Relaxation of rotational-vibrational energy and volume viscosity in H-H₂ mixtures

We investigate a kinetic model for H-H₂ mixtures in a regime where translational/rotational and vibrational-resonant energy exchanges are fast whereas vibrational energy variations are slow. In a relaxation regime, the effective volume viscosity is found to involve contributions from the rotational volume viscosity, the vibrational volume viscosity, the relaxation pressure, and the perturbed source term. In the thermodynamic equilibrium limit, the sum of these four terms converges toward the one-temperature two-mode volume viscosity. The theoretical results are applied to the calculation of the volume viscosities of molecular hydrogen in the trace limit on the basis of a complete set of state-selected cross sections for the H + H₂(v, j) system.