations and boundary conditions are determined by comparison with relevant literature. Our computational analysis includes conductive heat transfer between parallel plates, examination of sound wave behavior, and exploration of spontaneous Rayleigh-Brillouin scattering. The results provide valuable insights into the dynamics of polyatomic gases, contributing to various technological applications involving heat transfer and sound propagation.

State-specific boundary conditions for nonequilibrium gas flows in slip regime

Boundary conditions for fluid-dynamic variables of strongly nonequilibrium multicomponent gas mixture flows in slip regime are derived systematically by two different approaches. The flow is described in the framework of the state-to-state model for coupled detailed vibrational and chemical kinetics. The specular-diffusive model is applied for particles interaction with the solid wall, and the surface is assumed to be partially catalytic with possible state-specific chemical reactions and vibrational energy transitions described by a simple model based on the analogy with recombination coefficients. The first theoretical approach uses the technique proposed by Grad whereas the second one is based on the kinetic boundary condition. It is shown that for the Maxwell scattering kernel the two approaches are equivalent; at the same time, the approach based on the kinetic boundary condition provides more rigorous mathematical description of the problem and can be easily generalized for other scattering kernels and gas-surface interaction models accounting for surface inner geometry. The resulting boundary conditions are expressed in terms of state-specific transport coefficients: thermal conductivity, multicomponent diffusion of vibrational states, thermal diffusion, shear and bulk viscosity, and relaxation pressure. The dependence of the boundary conditions on the normal mean stress is obtained for the first time. Under thermal equilibrium conditions, the derived expressions reduce to known relations obtained earlier in the one-temperature approach.