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Fokker–Planck model for binary mixtures

Published online by Cambridge University Press:  24 July 2020

Samarth Agrawal ,
S. K. Singh  and
S. Ansumali Open the ORCID record for S. Ansumali [Opens in a new window]
Samarth Agrawal
Affiliation:
Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore560064, India
S. K. Singh
Affiliation:
Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore560064, India
S. Ansumali*
Affiliation:
Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore560064, India
*
†Email address for correspondence: ansumali@jncasr.ac.in
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Abstract

The Fokker–Planck approximation to the Boltzmann equation has emerged as an efficient alternative to the discrete simulation Monte Carlo method for various flow simulations. This method has been mostly limited to simulating single-component rarefied gas flows. In the present paper, we propose two models based on the Fokker–Planck equation and quasi-equilibrium models that are capable of describing the dynamics of rarefied binary gas mixtures over a large range of Schmidt numbers. We first prove that these models satisfy the necessary conservation laws and the $H$-theorem. We validate the model by simulating three benchmark problems – Graham's law for effusion, Couette flow and binary diffusion.

JFM classification

Rarefied Gas Flow: Kinetic theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 899 , 25 September 2020 , A25
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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