On lubrication flows in geometries with zero local curvature

H. A. Stone

doi:10.1016/j.ces.2005.03.021

On lubrication flows in geometries with zero local curvature

H. A. Stone

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

38 Scopus citations

Abstract

The familiar examples of lubrication theory for the approximate analysis of the motion of cylindrical and spherical particles near boundaries takes advantage of the local parabolic shape near contact. We generalize these studies to particles and boundaries of more general shape, which have the feature that the curvature is zero at the point of minimum separation in the gap. Order-of-magnitude estimates and detailed solutions are given. The translation of such a close-fitting object in a circular tube, and the pressure-driven flows between two surfaces with zero curvature at minimum separation and in a saddle-shaped channel, are considered in a similar fashion.

Original language	English (US)
Pages (from-to)	4838-4845
Number of pages	8
Journal	Chemical Engineering Science
Volume	60
Issue number	17
DOIs	https://doi.org/10.1016/j.ces.2005.03.021
State	Published - Sep 2005
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Chemistry
General Chemical Engineering
Industrial and Manufacturing Engineering

Keywords

Low Reynolds members
Lubrication
Particle motion

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10.1016/j.ces.2005.03.021

Cite this

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title = "On lubrication flows in geometries with zero local curvature",

abstract = "The familiar examples of lubrication theory for the approximate analysis of the motion of cylindrical and spherical particles near boundaries takes advantage of the local parabolic shape near contact. We generalize these studies to particles and boundaries of more general shape, which have the feature that the curvature is zero at the point of minimum separation in the gap. Order-of-magnitude estimates and detailed solutions are given. The translation of such a close-fitting object in a circular tube, and the pressure-driven flows between two surfaces with zero curvature at minimum separation and in a saddle-shaped channel, are considered in a similar fashion.",

keywords = "Low Reynolds members, Lubrication, Particle motion",

author = "Stone, {H. A.}",

note = "Funding Information: I thank G.H. McKinley for helpful feedback on the ideas in an early draft, H. Brenner for bringing the paper by R.G. Cox to my attention, W. Zimmerman for forwarding to me his paper, and F. Plourabou{\'e} for sharing with me his work related to saddle-shaped channels. This work was originally supported by the Army Research Office via the Harvard–Boston University-University of Maryland program on Control of Smart Structures. I am grateful to the Harvard MRSEC (DMR-0213805) for support. Copyright: Copyright 2008 Elsevier B.V., All rights reserved.",

year = "2005",

month = sep,

doi = "10.1016/j.ces.2005.03.021",

language = "English (US)",

volume = "60",

pages = "4838--4845",

journal = "Chemical Engineering Science",

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N1 - Funding Information: I thank G.H. McKinley for helpful feedback on the ideas in an early draft, H. Brenner for bringing the paper by R.G. Cox to my attention, W. Zimmerman for forwarding to me his paper, and F. Plouraboué for sharing with me his work related to saddle-shaped channels. This work was originally supported by the Army Research Office via the Harvard–Boston University-University of Maryland program on Control of Smart Structures. I am grateful to the Harvard MRSEC (DMR-0213805) for support. Copyright: Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2005/9

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N2 - The familiar examples of lubrication theory for the approximate analysis of the motion of cylindrical and spherical particles near boundaries takes advantage of the local parabolic shape near contact. We generalize these studies to particles and boundaries of more general shape, which have the feature that the curvature is zero at the point of minimum separation in the gap. Order-of-magnitude estimates and detailed solutions are given. The translation of such a close-fitting object in a circular tube, and the pressure-driven flows between two surfaces with zero curvature at minimum separation and in a saddle-shaped channel, are considered in a similar fashion.

AB - The familiar examples of lubrication theory for the approximate analysis of the motion of cylindrical and spherical particles near boundaries takes advantage of the local parabolic shape near contact. We generalize these studies to particles and boundaries of more general shape, which have the feature that the curvature is zero at the point of minimum separation in the gap. Order-of-magnitude estimates and detailed solutions are given. The translation of such a close-fitting object in a circular tube, and the pressure-driven flows between two surfaces with zero curvature at minimum separation and in a saddle-shaped channel, are considered in a similar fashion.

KW - Low Reynolds members

KW - Lubrication

KW - Particle motion

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DO - 10.1016/j.ces.2005.03.021

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SP - 4838

EP - 4845

JO - Chemical Engineering Science

JF - Chemical Engineering Science

IS - 17

ER -

On lubrication flows in geometries with zero local curvature

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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