Bending of elastic fibres in viscous flows: the influence of confinement
Identifieur interne : 005075 ( Main/Exploration ); précédent : 005074; suivant : 005076Bending of elastic fibres in viscous flows: the influence of confinement
Auteurs : Jason S. Wexler [États-Unis, France] ; Philippe H. Trinh [États-Unis] ; Helene Berthet [France] ; Nawal Quennouz [France] ; Olivia Du Roure [France] ; Herbert E. Huppert [Royaume-Uni, Australie] ; Anke Linder [France] ; Howard A. Stone [États-Unis]Source :
- Journal of Fluid Mechanics [ 0022-1120 ] ; 2013.
Descripteurs français
- Pascal (Inist)
English descriptors
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Abstract
We present a mathematical model and corresponding series of microfluidic experiments examining the flow of a viscous fluid past an elastic fibre in a three-dimensional channel. The fibre's axis lies perpendicular to the direction of flow and its base is clamped to one wall of the channel; the sidewalls of the channel are close to the fibre, confining the flow. Experiments show that there is a linear relationship between deflection and flow rate for highly confined fibres at low flow rates, which inspires an asymptotic treatment of the problem in this regime. The three-dimensional problem is reduced to a two-dimensional model, consisting of Hele-Shaw flow past a barrier, with boundary conditions at the barrier that allow for the effects of flexibility and three-dimensional leakage. The analysis yields insight into the competing effects of flexion and leakage, and an analytical solution is derived for the leading-order pressure field corresponding to a slit that partially blocks a two-dimensional channel. The predictions of our model show favourable agreement with experimental results, allowing measurement of the fibre's elasticity and the flow rate in the channel.
Affiliations:
- Australie, France, Royaume-Uni, États-Unis
- Angleterre, Angleterre de l'Est, New Jersey, Île-de-France
- Cambridge, Paris, Princeton (New Jersey)
- Université Pierre-et-Marie-Curie, Université de Cambridge, Université de Princeton
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Stone</name><affiliation wicri:level="4"><inist:fA14 i1="01"><s1>Department of Mechanical and Aerospace Engineering, Princeton University</s1><s2>Princeton, NJ 08544</s2><s3>USA</s3><sZ>1 aut.</sZ><sZ>8 aut.</sZ></inist:fA14><country>États-Unis</country><placeName><settlement type="city">Princeton (New Jersey)</settlement><region type="state">New Jersey</region></placeName><orgName type="university">Université de Princeton</orgName></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">INIST</idno><idno type="inist">13-0178261</idno><date when="2013">2013</date><idno type="stanalyst">PASCAL 13-0178261 INIST</idno><idno type="RBID">Pascal:13-0178261</idno><idno type="wicri:Area/PascalFrancis/Corpus">000A72</idno><idno type="wicri:Area/PascalFrancis/Curation">005399</idno><idno type="wicri:Area/PascalFrancis/Checkpoint">000A86</idno><idno type="wicri:explorRef" wicri:stream="PascalFrancis" wicri:step="Checkpoint">000A86</idno><idno type="wicri:doubleKey">0022-1120:2013:Wexler J:bending:of:elastic</idno><idno type="wicri:Area/Main/Merge">005260</idno><idno type="wicri:Area/Main/Curation">005075</idno><idno type="wicri:Area/Main/Exploration">005075</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a">Bending of elastic fibres in viscous flows: the influence of confinement</title><author><name sortKey="Wexler, Jason S" sort="Wexler, Jason S" uniqKey="Wexler J" first="Jason S." last="Wexler">Jason S. Wexler</name><affiliation wicri:level="4"><inist:fA14 i1="01"><s1>Department of Mechanical and Aerospace Engineering, Princeton University</s1><s2>Princeton, NJ 08544</s2><s3>USA</s3><sZ>1 aut.</sZ><sZ>8 aut.</sZ></inist:fA14><country>États-Unis</country><placeName><settlement type="city">Princeton (New Jersey)</settlement><region type="state">New Jersey</region></placeName><orgName type="university">Université de Princeton</orgName></affiliation><affiliation wicri:level="4"><inist:fA14 i1="03"><s1>PMMH, ESPCI, CNRS UMR 7636, Université Pierre et Marie Curie, Université Paris Diderot, 10 rue Vauquelin</s1><s2>75005 Paris</s2><s3>FRA</s3><sZ>1 aut.</sZ><sZ>3 aut.</sZ><sZ>4 aut.</sZ><sZ>5 aut.</sZ><sZ>7 aut.</sZ></inist:fA14><country>France</country><placeName><region type="region" nuts="2">Île-de-France</region><settlement type="city">Paris</settlement><settlement type="city">Paris</settlement></placeName><orgName type="university">Université Pierre-et-Marie-Curie</orgName></affiliation></author><author><name sortKey="Trinh, Philippe H" sort="Trinh, Philippe H" uniqKey="Trinh P" first="Philippe H." last="Trinh">Philippe H. Trinh</name><affiliation wicri:level="4"><inist:fA14 i1="02"><s1>Program in Applied and Computational Mathematics, Princeton University</s1><s2>Princeton, NJ 08544</s2><s3>USA</s3><sZ>2 aut.</sZ></inist:fA14><country>États-Unis</country><placeName><settlement type="city">Princeton (New Jersey)</settlement><region type="state">New Jersey</region></placeName><orgName type="university">Université de Princeton</orgName></affiliation></author><author><name sortKey="Berthet, Helene" sort="Berthet, Helene" uniqKey="Berthet H" first="Helene" last="Berthet">Helene Berthet</name><affiliation wicri:level="4"><inist:fA14 i1="03"><s1>PMMH, ESPCI, CNRS UMR 7636, Université Pierre et Marie Curie, Université Paris Diderot, 10 rue Vauquelin</s1><s2>75005 Paris</s2><s3>FRA</s3><sZ>1 aut.</sZ><sZ>3 aut.</sZ><sZ>4 aut.</sZ><sZ>5 aut.</sZ><sZ>7 aut.</sZ></inist:fA14><country>France</country><placeName><region type="region" nuts="2">Île-de-France</region><settlement type="city">Paris</settlement><settlement type="city">Paris</settlement></placeName><orgName type="university">Université Pierre-et-Marie-Curie</orgName></affiliation></author><author><name sortKey="Quennouz, Nawal" sort="Quennouz, Nawal" uniqKey="Quennouz N" first="Nawal" last="Quennouz">Nawal Quennouz</name><affiliation wicri:level="4"><inist:fA14 i1="03"><s1>PMMH, ESPCI, CNRS UMR 7636, Université Pierre et Marie Curie, Université Paris Diderot, 10 rue Vauquelin</s1><s2>75005 Paris</s2><s3>FRA</s3><sZ>1 aut.</sZ><sZ>3 aut.</sZ><sZ>4 aut.</sZ><sZ>5 aut.</sZ><sZ>7 aut.</sZ></inist:fA14><country>France</country><wicri:noRegion>75005 Paris</wicri:noRegion><placeName><settlement type="city">Paris</settlement><region type="région" nuts="2">Île-de-France</region><settlement type="city">Paris</settlement></placeName><orgName type="university">Université Pierre-et-Marie-Curie</orgName></affiliation></author><author><name sortKey="Du Roure, Olivia" sort="Du Roure, Olivia" uniqKey="Du Roure O" first="Olivia" last="Du Roure">Olivia Du Roure</name><affiliation wicri:level="4"><inist:fA14 i1="03"><s1>PMMH, ESPCI, CNRS UMR 7636, Université Pierre et Marie Curie, Université Paris Diderot, 10 rue Vauquelin</s1><s2>75005 Paris</s2><s3>FRA</s3><sZ>1 aut.</sZ><sZ>3 aut.</sZ><sZ>4 aut.</sZ><sZ>5 aut.</sZ><sZ>7 aut.</sZ></inist:fA14><country>France</country><wicri:noRegion>75005 Paris</wicri:noRegion><placeName><settlement type="city">Paris</settlement><region type="région" nuts="2">Île-de-France</region><settlement type="city">Paris</settlement></placeName><orgName type="university">Université Pierre-et-Marie-Curie</orgName></affiliation></author><author><name sortKey="Huppert, Herbert E" sort="Huppert, Herbert E" uniqKey="Huppert H" first="Herbert E." last="Huppert">Herbert E. Huppert</name><affiliation wicri:level="4"><inist:fA14 i1="04"><s1>Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road</s1><s2>Cambridge CB3 0WA</s2><s3>GBR</s3><sZ>6 aut.</sZ></inist:fA14><country>Royaume-Uni</country><wicri:noRegion>Cambridge CB3 0WA</wicri:noRegion><orgName type="university">Université de Cambridge</orgName><placeName><settlement type="city">Cambridge</settlement><region type="country">Angleterre</region><region type="région" nuts="1">Angleterre de l'Est</region></placeName></affiliation><affiliation wicri:level="1"><inist:fA14 i1="05"><s1>School of Mathematics, University of New South Wales</s1><s2>Kensington, NSW 2052</s2><s3>AUS</s3><sZ>6 aut.</sZ></inist:fA14><country>Australie</country><wicri:noRegion>Kensington, NSW 2052</wicri:noRegion></affiliation></author><author><name sortKey="Linder, Anke" sort="Linder, Anke" uniqKey="Linder A" first="Anke" last="Linder">Anke Linder</name><affiliation wicri:level="4"><inist:fA14 i1="03"><s1>PMMH, ESPCI, CNRS UMR 7636, Université Pierre et Marie Curie, Université Paris Diderot, 10 rue Vauquelin</s1><s2>75005 Paris</s2><s3>FRA</s3><sZ>1 aut.</sZ><sZ>3 aut.</sZ><sZ>4 aut.</sZ><sZ>5 aut.</sZ><sZ>7 aut.</sZ></inist:fA14><country>France</country><wicri:noRegion>75005 Paris</wicri:noRegion><placeName><settlement type="city">Paris</settlement><region type="région" nuts="2">Île-de-France</region><settlement type="city">Paris</settlement></placeName><orgName type="university">Université Pierre-et-Marie-Curie</orgName></affiliation></author><author><name sortKey="Stone, Howard A" sort="Stone, Howard A" uniqKey="Stone H" first="Howard A." last="Stone">Howard A. Stone</name><affiliation wicri:level="4"><inist:fA14 i1="01"><s1>Department of Mechanical and Aerospace Engineering, Princeton University</s1><s2>Princeton, NJ 08544</s2><s3>USA</s3><sZ>1 aut.</sZ><sZ>8 aut.</sZ></inist:fA14><country>États-Unis</country><placeName><settlement type="city">Princeton (New Jersey)</settlement><region type="state">New Jersey</region></placeName><orgName type="university">Université de Princeton</orgName></affiliation></author></analytic><series><title level="j" type="main">Journal of Fluid Mechanics</title><title level="j" type="abbreviated">J. Fluid Mech.</title><idno type="ISSN">0022-1120</idno><imprint><date when="2013">2013</date></imprint></series></biblStruct></sourceDesc><seriesStmt><title level="j" type="main">Journal of Fluid Mechanics</title><title level="j" type="abbreviated">J. Fluid Mech.</title><idno type="ISSN">0022-1120</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Bending</term><term>Elastic deformation</term><term>Experimental study</term><term>Fibers</term><term>Fluid-structure interactions</term><term>Hele Shaw cell</term><term>Microchannel</term><term>Microfluidics</term><term>Microstructure</term><term>Modelling</term><term>Obstacle</term><term>Rectangular pipe</term><term>Three dimensional flow</term><term>Viscous fluids</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>Microfluidique</term><term>Interaction fluide structure</term><term>Ecoulement tridimensionnel</term><term>Fluide visqueux</term><term>Fibre</term><term>Déformation élastique</term><term>Cellule Hele Shaw</term><term>Conduite rectangulaire</term><term>Modélisation</term><term>Etude expérimentale</term><term>Flexion</term><term>Microstructure</term><term>Obstacle</term><term>4785N</term><term>Microcanal</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">We present a mathematical model and corresponding series of microfluidic experiments examining the flow of a viscous fluid past an elastic fibre in a three-dimensional channel. The fibre's axis lies perpendicular to the direction of flow and its base is clamped to one wall of the channel; the sidewalls of the channel are close to the fibre, confining the flow. Experiments show that there is a linear relationship between deflection and flow rate for highly confined fibres at low flow rates, which inspires an asymptotic treatment of the problem in this regime. The three-dimensional problem is reduced to a two-dimensional model, consisting of Hele-Shaw flow past a barrier, with boundary conditions at the barrier that allow for the effects of flexibility and three-dimensional leakage. The analysis yields insight into the competing effects of flexion and leakage, and an analytical solution is derived for the leading-order pressure field corresponding to a slit that partially blocks a two-dimensional channel. The predictions of our model show favourable agreement with experimental results, allowing measurement of the fibre's elasticity and the flow rate in the channel.</div></front></TEI><affiliations><list><country><li>Australie</li><li>France</li><li>Royaume-Uni</li><li>États-Unis</li></country><region><li>Angleterre</li><li>Angleterre de l'Est</li><li>New Jersey</li><li>Île-de-France</li></region><settlement><li>Cambridge</li><li>Paris</li><li>Princeton (New Jersey)</li></settlement><orgName><li>Université Pierre-et-Marie-Curie</li><li>Université de Cambridge</li><li>Université de Princeton</li></orgName></list><tree><country name="États-Unis"><region name="New Jersey"><name sortKey="Wexler, Jason S" sort="Wexler, Jason S" uniqKey="Wexler J" first="Jason S." last="Wexler">Jason S. Wexler</name></region><name sortKey="Stone, Howard A" sort="Stone, Howard A" uniqKey="Stone H" first="Howard A." last="Stone">Howard A. Stone</name><name sortKey="Trinh, Philippe H" sort="Trinh, Philippe H" uniqKey="Trinh P" first="Philippe H." last="Trinh">Philippe H. Trinh</name></country><country name="France"><region name="Île-de-France"><name sortKey="Wexler, Jason S" sort="Wexler, Jason S" uniqKey="Wexler J" first="Jason S." last="Wexler">Jason S. Wexler</name></region><name sortKey="Berthet, Helene" sort="Berthet, Helene" uniqKey="Berthet H" first="Helene" last="Berthet">Helene Berthet</name><name sortKey="Du Roure, Olivia" sort="Du Roure, Olivia" uniqKey="Du Roure O" first="Olivia" last="Du Roure">Olivia Du Roure</name><name sortKey="Linder, Anke" sort="Linder, Anke" uniqKey="Linder A" first="Anke" last="Linder">Anke Linder</name><name sortKey="Quennouz, Nawal" sort="Quennouz, Nawal" uniqKey="Quennouz N" first="Nawal" last="Quennouz">Nawal Quennouz</name></country><country name="Royaume-Uni"><region name="Angleterre"><name sortKey="Huppert, Herbert E" sort="Huppert, Herbert E" uniqKey="Huppert H" first="Herbert E." last="Huppert">Herbert E. Huppert</name></region></country><country name="Australie"><noRegion><name sortKey="Huppert, Herbert E" sort="Huppert, Herbert E" uniqKey="Huppert H" first="Herbert E." last="Huppert">Herbert E. Huppert</name></noRegion></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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