Extended lubrication theory: Improved estimates of flow in channels with variable geometry

Behrouz Tavakol; Guillaume Froehlicher; Douglas P. Holmes; Howard A. Stone

doi:10.1098/rspa.2017.0234

Extended lubrication theory: Improved estimates of flow in channels with variable geometry

Behrouz Tavakol, Guillaume Froehlicher, Douglas P. Holmes, Howard A. Stone

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

Lubrication theory is broadly applicable to the flow characterization of thin fluid films and the motion of particles near surfaces. We offer an extension to lubrication theory by starting with Stokes equations and considering higher-order terms in a systematic perturbation expansion to describe the fluid flow in a channel with features of a modest aspect ratio. Experimental results qualitatively confirm the higher-order analytical solutions, while numerical results are in very good agreement with the higherorder analytical results. We show that the extended lubrication theory is a robust tool for an accurate estimate of pressure drop in channels with shape changes on the order of the channel height, accounting for both smooth and sharp changes in geometry.

Original language	English (US)
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	473
Issue number	2206
DOIs	https://doi.org/10.1098/rspa.2017.0234
State	Published - Oct 1 2017

All Science Journal Classification (ASJC) codes

Mathematics(all)
Engineering(all)
Physics and Astronomy(all)

Keywords

Lubrication theory
Perturbation expansion
Stokes flow

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10.1098/rspa.2017.0234

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title = "Extended lubrication theory: Improved estimates of flow in channels with variable geometry",

abstract = "Lubrication theory is broadly applicable to the flow characterization of thin fluid films and the motion of particles near surfaces. We offer an extension to lubrication theory by starting with Stokes equations and considering higher-order terms in a systematic perturbation expansion to describe the fluid flow in a channel with features of a modest aspect ratio. Experimental results qualitatively confirm the higher-order analytical solutions, while numerical results are in very good agreement with the higherorder analytical results. We show that the extended lubrication theory is a robust tool for an accurate estimate of pressure drop in channels with shape changes on the order of the channel height, accounting for both smooth and sharp changes in geometry.",

keywords = "Lubrication theory, Perturbation expansion, Stokes flow",

author = "Behrouz Tavakol and Guillaume Froehlicher and Holmes, {Douglas P.} and Stone, {Howard A.}",

note = "Funding Information: Data accessibility. All datasets presented in this work would be available upon request. Authors{\textquoteright} contributions. B.T., G.F., D.P.H. and H.A.S. derived the analytical approximations. B.T. and D.P.H. carried out the experiments. B.T. performed the numerical analyses. B.T., G.F., D.P.H. and H.A.S. wrote the paper. Competing interests. The authors have no competing interests. Funding. This work was supported by the National Science Foundation (B.T. and D.P.H., CMMI-1505125). Publisher Copyright: {\textcopyright} 2017 The Author(s) Published by the Royal Society.",

year = "2017",

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doi = "10.1098/rspa.2017.0234",

language = "English (US)",

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T2 - Improved estimates of flow in channels with variable geometry

AU - Tavakol, Behrouz

AU - Froehlicher, Guillaume

AU - Holmes, Douglas P.

AU - Stone, Howard A.

N1 - Funding Information: Data accessibility. All datasets presented in this work would be available upon request. Authors’ contributions. B.T., G.F., D.P.H. and H.A.S. derived the analytical approximations. B.T. and D.P.H. carried out the experiments. B.T. performed the numerical analyses. B.T., G.F., D.P.H. and H.A.S. wrote the paper. Competing interests. The authors have no competing interests. Funding. This work was supported by the National Science Foundation (B.T. and D.P.H., CMMI-1505125). Publisher Copyright: © 2017 The Author(s) Published by the Royal Society.

PY - 2017/10/1

Y1 - 2017/10/1

N2 - Lubrication theory is broadly applicable to the flow characterization of thin fluid films and the motion of particles near surfaces. We offer an extension to lubrication theory by starting with Stokes equations and considering higher-order terms in a systematic perturbation expansion to describe the fluid flow in a channel with features of a modest aspect ratio. Experimental results qualitatively confirm the higher-order analytical solutions, while numerical results are in very good agreement with the higherorder analytical results. We show that the extended lubrication theory is a robust tool for an accurate estimate of pressure drop in channels with shape changes on the order of the channel height, accounting for both smooth and sharp changes in geometry.

AB - Lubrication theory is broadly applicable to the flow characterization of thin fluid films and the motion of particles near surfaces. We offer an extension to lubrication theory by starting with Stokes equations and considering higher-order terms in a systematic perturbation expansion to describe the fluid flow in a channel with features of a modest aspect ratio. Experimental results qualitatively confirm the higher-order analytical solutions, while numerical results are in very good agreement with the higherorder analytical results. We show that the extended lubrication theory is a robust tool for an accurate estimate of pressure drop in channels with shape changes on the order of the channel height, accounting for both smooth and sharp changes in geometry.

KW - Lubrication theory

KW - Perturbation expansion

KW - Stokes flow

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Extended lubrication theory: Improved estimates of flow in channels with variable geometry

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