{"title":"基于流线的正弦粗糙度流体润滑模型","authors":"Haruki Okazaki, Shintaro Takeuchi","doi":"10.1007/s10404-024-02721-3","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":706,"journal":{"name":"Microfluidics and Nanofluidics","volume":null,"pages":null},"PeriodicalIF":2.3000,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fluid lubrication model over sinusoidal roughness with streamline-based approach\",\"authors\":\"Haruki Okazaki, Shintaro Takeuchi\",\"doi\":\"10.1007/s10404-024-02721-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>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.</p></div>\",\"PeriodicalId\":706,\"journal\":{\"name\":\"Microfluidics and Nanofluidics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2024-04-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Microfluidics and Nanofluidics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10404-024-02721-3\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"INSTRUMENTS & INSTRUMENTATION\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Microfluidics and Nanofluidics","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s10404-024-02721-3","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"INSTRUMENTS & INSTRUMENTATION","Score":null,"Total":0}
Fluid lubrication model over sinusoidal roughness with streamline-based approach
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.
期刊介绍:
Microfluidics and Nanofluidics is an international peer-reviewed journal that aims to publish papers in all aspects of microfluidics, nanofluidics and lab-on-a-chip science and technology. The objectives of the journal are to (1) provide an overview of the current state of the research and development in microfluidics, nanofluidics and lab-on-a-chip devices, (2) improve the fundamental understanding of microfluidic and nanofluidic phenomena, and (3) discuss applications of microfluidics, nanofluidics and lab-on-a-chip devices. Topics covered in this journal include:
1.000 Fundamental principles of micro- and nanoscale phenomena like,
flow, mass transport and reactions
3.000 Theoretical models and numerical simulation with experimental and/or analytical proof
4.000 Novel measurement & characterization technologies
5.000 Devices (actuators and sensors)
6.000 New unit-operations for dedicated microfluidic platforms
7.000 Lab-on-a-Chip applications
8.000 Microfabrication technologies and materials
Please note, Microfluidics and Nanofluidics does not publish manuscripts studying pure microscale heat transfer since there are many journals that cover this field of research (Journal of Heat Transfer, Journal of Heat and Mass Transfer, Journal of Heat and Fluid Flow, etc.).