Comment calculer nombre de Bingham Bn yield stress fluide

Calcule nombre de Bingham Bn = tau_y*L/(mu*v) rapport yield stress sur shear stress visqueux fluides Bingham plastiques. Bn<<1 Newtonien; Bn>>1 plug flow boues forage beton dentifrice magma. Eugene Bingham 1916 + Society Rheology 1929. Total Lafarge Sanofi applications.

Paramètres de calcul
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Nombre de Bingham Bn rapport adimensionnel yield stress vs shear stress visqueux dans fluides non-Newtoniens Bingham plastiques visco-plastiques: Bn = tau_y * L / (mu * v). tau_y yield stress Pa (sang 0.005; boues forage bentonite 5-50; beton frais 50-500; dentifrice 100-300; ketchup 50-100; magma 1-10000); L m; mu Pa*s; v m/s.

Modèle Bingham: tau = tau_y + mu*gamma_dot.

Hedstrom: He = Bn*Re.

Regimes: Bn<0.1 viscous-like; 1-10 moderate; 10-100 strong boues beton; Bn>100 dominant magma dentifrice.

Buckingham-Reiner.

Modèles: Bingham + Herschel-Bulkley + Casson sang. Histoire: Eugene Cook Bingham (Cornwall VT USA 1878 - Easton PA 1945) Middlebury + Johns Hopkins PhD 1905 + Bureau Standards 1908-1916 + Lafayette 1916-1944; 1916 Bureau Standards Bull 13:309 + 1922 'Fluidity and Plasticity' McGraw-Hill 440 pages + 1929 Society of Rheology founder.

Edgar Buckingham USA 1867-1940 + 1921 Trans ASME 43:1097 + 1914 pi-theorem.

Markus Reiner Vienna 1886 - Haifa Israel 1976 Technion 1948-1976 + 1928 Kolloid Z 44:1 + Society Rheology co-founder + Deborah 1964. Bird-Stewart-Lightfoot Wisconsin 1960 'Transport Phenomena' classic. Macosko 1994 Wiley.

France recherche Bingham + rheologie + ciment + boues + magma: CEA Saclay + Cadarache + Grenoble + Marcoule 16000; CNRS Paris 11000 + LIMSI + LEMTA + LRP Laboratoire Rheologie Procedes Grenoble; Mines Paris PSL CES Sophia 2000; IFP Énergies Nouvelles Rueil-Malmaison 1944 1700 + IFPEN forage rheology + boues bentonite; BRGM Bureau Recherches Geologiques Minieres Orleans 1959 1100 + sediment magma + volcanism; EDF R&D 158000; IRSN 1740; OPGC Observatoire Physique Globe Clermont-Ferrand + magma volcanology Auvergne; IPGP Institut Physique Globe Paris 1921 800 + magma volcanology + Soufriere Guadeloupe + Piton de la Fournaise + Mont Pelee Martinique + La Soufriere Martinique.

France universites Bingham + rheologie + ciment + magma: Sorbonne Paris 55000 LIMSI + Lagree fluides; PSL 17000 ENS + ESPCI Patrick Tabeling microfluidique + Mines Paris; X Polytechnique Palaiseau 3500 LadHyX + Charles Baroud + Patrick Huerre; Centrale Supelec Saclay 7000 EM2C combustion; INSA Lyon 6000 LMFA + LAGEPP Genie Procedes + LRP Frederic Pignon polymer rheology + Christophe Charpentier; Centrale Lyon 1700 + LMFA Marc Buffat; Toulouse III 35000 + IMFT Olivier Eiff sediment; Aix-Marseille 80000 + IRPHE Patrice Le Gal + IUSTI Pierre Lance sediment; UGA Grenoble 60000 + LEGI Sommeria + LRP Charpentier rheology + LJK Pellenq sediment + Hospital Roque-Carmes geology; ENSAM 6000; Universite Bordeaux 50000 + I2M Patrick Sebastian + LCBM polymer; Lille 50000 + UCCS catalysis + LMFL fluides; Strasbourg 50000 + ICPEES + LRP rheology; ENS Lyon Christophe Coperet polymer rheology.

France industrie oil&gas drilling muds: Total Énergies Courbevoie 102000 + Total Drilling + drilling fluids bentonite + Forages Total; Petroineos Lavera 1500; Esso France 1500; BP France 800; Halliburton France Pau 1000 + drilling fluids; Schlumberger France Aulnay-sous-Bois 1972 1500 + Pau + Clamart + drilling fluids M-I SWACO; Baker Hughes France 200; NOV France 200; Geosun France 100 + Geosciences.

France industrie ciment + beton + admixtures rheology: Lafarge SA Paris 1833 + Holcim 2015 11000 France + cement + admixtures + Lafarge R&D Centre LCR Saint-Quentin Fallavier world-leading + Plaster + Aggregates; Vicat Group L'Isle-d'Abeau 1853 9500 + cement plants Vicat + admixtures; Cemex France Rungis 1000; HeidelbergCement France 800; Imerys Paris 1880 17000 + minerals + admixtures; Saint-Gobain Courbevoie 1665 167000 + glass + ceramics + plaster + cement Weber; Sika France Saint-Quentin Fallavier 1500 + admixtures Sikament Plastiment Plastocrete; BASF Master Builders Solutions France 800 + Glenium MasterGlenium; Chryso Sermaises 1934 1500 + admixtures cement world-leading + Chryso ASF; Eqiom France 1000; Calcia Italcementi France 1500; Mapei France 200; GCP Applied Technologies France 200.

France industrie alimentaire ketchup + cosmetique pates + dentifrice: Danone Paris 1919 100000; Lactalis Laval 85000; Bel Group Paris 12000; Heinz Kraft Heinz France 200; Hellmann's Unilever France 600; Calve Unilever France 600 + sauces ketchup; Bonduelle Renescure 11000; Andros Biars 3500; L'Oreal Paris 88000 + Lancome + Maybelline + Garnier creams + dentifrices; LVMH Paris 196000 + Christian Dior + Givenchy + Guerlain creams + perfumes; Kering Paris 47000; Coty 11000; Chanel 32000 creams; Hermes 19000; Colgate-Palmolive France 200 + Colgate toothpaste; P&G France 1000 + Crest toothpaste + Olay creams; Sanofi Paris 91000 + creams ointments; Pierre Fabre 9500 + creams.

France industrie magma volcanology Outre-Mer: IPGP Paris 800 + Soufriere Guadeloupe Petit-Bourg + Piton de la Fournaise Reunion + Mont Pelee Martinique + La Soufriere Saint-Vincent + Iceland partnerships + Lo Sueve Cabo Verde; OVPF Observatoire Volcanologique Piton de la Fournaise Reunion 50 + La Reunion volcano monitoring; OVSM Observatoire Volcanologique Sismologique Martinique Mont Pelee Saint-Pierre 30; OVSG Observatoire Volcanologique Sismologique Guadeloupe Soufriere 30; OPGC Clermont-Ferrand Auvergne + dormant volcanos Massif Central; BRGM Orleans 1100 + magma sediment + tectonics; CNRS-INSU Paris 1900.

France industrie 3D printing pasta clay ceramic: BeAM Strasbourg 100 + 3D printing metal DED; AddUp Cebora Cebora Cebora 200 + Michelin JV 3D printing metal; Volum-e Marolles 100; Trumpf France 600; BCN3D France 50; WASP France 50; HP 3D France 200; Stratasys France 200.

Formule Bingham

Définition: Bn = tau_y*L/(mu*v) + tau = tau_y + mu*gamma_dot.

Histoire

Eugene Bingham (Cornwall 1878 - Easton 1945) Lafayette + 1916 Bureau Standards Bull + 1922 'Fluidity and Plasticity' + 1929 Society Rheology founder. Buckingham USA 1921 + 1914 pi-theorem. Reiner Vienna - Haifa Technion 1948-1976 + 1928 Kolloid Z + Society Rheology co-founder + Deborah 1964. Bird-Stewart-Lightfoot 1960 'Transport Phenomena' classic. Macosko 1994.

France recherche: CEA 16000; CNRS 11000 LIMSI LEMTA + LRP Grenoble; Mines Paris PSL 2000; IFPEN 1700 forage rheology boues bentonite; BRGM Orleans 1100 sediment magma; EDF R&D 158000; IRSN 1740; OPGC Clermont-Ferrand + magma; IPGP Paris 800 + Soufriere Piton Mont Pelee La Soufriere + Outre-Mer.

France universites: Sorbonne 55000 LIMSI; PSL 17000 ENS ESPCI Tabeling; X 3500 LadHyX Baroud; Centrale Supelec 7000; INSA Lyon 6000 LMFA + LAGEPP + LRP Pignon Charpentier; Centrale Lyon 1700; Toulouse III 35000 IMFT Eiff; Aix-Marseille 80000 IRPHE Le Gal + IUSTI Lance; UGA Grenoble 60000 LEGI + LRP Charpentier + LJK Pellenq; ENSAM 6000; Bordeaux 50000 I2M; Lille 50000 UCCS LMFL; Strasbourg 50000 ICPEES; ENS Lyon Coperet.

France oil&gas drilling: Total Énergies 102000 Forages; Petroineos 1500; Esso France 1500; BP France 800; Halliburton Pau 1000; Schlumberger Aulnay Pau Clamart 1500 M-I SWACO; Baker Hughes 200; NOV 200.

France ciment: Lafarge Holcim 11000 LCR Saint-Quentin Fallavier world-leading; Vicat 9500; Cemex 1000; HeidelbergCement 800; Imerys 17000; Saint-Gobain 167000 Weber; Sika France 1500; BASF Master Builders 800; Chryso Sermaises 1500 world-leading admixtures; Eqiom 1000; Calcia Italcementi 1500; Mapei France 200; GCP 200.

France alimentaire: Danone 100000; Lactalis 85000; Bel Group 12000; Heinz Kraft 200; Hellmann's Unilever 600; Calve Unilever 600; Bonduelle 11000; Andros 3500.

France cosmetique: L'Oreal 88000 Lancome Maybelline Garnier + dentifrices; LVMH 196000 Dior Givenchy Guerlain; Kering 47000; Coty 11000; Chanel 32000; Hermes 19000; Colgate-Palmolive France 200; P&G France 1000; Sanofi 91000; Pierre Fabre 9500.

France magma Outre-Mer: IPGP Paris 800 Soufriere Guadeloupe + Piton Reunion + Mont Pelee + La Soufriere Saint-Vincent; OVPF Reunion 50; OVSM Martinique 30; OVSG Guadeloupe 30; OPGC Clermont Massif Central.

France 3D printing: BeAM 100 DED metal; AddUp Michelin 200; Trumpf France 600; HP 3D France 200; Stratasys France 200.

Tableau valeurs

  • Bn = tau_y*L/(mu*v)
  • tau = tau_y + mu*gamma_dot
  • He = Bn*Re
  • Bn<0.1 viscous
  • 1-10 moderate
  • 10-100 strong
  • Bn>100 dominant
  • Sang 0.005
  • Boues 5-50
  • Beton 50-500
  • Magma 1-10000
  • Bingham 1916
  • Buckingham 1921
  • Reiner 1928
  • Society Rheology 1929
  • France IFPEN 1700
  • France BRGM 1100
  • France IPGP 800: Outre-Mer magma
  • France Total Énergies 102000
  • France Schlumberger 1500
  • France Lafarge Holcim 11000: LCR world-leading
  • France Vicat 9500
  • France Chryso 1500: admixtures world-leading
  • France L'Oreal 88000
  • France BeAM 100: 3D DED

Exemples numériques

Exemple 1 - Sang. Bn=0.0125. France: Sorbonne LIMSI + IPGP biophysics.

Exemple 2 - Boues forage. Bn=20 strong. France: Total Énergies + Halliburton Pau + Schlumberger Aulnay Pau Clamart.

Exemple 3 - Beton frais. Bn=4. France: Lafarge Holcim LCR Saint-Quentin Fallavier + Vicat + Sika + Chryso + BASF Master Builders + Saint-Gobain Weber.

Exemple 4 - Dentifrice. Bn=1. France: L'Oreal Paris + Colgate-Palmolive France + P&G Crest + Sensodyne.

Exemple 5 - Magma Piton Reunion. Bn=1000 yield dominant lava. France: IPGP Paris + OVPF Reunion + OVSM Martinique Mont Pelee + OVSG Soufriere Guadeloupe.

Limites

  1. Bingham vs Herschel-Bulkley.
  2. Yield measurement.
  3. Thixotropy.
  4. Compressibility.
  5. Température.
  6. Multi-component.
  7. Wall slip.
  8. Turbulence.
  9. Surface tension.
  10. Particle suspensions.

Erreurs courantes

Bingham vs Newton.

Yield stress.

Plastic vs apparent.

Herschel-Bulkley.

Hedstrom.

Applications

  1. Boues forage France: Total Énergies 102000 Forages + Halliburton Pau 1000 + Schlumberger 1500 Aulnay Pau Clamart M-I SWACO + Baker Hughes + NOV.
  2. Beton ciment France: Lafarge Holcim 11000 LCR Saint-Quentin Fallavier world-leading + Vicat 9500 + Cemex + Sika 1500 + Chryso 1500 admixtures world-leading + BASF Master Builders + Saint-Gobain Weber.
  3. Alimentaire ketchup France: Heinz Kraft + Calve Hellmann's Unilever + Andros + Bonduelle.
  4. Cosmetique creams France: L'Oreal 88000 + LVMH 196000 + Kering + Coty + Chanel + Hermes + P&G Crest + Colgate-Palmolive + Sanofi creams + Pierre Fabre.
  5. Pharma ointments France: Sanofi 91000 + Pierre Fabre 9500 + Servier + Ipsen + Boiron + Urgo + L'Oreal Active Cosmetics.
  6. Magma Outre-Mer France: IPGP Paris 800 + OVPF Reunion Piton de la Fournaise + OVSM Martinique Mont Pelee + OVSG Guadeloupe Soufriere + OPGC Clermont-Ferrand Auvergne + BRGM.
  7. 3D printing pasta France: BeAM Strasbourg DED + AddUp Michelin + Trumpf France + HP 3D France.
  8. Sediment transport France: BRGM Orleans + IFREMER + Toulouse IMFT Eiff + Aix-Marseille IUSTI Lance.
  9. Sangue rheology France: Sanofi + IPGP biophysics + ENS Lyon.
  10. Universites rheologie: Sorbonne LIMSI + X LadHyX + INSA Lyon LRP Pignon Charpentier + UGA LRP + ENS Lyon Coperet.

Mis à jour en juillet 2026

Questions fréquentes

Qu est-ce que le nombre de Bingham?

Bn = tau_y*L/(mu*v) rapport adimensionnel yield stress vs shear visqueux fluides Bingham plastiques visco-plastiques. Bn<0.1 viscous Newtonien; 1-10 moderate plug flow; Bn>100 dominant magma. Modèle tau=tau_y+mu*gamma_dot. Eugene Bingham USA 1916 + Society Rheology 1929. France: CEA 16000 + IFPEN 1700 + Lafarge Holcim 11000 + Total 102000 + IPGP Paris 800.

Comment calculer Bingham?

Procedure: (1) Bn = tau_y*L/(mu*v); (2) tau_y Pa; (3) L m; (4) mu Pa*s; (5) v m/s; (6) régime; (7) tau = tau_y + mu*gamma_dot. Forage: Bn=20. Beton: Bn=4. France: INSA Lyon LRP Pignon + UGA LRP Charpentier + Aix-Marseille IUSTI.

Qu est-ce que le modèle Bingham?

Modèle Bingham Eugene Bingham USA 1878-1945 Lafayette + 1916 Bureau Standards Bull 13:309 + 1922 'Fluidity and Plasticity' McGraw-Hill + tau = tau_y + mu*gamma_dot per tau>tau_y; gamma_dot=0 per tau<tau_y. France: Total Forages + Lafarge Holcim LCR + Chryso admixtures.

Quels régimes classifie Bn?

Bn<0.1 viscous Newtonien; 1-10 moderate plug; 10-100 strong boues forage beton; Bn>100 dominant magma dentifrice. France: Total Énergies forages + Lafarge Holcim Vicat ciment + L'Oreal Colgate cosmetique + IPGP Outre-Mer magma.

Qui etait Eugene Bingham?

Eugene Cook Bingham (Cornwall VT USA 1878 - Easton PA 1945) Middlebury + Johns Hopkins PhD 1905 + Bureau Standards Washington DC 1908-1916 + Lafayette College Easton PA 1916-1944 chair chemistry director laboratory; 1916 Bureau Standards Bull 13:309 + 1922 'Fluidity and Plasticity' McGraw-Hill + 1929 Society Rheology founder.

Qu est-ce que Buckingham-Reiner équation?

Buckingham-Reiner équation Edgar Buckingham USA 1921 Trans ASME 43:1097 'Plastic flow capillary tubes' + Markus Reiner Israel 1928 Kolloid Z 44:1 + Bingham fluid tube flow + plug radius + Buckingham pi-theorem 1914. France: Total Forages + IFPEN tribology + Lafarge LCR ciment.

Quelles applications de Bingham?

Applications: boues forage Total Énergies 102000 Forages + Halliburton Pau + Schlumberger 1500 M-I SWACO + Baker Hughes + NOV; beton ciment Lafarge Holcim 11000 LCR + Vicat 9500 + Sika + Chryso + BASF Master Builders + Saint-Gobain Weber; alimentaire Heinz Kraft + Calve Unilever + Andros; cosmetique L'Oreal 88000 + LVMH + Chanel + Colgate + P&G Crest; magma Outre-Mer IPGP 800 + OVPF Piton + OVSM Mont Pelee + OVSG Soufriere; 3D printing BeAM + AddUp Michelin + Trumpf.

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