Consistent closure schemes for statistical models of anisotropic fluids
Identifieur interne :
003540 ( PascalFrancis/Corpus );
précédent :
003539;
suivant :
003541
Consistent closure schemes for statistical models of anisotropic fluids
Auteurs : Martin Kröger ;
Amine Ammar ;
Francisco ChinestaSource :
-
Journal of non-newtonian fluid mechanics [ 0377-0257 ] ; 2008.
RBID : Pascal:08-0281326
Descripteurs français
- Pascal (Inist)
- Ordre orientationnel,
Fonction distribution,
Modèle mathématique,
Equation Fokker Planck,
Transformation liquide nématique,
Fluide ferromagnétique,
Approximation rationnelle,
Modèle fermeture,
Cristal liquide,
Cristal nématique,
Fluide magnétorhéologique.
English descriptors
- KwdEn :
- Closure model,
Distribution functions,
Ferromagnetic fluid,
Fokker-Planck equation,
Liquid crystals,
Liquid nematic transformation,
Magnetorheological fluid,
Mathematical models,
Nematic crystals,
Orientational order,
Rational approximation.
Abstract
We propose a rational approach to approximating the various alignment tensors. It preserves the correct symmetry and leads to consistent results. For the case of uniaxial nematic fluids, the decoupling approximation for a tensor of rank n involves (n - 2)/2 scalar functions Sn(S2) in terms of a scalar argument S2, with Sn (0) = 0 and Sn (1) = 1. Nothing else can be concluded about the mathematical relationship between moments of the distribution function, and in particular, all consistent decoupling approximations for fourth-order moment in terms of second-order moments can be characterized by a single S4(S2) function. We propose using the simple model dependent convex shaped equilibrium relationship between S4 and S2 to characterize new (and simple) decoupling approximations K-I and K-II for the biaxial (including uniaxial) phase. In order to test the new against earlier proposed approximations rigorously, and to discuss consistency issues, we solve the Hess-Doi Fokker-Planck equation for nematic and nematic-discotic liquid crystals efficiently for a wide range of (2300 distinct) possible conditions including mixed shear and elongational flows, diverse field strengths, and molecular shapes. As a result, we confirm the closures K-I and K-II with correct tensorial symmetry; they are valid under arbitrary conditions to high precision, exact in the isotropic and totally aligned phases, improve upon earlier parameter-free closures in particular in the temperature regime T∈ [0.6, ∞] x TNI with the nematic-isotropic transition temperature TNI (or alternatively, for mean-field strengths U ∈ [0, 8]). K-II performs as good as the so-called Bingham closure, which usually requires 30 empirical coefficients, while K-I and K-II are essentially parameter-free, and their quality can be expected to be insensitive to the particular model.
Notice en format standard (ISO 2709)
Pour connaître la documentation sur le format Inist Standard.
| pA |
| A01 | 01 | 1 | | @0 0377-0257 |
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| A02 | 01 | | | @0 JNFMDI |
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| A03 | | 1 | | @0 J. non-newton. fluid mech. |
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| A05 | | | | @2 149 |
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| A06 | | | | @2 1-3 |
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| A08 | 01 | 1 | ENG | @1 Consistent closure schemes for statistical models of anisotropic fluids |
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| A09 | 01 | 1 | ENG | @1 International Workshop on Mesoscale and Multiscale Description of Complex Fluids |
|---|
| A11 | 01 | 1 | | @1 KRÖGER (Martin) |
|---|
| A11 | 02 | 1 | | @1 AMMAR (Amine) |
|---|
| A11 | 03 | 1 | | @1 CHINESTA (Francisco) |
|---|
| A12 | 01 | 1 | | @1 SHAQFEH (Eric S. G.) @9 ed. |
|---|
| A12 | 02 | 1 | | @1 RAVI PRAKASH (Jagadeeshan) @9 ed. |
|---|
| A14 | 01 | | | @1 Polymer Physics, ETH Zurich, Department of Materials, Wolfgang-Pauli-Str. 10 @2 8093 Zürich @3 CHE @Z 1 aut. |
|---|
| A14 | 02 | | | @1 Laboratoire de Rhéologie, UMR 5520 CNRS-UJF-INPG, 1301 Rue de la Piscine, BP 53 Domaine Universitaire @2 38041 Grenoble @3 FRA @Z 2 aut. |
|---|
| A14 | 03 | | | @1 LMSP UMR 8106 CNRS-ENSAM-ESEM, 151 Boulevard de l'Hôpital @2 75013 Paris @3 FRA @Z 3 aut. |
|---|
| A15 | 01 | | | @1 Stanford University @3 USA @Z 1 aut. |
|---|
| A15 | 02 | | | @1 Monash University @3 AUS @Z 2 aut. |
|---|
| A20 | | | | @1 40-55 |
|---|
| A21 | | | | @1 2008 |
|---|
| A23 | 01 | | | @0 ENG |
|---|
| A43 | 01 | | | @1 INIST @2 17234 @5 354000161895090060 |
|---|
| A44 | | | | @0 0000 @1 © 2008 INIST-CNRS. All rights reserved. |
|---|
| A45 | | | | @0 48 ref. |
|---|
| A47 | 01 | 1 | | @0 08-0281326 |
|---|
| A60 | | | | @1 P @2 C |
|---|
| A61 | | | | @0 A |
|---|
| A64 | 01 | 1 | | @0 Journal of non-newtonian fluid mechanics |
|---|
| A66 | 01 | | | @0 NLD |
|---|
| C01 | 01 | | ENG | @0 We propose a rational approach to approximating the various alignment tensors. It preserves the correct symmetry and leads to consistent results. For the case of uniaxial nematic fluids, the decoupling approximation for a tensor of rank n involves (n - 2)/2 scalar functions Sn(S2) in terms of a scalar argument S2, with Sn (0) = 0 and Sn (1) = 1. Nothing else can be concluded about the mathematical relationship between moments of the distribution function, and in particular, all consistent decoupling approximations for fourth-order moment in terms of second-order moments can be characterized by a single S4(S2) function. We propose using the simple model dependent convex shaped equilibrium relationship between S4 and S2 to characterize new (and simple) decoupling approximations K-I and K-II for the biaxial (including uniaxial) phase. In order to test the new against earlier proposed approximations rigorously, and to discuss consistency issues, we solve the Hess-Doi Fokker-Planck equation for nematic and nematic-discotic liquid crystals efficiently for a wide range of (2300 distinct) possible conditions including mixed shear and elongational flows, diverse field strengths, and molecular shapes. As a result, we confirm the closures K-I and K-II with correct tensorial symmetry; they are valid under arbitrary conditions to high precision, exact in the isotropic and totally aligned phases, improve upon earlier parameter-free closures in particular in the temperature regime T∈ [0.6, ∞] x TNI with the nematic-isotropic transition temperature TNI (or alternatively, for mean-field strengths U ∈ [0, 8]). K-II performs as good as the so-called Bingham closure, which usually requires 30 empirical coefficients, while K-I and K-II are essentially parameter-free, and their quality can be expected to be insensitive to the particular model. |
|---|
| C02 | 01 | 3 | | @0 001B60A30 |
|---|
| C03 | 01 | 3 | FRE | @0 Ordre orientationnel @5 02 |
|---|
| C03 | 01 | 3 | ENG | @0 Orientational order @5 02 |
|---|
| C03 | 02 | 3 | FRE | @0 Fonction distribution @5 03 |
|---|
| C03 | 02 | 3 | ENG | @0 Distribution functions @5 03 |
|---|
| C03 | 03 | 3 | FRE | @0 Modèle mathématique @5 04 |
|---|
| C03 | 03 | 3 | ENG | @0 Mathematical models @5 04 |
|---|
| C03 | 04 | 3 | FRE | @0 Equation Fokker Planck @5 05 |
|---|
| C03 | 04 | 3 | ENG | @0 Fokker-Planck equation @5 05 |
|---|
| C03 | 05 | X | FRE | @0 Transformation liquide nématique @5 06 |
|---|
| C03 | 05 | X | ENG | @0 Liquid nematic transformation @5 06 |
|---|
| C03 | 05 | X | SPA | @0 Transformación líquido nemático @5 06 |
|---|
| C03 | 06 | X | FRE | @0 Fluide ferromagnétique @5 11 |
|---|
| C03 | 06 | X | ENG | @0 Ferromagnetic fluid @5 11 |
|---|
| C03 | 06 | X | SPA | @0 Fluido ferromagnético @5 11 |
|---|
| C03 | 07 | X | FRE | @0 Approximation rationnelle @5 12 |
|---|
| C03 | 07 | X | ENG | @0 Rational approximation @5 12 |
|---|
| C03 | 07 | X | SPA | @0 Aproximación racional @5 12 |
|---|
| C03 | 08 | X | FRE | @0 Modèle fermeture @5 13 |
|---|
| C03 | 08 | X | ENG | @0 Closure model @5 13 |
|---|
| C03 | 08 | X | SPA | @0 Modelo cierre @5 13 |
|---|
| C03 | 09 | 3 | FRE | @0 Cristal liquide @5 15 |
|---|
| C03 | 09 | 3 | ENG | @0 Liquid crystals @5 15 |
|---|
| C03 | 10 | 3 | FRE | @0 Cristal nématique @5 16 |
|---|
| C03 | 10 | 3 | ENG | @0 Nematic crystals @5 16 |
|---|
| C03 | 11 | X | FRE | @0 Fluide magnétorhéologique @5 17 |
|---|
| C03 | 11 | X | ENG | @0 Magnetorheological fluid @5 17 |
|---|
| C03 | 11 | X | SPA | @0 Fluido magnetoreologico @5 17 |
|---|
| N21 | | | | @1 175 |
|---|
|
|---|
| pR |
| A30 | 01 | 1 | ENG | @1 IWMMCOF'06 International Workshop on Mesoscale and Multiscale Description of Complex Fluids @3 Prato ITA @4 2006-07-05 |
|---|
|
|---|
Format Inist (serveur)
| NO : | PASCAL 08-0281326 INIST |
|---|
| ET : | Consistent closure schemes for statistical models of anisotropic fluids |
|---|
| AU : | KRÖGER (Martin); AMMAR (Amine); CHINESTA (Francisco); SHAQFEH (Eric S. G.); RAVI PRAKASH (Jagadeeshan) |
|---|
| AF : | Polymer Physics, ETH Zurich, Department of Materials, Wolfgang-Pauli-Str. 10/8093 Zürich/Suisse (1 aut.); Laboratoire de Rhéologie, UMR 5520 CNRS-UJF-INPG, 1301 Rue de la Piscine, BP 53 Domaine Universitaire/38041 Grenoble/France (2 aut.); LMSP UMR 8106 CNRS-ENSAM-ESEM, 151 Boulevard de l'Hôpital/75013 Paris/France (3 aut.); Stanford University/Etats-Unis (1 aut.); Monash University/Australie (2 aut.) |
|---|
| DT : | Publication en série; Congrès; Niveau analytique |
|---|
| SO : | Journal of non-newtonian fluid mechanics; ISSN 0377-0257; Coden JNFMDI; Pays-Bas; Da. 2008; Vol. 149; No. 1-3; Pp. 40-55; Bibl. 48 ref. |
|---|
| LA : | Anglais |
|---|
| EA : | We propose a rational approach to approximating the various alignment tensors. It preserves the correct symmetry and leads to consistent results. For the case of uniaxial nematic fluids, the decoupling approximation for a tensor of rank n involves (n - 2)/2 scalar functions Sn(S2) in terms of a scalar argument S2, with Sn (0) = 0 and Sn (1) = 1. Nothing else can be concluded about the mathematical relationship between moments of the distribution function, and in particular, all consistent decoupling approximations for fourth-order moment in terms of second-order moments can be characterized by a single S4(S2) function. We propose using the simple model dependent convex shaped equilibrium relationship between S4 and S2 to characterize new (and simple) decoupling approximations K-I and K-II for the biaxial (including uniaxial) phase. In order to test the new against earlier proposed approximations rigorously, and to discuss consistency issues, we solve the Hess-Doi Fokker-Planck equation for nematic and nematic-discotic liquid crystals efficiently for a wide range of (2300 distinct) possible conditions including mixed shear and elongational flows, diverse field strengths, and molecular shapes. As a result, we confirm the closures K-I and K-II with correct tensorial symmetry; they are valid under arbitrary conditions to high precision, exact in the isotropic and totally aligned phases, improve upon earlier parameter-free closures in particular in the temperature regime T∈ [0.6, ∞] x TNI with the nematic-isotropic transition temperature TNI (or alternatively, for mean-field strengths U ∈ [0, 8]). K-II performs as good as the so-called Bingham closure, which usually requires 30 empirical coefficients, while K-I and K-II are essentially parameter-free, and their quality can be expected to be insensitive to the particular model. |
|---|
| CC : | 001B60A30 |
|---|
| FD : | Ordre orientationnel; Fonction distribution; Modèle mathématique; Equation Fokker Planck; Transformation liquide nématique; Fluide ferromagnétique; Approximation rationnelle; Modèle fermeture; Cristal liquide; Cristal nématique; Fluide magnétorhéologique |
|---|
| ED : | Orientational order; Distribution functions; Mathematical models; Fokker-Planck equation; Liquid nematic transformation; Ferromagnetic fluid; Rational approximation; Closure model; Liquid crystals; Nematic crystals; Magnetorheological fluid |
|---|
| SD : | Transformación líquido nemático; Fluido ferromagnético; Aproximación racional; Modelo cierre; Fluido magnetoreologico |
|---|
| LO : | INIST-17234.354000161895090060 |
|---|
| ID : | 08-0281326 |
|---|
Links to Exploration step
Pascal:08-0281326
Le document en format XML
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<author><name sortKey="Kroger, Martin" sort="Kroger, Martin" uniqKey="Kroger M" first="Martin" last="Kröger">Martin Kröger</name>
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<s3>FRA</s3>
<sZ>2 aut.</sZ>
</inist:fA14><author><name sortKey="Chinesta, Francisco" sort="Chinesta, Francisco" uniqKey="Chinesta F" first="Francisco" last="Chinesta">Francisco Chinesta</name>
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</publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a">Consistent closure schemes for statistical models of anisotropic fluids</title>
<author><name sortKey="Kroger, Martin" sort="Kroger, Martin" uniqKey="Kroger M" first="Martin" last="Kröger">Martin Kröger</name>
<affiliation><inist:fA14 i1="01"><s1>Polymer Physics, ETH Zurich, Department of Materials, Wolfgang-Pauli-Str. 10</s1>
<s2>8093 Zürich</s2>
<s3>CHE</s3>
<sZ>1 aut.</sZ>
</inist:fA14><author><name sortKey="Ammar, Amine" sort="Ammar, Amine" uniqKey="Ammar A" first="Amine" last="Ammar">Amine Ammar</name>
<affiliation><inist:fA14 i1="02"><s1>Laboratoire de Rhéologie, UMR 5520 CNRS-UJF-INPG, 1301 Rue de la Piscine, BP 53 Domaine Universitaire</s1>
<s2>38041 Grenoble</s2>
<s3>FRA</s3>
<sZ>2 aut.</sZ>
</inist:fA14><author><name sortKey="Chinesta, Francisco" sort="Chinesta, Francisco" uniqKey="Chinesta F" first="Francisco" last="Chinesta">Francisco Chinesta</name>
<affiliation><inist:fA14 i1="03"><s1>LMSP UMR 8106 CNRS-ENSAM-ESEM, 151 Boulevard de l'Hôpital</s1>
<s2>75013 Paris</s2>
<s3>FRA</s3>
<sZ>3 aut.</sZ>
</inist:fA14><series><title level="j" type="main">Journal of non-newtonian fluid mechanics</title>
<title level="j" type="abbreviated">J. non-newton. fluid mech.</title>
<idno type="ISSN">0377-0257</idno>
<imprint><date when="2008">2008</date>
</imprint><seriesStmt><title level="j" type="main">Journal of non-newtonian fluid mechanics</title>
<title level="j" type="abbreviated">J. non-newton. fluid mech.</title>
<idno type="ISSN">0377-0257</idno>
</seriesStmt><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Closure model</term>
<term>Distribution functions</term>
<term>Ferromagnetic fluid</term>
<term>Fokker-Planck equation</term>
<term>Liquid crystals</term>
<term>Liquid nematic transformation</term>
<term>Magnetorheological fluid</term>
<term>Mathematical models</term>
<term>Nematic crystals</term>
<term>Orientational order</term>
<term>Rational approximation</term>
</keywords><keywords scheme="Pascal" xml:lang="fr"><term>Ordre orientationnel</term>
<term>Fonction distribution</term>
<term>Modèle mathématique</term>
<term>Equation Fokker Planck</term>
<term>Transformation liquide nématique</term>
<term>Fluide ferromagnétique</term>
<term>Approximation rationnelle</term>
<term>Modèle fermeture</term>
<term>Cristal liquide</term>
<term>Cristal nématique</term>
<term>Fluide magnétorhéologique</term>
</keywords><front><div type="abstract" xml:lang="en">We propose a rational approach to approximating the various alignment tensors. It preserves the correct symmetry and leads to consistent results. For the case of uniaxial nematic fluids, the decoupling approximation for a tensor of rank n involves (n - 2)/2 scalar functions S<sub>n</sub>
(S<sub>2</sub>
) in terms of a scalar argument S<sub>2</sub>
, with S<sub>n</sub>
(0) = 0 and S<sub>n</sub>
(1) = 1. Nothing else can be concluded about the mathematical relationship between moments of the distribution function, and in particular, all consistent decoupling approximations for fourth-order moment in terms of second-order moments can be characterized by a single S<sub>4</sub>
(S<sub>2</sub>
) function. We propose using the simple model dependent convex shaped equilibrium relationship between S<sub>4</sub>
and S<sub>2</sub>
to characterize new (and simple) decoupling approximations K-I and K-II for the biaxial (including uniaxial) phase. In order to test the new against earlier proposed approximations rigorously, and to discuss consistency issues, we solve the Hess-Doi Fokker-Planck equation for nematic and nematic-discotic liquid crystals efficiently for a wide range of (2300 distinct) possible conditions including mixed shear and elongational flows, diverse field strengths, and molecular shapes. As a result, we confirm the closures K-I and K-II with correct tensorial symmetry; they are valid under arbitrary conditions to high precision, exact in the isotropic and totally aligned phases, improve upon earlier parameter-free closures in particular in the temperature regime T∈ [0.6, ∞] x T<sub>NI</sub>
with the nematic-isotropic transition temperature T<sub>NI</sub>
(or alternatively, for mean-field strengths U ∈ [0, 8]). K-II performs as good as the so-called Bingham closure, which usually requires 30 empirical coefficients, while K-I and K-II are essentially parameter-free, and their quality can be expected to be insensitive to the particular model.</div><inist><standard h6="B"><pA><fA01 i1="01" i2="1"><s0>0377-0257</s0>
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</fA02><fA03 i2="1"><s0>J. non-newton. fluid mech.</s0>
</fA03><fA05><s2>149</s2>
</fA05><fA06><s2>1-3</s2>
</fA06><fA08 i1="01" i2="1" l="ENG"><s1>Consistent closure schemes for statistical models of anisotropic fluids</s1>
</fA08><fA09 i1="01" i2="1" l="ENG"><s1>International Workshop on Mesoscale and Multiscale Description of Complex Fluids</s1>
</fA09><fA11 i1="01" i2="1"><s1>KRÖGER (Martin)</s1>
</fA11><fA11 i1="02" i2="1"><s1>AMMAR (Amine)</s1>
</fA11><fA11 i1="03" i2="1"><s1>CHINESTA (Francisco)</s1>
</fA11><fA12 i1="01" i2="1"><s1>SHAQFEH (Eric S. G.)</s1>
<s9>ed.</s9>
</fA12><fA12 i1="02" i2="1"><s1>RAVI PRAKASH (Jagadeeshan)</s1>
<s9>ed.</s9>
</fA12><fA14 i1="01"><s1>Polymer Physics, ETH Zurich, Department of Materials, Wolfgang-Pauli-Str. 10</s1>
<s2>8093 Zürich</s2>
<s3>CHE</s3>
<sZ>1 aut.</sZ>
</fA14><fA14 i1="02"><s1>Laboratoire de Rhéologie, UMR 5520 CNRS-UJF-INPG, 1301 Rue de la Piscine, BP 53 Domaine Universitaire</s1>
<s2>38041 Grenoble</s2>
<s3>FRA</s3>
<sZ>2 aut.</sZ>
</fA14><fA14 i1="03"><s1>LMSP UMR 8106 CNRS-ENSAM-ESEM, 151 Boulevard de l'Hôpital</s1>
<s2>75013 Paris</s2>
<s3>FRA</s3>
<sZ>3 aut.</sZ>
</fA14><fA15 i1="01"><s1>Stanford University</s1>
<s3>USA</s3>
<sZ>1 aut.</sZ>
</fA15><fA15 i1="02"><s1>Monash University</s1>
<s3>AUS</s3>
<sZ>2 aut.</sZ>
</fA15><fA20><s1>40-55</s1>
</fA20><fA21><s1>2008</s1>
</fA21><fA23 i1="01"><s0>ENG</s0>
</fA23><fA43 i1="01"><s1>INIST</s1>
<s2>17234</s2>
<s5>354000161895090060</s5>
</fA43><fA44><s0>0000</s0>
<s1>© 2008 INIST-CNRS. All rights reserved.</s1>
</fA44><fA45><s0>48 ref.</s0>
</fA45><fA47 i1="01" i2="1"><s0>08-0281326</s0>
</fA47><fA60><s1>P</s1>
<s2>C</s2>
</fA60><fA64 i1="01" i2="1"><s0>Journal of non-newtonian fluid mechanics</s0>
</fA64><fA66 i1="01"><s0>NLD</s0>
</fA66><fC01 i1="01" l="ENG"><s0>We propose a rational approach to approximating the various alignment tensors. It preserves the correct symmetry and leads to consistent results. For the case of uniaxial nematic fluids, the decoupling approximation for a tensor of rank n involves (n - 2)/2 scalar functions S<sub>n</sub>
(S<sub>2</sub>
) in terms of a scalar argument S<sub>2</sub>
, with S<sub>n</sub>
(0) = 0 and S<sub>n</sub>
(1) = 1. Nothing else can be concluded about the mathematical relationship between moments of the distribution function, and in particular, all consistent decoupling approximations for fourth-order moment in terms of second-order moments can be characterized by a single S<sub>4</sub>
(S<sub>2</sub>
) function. We propose using the simple model dependent convex shaped equilibrium relationship between S<sub>4</sub>
and S<sub>2</sub>
to characterize new (and simple) decoupling approximations K-I and K-II for the biaxial (including uniaxial) phase. In order to test the new against earlier proposed approximations rigorously, and to discuss consistency issues, we solve the Hess-Doi Fokker-Planck equation for nematic and nematic-discotic liquid crystals efficiently for a wide range of (2300 distinct) possible conditions including mixed shear and elongational flows, diverse field strengths, and molecular shapes. As a result, we confirm the closures K-I and K-II with correct tensorial symmetry; they are valid under arbitrary conditions to high precision, exact in the isotropic and totally aligned phases, improve upon earlier parameter-free closures in particular in the temperature regime T∈ [0.6, ∞] x T<sub>NI</sub>
with the nematic-isotropic transition temperature T<sub>NI</sub>
(or alternatively, for mean-field strengths U ∈ [0, 8]). K-II performs as good as the so-called Bingham closure, which usually requires 30 empirical coefficients, while K-I and K-II are essentially parameter-free, and their quality can be expected to be insensitive to the particular model.</s0><fC02 i1="01" i2="3"><s0>001B60A30</s0>
</fC02><fC03 i1="01" i2="3" l="FRE"><s0>Ordre orientationnel</s0>
<s5>02</s5>
</fC03><fC03 i1="01" i2="3" l="ENG"><s0>Orientational order</s0>
<s5>02</s5>
</fC03><fC03 i1="02" i2="3" l="FRE"><s0>Fonction distribution</s0>
<s5>03</s5>
</fC03><fC03 i1="02" i2="3" l="ENG"><s0>Distribution functions</s0>
<s5>03</s5>
</fC03><fC03 i1="03" i2="3" l="FRE"><s0>Modèle mathématique</s0>
<s5>04</s5>
</fC03><fC03 i1="03" i2="3" l="ENG"><s0>Mathematical models</s0>
<s5>04</s5>
</fC03><fC03 i1="04" i2="3" l="FRE"><s0>Equation Fokker Planck</s0>
<s5>05</s5>
</fC03><fC03 i1="04" i2="3" l="ENG"><s0>Fokker-Planck equation</s0>
<s5>05</s5>
</fC03><fC03 i1="05" i2="X" l="FRE"><s0>Transformation liquide nématique</s0>
<s5>06</s5>
</fC03><fC03 i1="05" i2="X" l="ENG"><s0>Liquid nematic transformation</s0>
<s5>06</s5>
</fC03><fC03 i1="05" i2="X" l="SPA"><s0>Transformación líquido nemático</s0>
<s5>06</s5>
</fC03><fC03 i1="06" i2="X" l="FRE"><s0>Fluide ferromagnétique</s0>
<s5>11</s5>
</fC03><fC03 i1="06" i2="X" l="ENG"><s0>Ferromagnetic fluid</s0>
<s5>11</s5>
</fC03><fC03 i1="06" i2="X" l="SPA"><s0>Fluido ferromagnético</s0>
<s5>11</s5>
</fC03><fC03 i1="07" i2="X" l="FRE"><s0>Approximation rationnelle</s0>
<s5>12</s5>
</fC03><fC03 i1="07" i2="X" l="ENG"><s0>Rational approximation</s0>
<s5>12</s5>
</fC03><fC03 i1="07" i2="X" l="SPA"><s0>Aproximación racional</s0>
<s5>12</s5>
</fC03><fC03 i1="08" i2="X" l="FRE"><s0>Modèle fermeture</s0>
<s5>13</s5>
</fC03><fC03 i1="08" i2="X" l="ENG"><s0>Closure model</s0>
<s5>13</s5>
</fC03><fC03 i1="08" i2="X" l="SPA"><s0>Modelo cierre</s0>
<s5>13</s5>
</fC03><fC03 i1="09" i2="3" l="FRE"><s0>Cristal liquide</s0>
<s5>15</s5>
</fC03><fC03 i1="09" i2="3" l="ENG"><s0>Liquid crystals</s0>
<s5>15</s5>
</fC03><fC03 i1="10" i2="3" l="FRE"><s0>Cristal nématique</s0>
<s5>16</s5>
</fC03><fC03 i1="10" i2="3" l="ENG"><s0>Nematic crystals</s0>
<s5>16</s5>
</fC03><fC03 i1="11" i2="X" l="FRE"><s0>Fluide magnétorhéologique</s0>
<s5>17</s5>
</fC03><fC03 i1="11" i2="X" l="ENG"><s0>Magnetorheological fluid</s0>
<s5>17</s5>
</fC03><fC03 i1="11" i2="X" l="SPA"><s0>Fluido magnetoreologico</s0>
<s5>17</s5>
</fC03><fN21><s1>175</s1>
</fN21><pR><fA30 i1="01" i2="1" l="ENG"><s1>IWMMCOF'06 International Workshop on Mesoscale and Multiscale Description of Complex Fluids</s1>
<s3>Prato ITA</s3>
<s4>2006-07-05</s4>
</fA30><server><NO>PASCAL 08-0281326 INIST</NO>
<ET>Consistent closure schemes for statistical models of anisotropic fluids</ET>
<AU>KRÖGER (Martin); AMMAR (Amine); CHINESTA (Francisco); SHAQFEH (Eric S. G.); RAVI PRAKASH (Jagadeeshan)</AU>
<AF>Polymer Physics, ETH Zurich, Department of Materials, Wolfgang-Pauli-Str. 10/8093 Zürich/Suisse (1 aut.); Laboratoire de Rhéologie, UMR 5520 CNRS-UJF-INPG, 1301 Rue de la Piscine, BP 53 Domaine Universitaire/38041 Grenoble/France (2 aut.); LMSP UMR 8106 CNRS-ENSAM-ESEM, 151 Boulevard de l'Hôpital/75013 Paris/France (3 aut.); Stanford University/Etats-Unis (1 aut.); Monash University/Australie (2 aut.)</AF>
<DT>Publication en série; Congrès; Niveau analytique</DT>
<SO>Journal of non-newtonian fluid mechanics; ISSN 0377-0257; Coden JNFMDI; Pays-Bas; Da. 2008; Vol. 149; No. 1-3; Pp. 40-55; Bibl. 48 ref.</SO>
<LA>Anglais</LA>
<EA>We propose a rational approach to approximating the various alignment tensors. It preserves the correct symmetry and leads to consistent results. For the case of uniaxial nematic fluids, the decoupling approximation for a tensor of rank n involves (n - 2)/2 scalar functions S<sub>n</sub>
(S<sub>2</sub>
) in terms of a scalar argument S<sub>2</sub>
, with S<sub>n</sub>
(0) = 0 and S<sub>n</sub>
(1) = 1. Nothing else can be concluded about the mathematical relationship between moments of the distribution function, and in particular, all consistent decoupling approximations for fourth-order moment in terms of second-order moments can be characterized by a single S<sub>4</sub>
(S<sub>2</sub>
) function. We propose using the simple model dependent convex shaped equilibrium relationship between S<sub>4</sub>
and S<sub>2</sub>
to characterize new (and simple) decoupling approximations K-I and K-II for the biaxial (including uniaxial) phase. In order to test the new against earlier proposed approximations rigorously, and to discuss consistency issues, we solve the Hess-Doi Fokker-Planck equation for nematic and nematic-discotic liquid crystals efficiently for a wide range of (2300 distinct) possible conditions including mixed shear and elongational flows, diverse field strengths, and molecular shapes. As a result, we confirm the closures K-I and K-II with correct tensorial symmetry; they are valid under arbitrary conditions to high precision, exact in the isotropic and totally aligned phases, improve upon earlier parameter-free closures in particular in the temperature regime T∈ [0.6, ∞] x T<sub>NI</sub>
with the nematic-isotropic transition temperature T<sub>NI</sub>
(or alternatively, for mean-field strengths U ∈ [0, 8]). K-II performs as good as the so-called Bingham closure, which usually requires 30 empirical coefficients, while K-I and K-II are essentially parameter-free, and their quality can be expected to be insensitive to the particular model.</EA><CC>001B60A30</CC>
<FD>Ordre orientationnel; Fonction distribution; Modèle mathématique; Equation Fokker Planck; Transformation liquide nématique; Fluide ferromagnétique; Approximation rationnelle; Modèle fermeture; Cristal liquide; Cristal nématique; Fluide magnétorhéologique</FD>
<ED>Orientational order; Distribution functions; Mathematical models; Fokker-Planck equation; Liquid nematic transformation; Ferromagnetic fluid; Rational approximation; Closure model; Liquid crystals; Nematic crystals; Magnetorheological fluid</ED>
<SD>Transformación líquido nemático; Fluido ferromagnético; Aproximación racional; Modelo cierre; Fluido magnetoreologico</SD>
<LO>INIST-17234.354000161895090060</LO>
<ID>08-0281326</ID>
</server>
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