On the Slip Correction Factor for Simple Gas Molecules Diffusing in Air

We examine the functional form of the slip correction factor C(Π), where Π is a dimensionless group to be determined, for simple (monoatomic, diatomic, and triatomic) gas molecules diffusing in air at normal conditions. We express C(Π) in terms of the molecular Reynolds number, Re_(mi) = u_id_(ki)/2ν_j, where u_i and d_(ki) are the Maxwell–Boltzmann mean molecular speed and the kinetic diameter of the diffusing gas molecules, and ν_j is the kinematic viscosity of the background gas (dry air). We show that the slip correction is given simply by C(Re_(mi)) = Re_(mi)/Re_(j,ns) where Re_(j,ns) is a reference no-slip Reynolds number that depends only on the thermodynamic state and viscosity of the background gas j. For dry air at 300 K and 1 atm, Re_(j,ns) = 1.36 × 10⁻⁵, so that C(Re_(mi)) = 7.35 × 10⁴ Re_(mi). The approach presented here can be easily generalized to other gas media and leads to a remarkably simple correlation for estimation of Schmidt numbers and binary diffusion coefficients for both stable and unstable trace gases in air. While this correlation depends only on the molecular weight M_i and the number of atoms in the molecule of the diffusing gas, it performs competitively against more complex models.