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

Abstract

We examine the functional form of the slip correction factor , where is a dimensionless group to be determined, for simple (monoatomic, diatomic, and triatomic) gas molecules diffusing in air at normal conditions. We express in terms of the molecular Reynolds number, , where and are the Maxwell–Boltzmann mean molecular speed and the kinetic diameter of the diffusing gas molecules, and is the kinematic viscosity of the background gas (dry air). We show that the slip correction is given simply by , where is a reference no-slip Reynolds number that depends only on the thermodynamic state and viscosity of the background gas . For dry air at 300 K and 1 atm, , so that . 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 and the number of atoms in the molecule of the diffusing gas, it performs competitively against more complex models.