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Drag force on spherical particle moving near a plane wall in highly rarefied gas

Published online by Cambridge University Press:  28 November 2019

P. Goswami ,
T. Baier Open the ORCID record for T. Baier [Opens in a new window] ,
S. Tiwari ,
C. Lv Open the ORCID record for C. Lv [Opens in a new window] ,
S. Hardt Open the ORCID record for S. Hardt [Opens in a new window]  and
A. Klar
P. Goswami
Affiliation:
Institute for Nano- and Microfluidics, Technische Universität Darmstadt, 64287Darmstadt, Germany
T. Baier
Affiliation:
Institute for Nano- and Microfluidics, Technische Universität Darmstadt, 64287Darmstadt, Germany
S. Tiwari
Affiliation:
Department of Mathematics, Technische Universität Kaiserslautern, 67663Kaiserslautern, Germany
C. Lv
Affiliation:
Institute for Nano- and Microfluidics, Technische Universität Darmstadt, 64287Darmstadt, Germany Department of Engineering Mechanics, Tsinghua University, 100084Beijing, China
S. Hardt*
Affiliation:
Institute for Nano- and Microfluidics, Technische Universität Darmstadt, 64287Darmstadt, Germany
A. Klar
Affiliation:
Department of Mathematics, Technische Universität Kaiserslautern, 67663Kaiserslautern, Germany
*
†Email address for correspondence: [email protected]
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Abstract

The drag force on a sphere in tangential and normal motion to a plane wall is evaluated in the limit of large Knudsen number and small Mach (and Strouhal) number assuming isothermal conditions and diffuse reflection of gas molecules on walls. In the limit of free molecular flow, the molecular distribution function of the gas is evaluated using a set of coupled Fredholm integral equations. The results are compared with direct simulation Monte Carlo calculations and extended for finite Knudsen numbers. In all cases stronger dependence of the force on the width of the gap is found for normal compared to tangential motion. When the flow within the gap can be considered as essentially collisionless in nature, a similar dependence of the force on the gap width is observed at finite Knudsen numbers as in the free molecular case.

JFM classification

Rarefied Gas Flow: Kinetic theory Micro-/Nano-fluid dynamics: Non-continuum effects
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 883 , 25 January 2020 , A47
Copyright
© 2019 Cambridge University Press

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