Kinetic theory analysis of microscale lubrication of a gas between walls with an arbitrary temperature difference

2023 Fiscal Year Final Research Report

• Project/Area Number: 21K03877
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 19010:Fluid engineering-related
• Research Institution: Tottori University
• Principal Investigator: Doi Toshiyuki 鳥取大学, 工学研究科, 准教授 (00227688)
• Project Period (FY): 2021-04-01 – 2024-03-31
• Keywords: 分子気体力学 / マイクロ潤滑 / 非連続体効果

Outline of Final Research Achievements

Microscale lubrication of a gas between circular cylinders with the clearance of the order of the mean free path of the gas is studied on the basis of kinetic theory. The dimensionless curvature, defined as the clearance divided by the radius of the spindle, is small. The Boltzmann equation is studied analytically using a perturbation method. It was clarified that a lubrication equation derived by the direct application of the conventional lubrication theory yields a non-negligible error proportional to the square root of the dimensionless curvature, when the clearance is much smaller than the mean free path. An improved lubrication equation is derived by correctly taking the effect of small curvature into account. It was also demonstrated that the improved equation provides the solution that perfectly agrees with the direct numerical solution of the Boltzmann equation over the entire range of the clearance.

Free Research Field

流体工学

Academic Significance and Societal Importance of the Research Achievements

本研究課題の成果として、本来連続体力学で扱えないようなマイクロ潤滑問題を、連続体潤滑理論と同程度の容易さで解析できる改良潤滑方程式および必要な数値データを社会に提供した。研究詳細を示した文献はオープンアクセス化し、万人が読めるようにした。改良潤滑方程式を実際に使用する際に必要な数値データを研究代表者のホームページから公開した。