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Extended Reynolds lubrication model for incompressible Newtonian fluid

Shintaro Takeuchi and Jingchen Gu

  • Department of Mechanical Engineering, Osaka University, 2-1 Yamada-oka, Suita-city, Osaka 565-0871, Japan

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Phys. Rev. Fluids 4, 114101 – Published 19 November, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.114101

Abstract

An extended lubrication model is proposed for improvement of the lubrication theory by taking into account a larger surface-to-surface distance than that for the Reynolds lubrication theory. The analysis shows that when considering the non-negligible pressure gradient in the surface-normal direction, the local pressure is separated into (i) a base component satisfying the Reynolds lubrication theory and (ii) an adjusting component varying in the surface-normal direction, which is found to take the form proportional to the longitudinal derivative of the local velocity of the Couette-Poiseuille flow. Comparison of the results obtained by analytical and numerical methods for the lubrication between a moving curved object and stationary object shows that the proposed lubrication model reproduces the pressure distribution in both wall-normal and longitudinal directions. In a problem of a spherical particle approaching to a plane wall, the hydrodynamic force calculated by the proposed model exhibits an inverse-proportional trend to the surface-to-surface distance. The results suggest extended applicability of the lubrication theory to a non-Reynolds regime.

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Phys. Rev. Fluids 4, 114101– Published 19 November, 2019
  • Received 12 March 2019
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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