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Fluid Permeation Through A Membrane With Infinitesimal Permeability Under Reynolds Lubrication

Published online by Cambridge University Press:  14 August 2020

Asahi Tazaki ,
Shintaro Takeuchi Open the ORCID record for Shintaro Takeuchi [Opens in a new window] ,
Suguru Miyauchi ,
Lucy T. Zhang ,
Ryo Onishi  and
Takeo Kajishima
Asahi Tazaki
Affiliation:
Dept. of Mechanical Engineering, Osaka University, Osaka, Japan
Shintaro Takeuchi*
Affiliation:
Dept. of Mechanical Engineering, Osaka University, Osaka, Japan
Suguru Miyauchi
Affiliation:
Institute of Fluid Science, Tohoku University, Miyagi, Japan Dept. of Mechanical Engineering, University College London, Torrington Place, London, UK
Lucy T. Zhang
Affiliation:
Dept. of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, New York, USA
Ryo Onishi
Affiliation:
Center for Earth Information Science and Technology, Japan Agency for Marine-Earth Science and Technology, Kanagawa, Japan
Takeo Kajishima
Affiliation:
Dept. of Mechanical Engineering, Osaka University, Osaka, Japan
*
*Corresponding author ([email protected])

Abstract

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To understand the lubrication-dominated permeation through a membrane, numerical simulations of permeation through a moving corrugated permeable membrane is carried out with a fully validated numerical method. Through comparisons between the numerical results and the results of an asymptotic analysis of permeate flux (under an infinitesimal permeability condition) using Reynolds lubrication equation, the effect of permeation on lubrication and its inverse effect (i.e., the dependence of permeation on lubrication) are discussed. The linear and non-linear dependences of the relaxation of the lubrication pressure due to membrane permeation are identified. The effect of the tangential component of the permeate flux is evaluated by a linear analysis, and the limitation of Reynolds-type lubrication is discussed.

Keywords

LubricationPermeable membranePressure discontinuityDiscrete-forcing immersed boundary method
Type
Research Article
Information
Journal of Mechanics , Volume 36 , Issue 5 , October 2020 , pp. 637 - 648
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
Copyright © 2020 The Society of Theoretical and Applied Mechanics

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