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

Coimbra, Kaila M. Y. and Coimbra, Miya C. Y. and Coimbra, Carlos F. M. (2022) On the Slip Correction Factor for Simple Gas Molecules Diffusing in Air. AIAA Journal . ISSN 0001-1452. doi:10.2514/1.j061338. (In Press)

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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.

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Coimbra, Carlos F. M.0000-0002-9428-3931
Additional Information:© 2022 by CFM Coimbra. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Received 2 October 2021; Accepted 24 February 2022; Published online 4 April 2022. This work was researched and executed as part of summer research internships at University of California San Diego by the first two coauthors, who are listed alphabetically, under the supervision of the corresponding author. All authors wish to gratefully acknowledge the generosity of David R. Miller (University of California San Diego), who provided access to difficult-to-find reference materials during the COVID-19 lockdown of 2020–21. Engaging discussions with Anthony F. Mills (University of California, Los Angeles) and support from the John Dove Isaacs Endowed Chair at University of California San Diego are also gratefully acknowledged.
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University of California San DiegoUNSPECIFIED
Subject Keywords:Binary Diffusion Coefficient; Kinematic Viscosity; Aerodynamic Drag; Schmidt Numbers; Lennard Jones Potential; Friction Coefficient; Aspect Ratio; Universal Gas Constant; Absolute Temperature; Thermal Conductivity
Record Number:CaltechAUTHORS:20220429-306495700
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Official Citation:On the Slip Correction Factor for Simple Gas Molecules Diffusing in Air. Kaila M. Y. Coimbra, Miya C. Y. Coimbra, and Carlos F. M. Coimbra. AIAA Journal 0 0:0, 1-10; DOI: 10.2514/1.j061338
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:114530
Deposited By: Tony Diaz
Deposited On:29 Apr 2022 22:13
Last Modified:29 Apr 2022 22:13

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