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Lubrication pressure model in a non-negligible gap for fluid permeation through a membrane with finite permeability

Shintaro Takeuchi1,*, Toshiaki Fukada2, Shuji Yamada1, Suguru Miyauchi3, and Takeo Kajishima1

  • 1Department of Mechanical Engineering, Osaka University, 2-1 Yamada-oka, Suita-city, Osaka 565-0871, Japan
  • 2Central Research Institute of Electric Power Industry, 2-6-1 Nagasaka, Yokosuka, Kanagawa 240-0196, Japan
  • 3Faculty of Engineering, University of Miyazaki, 1-1 Gakuen Kibanadai-nishi, Miyazaki 889-2192, Japan

  • *Corresponding author: shintaro.takeuchi@mech.eng.osaka-u.ac.jp
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Phys. Rev. Fluids 6, 114101 – Published 5 November, 2021

DOI: https://doi.org/10.1103/PhysRevFluids.6.114101

Abstract

The membrane permeation of a fluid occurring near the wall is strongly influenced by lubrication because the generated pressure accelerates the fluid passing through the membrane. In the present study, the membrane permeation of a pure fluid driven by the lubrication pressure is modeled for a general wall-membrane geometry to understand the effect of permeability on the permeate flux in a range of wall-membrane gap widths that cannot be treated by the Reynolds lubrication equation. This lubrication effect (referred to as the non-Reynolds lubrication effect) is modeled by including a higher-order pressure component described by the wall-tangential derivative of the local Couette-Poiseuille velocity, and a permeate flux model with the non-Reynolds lubrication effect is developed. The permeation model is validated with a corrugated membrane placed in a two-dimensional parallel channel with a fixed aspect ratio (i.e., the average wall-membrane distance to the longitudinal membrane length) of 0.1. The permeation driven by the lubrication pressure between the membrane and wall is studied by varying the nondimensional permeability. At an infinitesimal permeability, the permeate flux model shows good agreement with the fully resolved numerical simulation owing to the comparable contribution of the Couette and Poiseuille components in the permeation model, whereas the permeation model exhibits a diverging trend at finite permeabilities because the Couette component in the model produces an excessive contribution to the lubrication pressure. However, by applying a simplified renormalization procedure to the Couette component into the lowest-order pressure component, the diverging trend is suppressed and the permeate flux in a finite permeability range is reproduced. The applicability of the renormalization-group permeation model is discussed in terms of the conditions of the wall-membrane gap and permeability range.

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Phys. Rev. Fluids 6, 114101– Published 5 November, 2021
  • Received 31 March 2021
  • Accepted 13 October 2021
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