Fluid lubrication model over sinusoidal roughness with streamline-based approach

Okazaki, Haruki; Takeuchi, Shintaro

Microfluidics and Nanofluidics, 2024, 28(30), 402

Number of Access:410（2025-08-14 03:30 Counts）

Identifier to cite or link to this item: https://hdl.handle.net/11094/95262

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Title
Fluid lubrication model over sinusoidal roughness with streamline-based approach
Creator
CreatorName
Okazaki, Haruki
NRID
1000050372628 1000050372628
ORCID
0000-0003-0091-4542 0000-0003-0091-4542
researchmap permalink
50372628 50372628
Scopus Author ID
35474283000 35474283000
CreatorName
Takeuchi, Shintaro
Subject
Lubrication pressure
Wall-normal pressure distribution
Sinusoidal roughness
Deterministic treatment
Description
This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s10404-024-02721-3.
Abstract
A method is proposed to deterministically obtain steady lubrication pressure for the Stokes flow in a channel bounded by a flat wall and a surface with roughness represented by sinusoidal waves. A streamline sufficiently far away from the rough surface is used to formulate a streamline-based lubrication equation with the velocity on the streamline, and the velocities on the streamline is imposed as a boundary condition. In the solution of the lubrication equation, by virtually moving the streamline towards the flat wall, the pressure on the flat wall is obtained, and then the wall-normal variation of the pressure is recovered from the wall pressure by a lubrication model that considers higher order terms. The proposed method is applied to lubrication flows in channels with roughness represented by a single sinusoidal wave and a superposition of several sinusoidal waves. Through comparison with analytical solutions, the validity of the proposed method is established, and the applicable range of superposition of waves is explained that lowest-wavenumber component in surface profile is sufficiently isolated from higher-wavenumber components. Although the problem setting intrinsically prohibits the application of the conventional Reynolds lubrication equation, this study provides new understandings for the pressure obeying the Reynolds lubrication equation and the role of the higher-order terms.
Publisher
Springer Science and Business Media LLC
Source Title
Microfluidics and Nanofluidics
Volume (Issue)
28(30)
Page
402
Date of Issued
2024-05-01
Handle URL
https://hdl.handle.net/11094/95262
PISSN
16134982
eISSN
16134990
Relation.isVersionOf
DOI (Publisher Version)
https://doi.org/10.1007/s10404-024-02721-3
Access Rights
open access
CopyRight
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024
oaire:version
Accepted Manuscript
Category
学術雑誌論文 Journal Article