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Rheologica Acta

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08-10-2021 | Original Contribution

Compatibility of the generalized BMP model and the two-fluid Langevin formulations

Authors: C. Fierro, F. Bautista, J. P. García-Sandoval, E. Hernández, J. E. Puig, O. Manero

Published in: Rheologica Acta | Issue 12/2021

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Abstract

The main objective of this work is to demonstrate the agreement between the two-fluid linear Langevin formulation and that described by the extended irreversible thermodynamics (EIT). The two-fluid model, originally proposed by de Gennes, has been widely analyzed by many authors in various flow situations, especially to compare predictions with experimental data of the structure factor in many complex flows. The canonical Langevin equations together with the fluctuation-dissipation theorem ensure consistent thermodynamic behavior for constitutive equations. Therefore, agreement between the EIT formulation and the two-fluid Langevin equations demonstrates the thermodynamic consistency of the EIT formulation. Extension of this analysis to include normal stresses is also considered.

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Bautista F, Soltero JFA, Pérez-López JH, Puig JE, Manero O (2000) On the shear banding flow of elongated micellar solutions. J Non-Newtonian Fluid Mech 94:57–66. https://doi.org/10.1016/S0377-0257(00)00128-2CrossRef

Bautista F, Soltero JFA, Macías ER, Puig JE, Manero O (2002) Irreversible thermodynamics approach and modeling of shear banding flow of wormlike micelles. J Phys Chem B 106:13018–13026. https://doi.org/10.1021/jp0206370CrossRef

Bautista F, Pérez-López JH, García-Sandoval JP, Puig JE, Manero O (2007) Stability analysis of shear banding flow with the BMP model. J Non-Newtonian Fluid Mech 144:160–169. https://doi.org/10.1016/j.jnnfm.2007.04.001CrossRef

Bautista F, Muñoz M, Castillo-Tejas J, Pérez-López JH, Puig JE, Manero O (2009) Critical phenomenon analysis of shear banding flow in polymer-like micellar solutions.1. Theoretical approach. J Phys Chem B 113:16101–16109. https://doi.org/10.1021/jp906310kCrossRef

Bautista F, Fernández V, Macías ER, Pérez-López JH, Escalante JI, Puig JE, Manero O (2012) Experimental evidence of the critical phenomenon of shear banding flow in polymer-like micellar solutions. J Non-Newtonian Fluid Mech 177:89–96. https://doi.org/10.1016/j.jnnfm.2012.03.006CrossRef

Brochard F, de Gennes P-G(1977) Dynamical scaling of polymers in theta solvents. Macromolecules 10:1157–1161. https://doi.org/10.1021/ma60059a048CrossRef

Cromer M, Villet MC, Fredrickson GH, Leal LG, Stepanyan R, Bulters MJH (2013) Concentration fluctuations in polymer solution under extensional flow. J Rheol 57:1211–1235. https://doi.org/10.1122/1.4808411CrossRef

de Gennes PG (1976a) Dynamics of entangled polymer solutions I The Rouse model. Macromolecules 1976(9):587–593. https://doi.org/10.1021/ma60052a011CrossRef

de Gennes PG (1976b) Dynamics of entangled polymer solutions II Inclusion of hydrodynamic interactions. Macromolecules 9:594–598. https://doi.org/10.1021/ma60052a012CrossRef

Doi M, Onuki A (1992) Dynamic coupling between stress and composition in polymer solutions and blends. J Phys II France 2:1631–1656. https://doi.org/10.1051/jp2:1992225CrossRef

Fierro C, Medina-Torres L, Bautista F, Herrera-Valencia EE, Calderas Manero O (2021) The structure factor in flowing worm-like micellar solutions. J Non-Newtonian Fluid Mech 289(17):104469. https://doi.org/10.1016/j.jnnfm.2020.104469CrossRef

García-Sandoval JP, Bautista F, Puig JE, Manero O (2019) Inhomogeneous flow of wormlike micelles: predictions of the generalized BMP model with normal stresses. Fluids 4:45. https://doi.org/10.3390/fluids4010045CrossRef

García-Sandoval JP, Bautista F, Puig JE, Manero O (2012) Inhomogeneous flow and shear banding formation in micellar solutions: predictions of the BMP model. J Non-Newtonian Fluid Mech 179-180:43–54. https://doi.org/10.1016/j.jnnfm.2012.05.006CrossRef

García-Sandoval JP, Bautista F, Puig JE, Manero O (2017) The interface migration in shear banded micellar solutions. Rheol Acta 56:765–778. https://doi.org/10.1007/s00397-017-1031-2CrossRef

Helfand E, Fredrickson HG (1989) Large fluctuations in polymer solutions under shear. Phys Rev Lett 62:2468–2471. https://doi.org/10.1103/PhysRevLett.62.2468CrossRef

Ji H, Helfand E (1995) Concentration fluctuations in sheared polymer solutions. Macromolecules 28:3869–3880. https://doi.org/10.1021/ma00115a017CrossRef

Jou D, Camacho J, Grmela M (1991) On the non-equilibrium thermodynamics of non-Fickian diffusion. Macromolecules 24:3597–3602. https://doi.org/10.1021/ma00012a021CrossRef

Jou D, Casas-Vázquez J, Lebon G (2010) Extended irreversible thermodynamics. 4th Ed. Berlin: Springer

Jou D, Casas Vázquez J, Criado-Sancho M (2011) Thermodynamics of fluids under flow. 2nd Ed. Berlin: Springer

Lai J, Fuller GG (1994) Structure and dynamics of concentration fluctuations in a polymer blend solution under shear flow. J Polym Sci B Polym Phys 32:2461–2474. https://doi.org/10.1002/polb.1994.090321503CrossRef

Manero O, Bautista F, Soltero JFA, Puig JE (2002) Dynamics of worm-like micelles: the Cox-merz rule. J Non-Newtonian Fluid Mech 106(1):1–15. https://doi.org/10.1016/S0377-0257(02)00082-4CrossRef

Manero O, Perez-López JH, Puig JE, Bautista F (2007) A thermodynamic approach to rheology of complex fluids: the generalized BMP model. J Non-Newtonian Fluid Mech 146:22–29. https://doi.org/10.1016/j.jnnfm.2007.02.012CrossRef

Milner ST (1993) Dynamical theory of concentration fluctuations in polymer solutions under shear. Phys Rev E 48:3674–3691. https://doi.org/10.1103/PhysRevE.48.3674CrossRef

Onuki A (1989) Elastic effects in the phase transition of polymer solutions under shear flow. Phys Rev Lett 62:2472–2475. https://doi.org/10.1103/PhysRevLett.62.2472CrossRef

Onuki A (1990) Dynamic equations of polymers with deformations in semidilute regions. J Phys Soc Jpn 59:3423–3426. https://doi.org/10.1143/JPSJ.59.3423CrossRef

Onuki A (1997) Phase transitions of fluids in shear flow. J Phys Condens Matter 9:6119–6157. https://doi.org/10.1088/0953-8984/9/29/001CrossRef

Öttinger HC, Grmela M (1997) Dynamics and thermodynamics of complex fluids. II. Illustrations of a general formalism. Phys Rev E 56:6633–6655CrossRef

Saito S, Takenaka M, Toyoda N, HashimotoT (2001) Structure factor of semidilute polymer solution under continuous shear flow: numerical analysis of a two-fluid model and comparison with experiments. Macromolecules 34:6461–6473. https://doi.org/10.1021/ma0021390CrossRef

Title: Compatibility of the generalized BMP model and the two-fluid Langevin formulations
Authors: C. Fierro
F. Bautista
J. P. García-Sandoval
E. Hernández
J. E. Puig
O. Manero
Publication date: 08-10-2021
Publisher: Springer Berlin Heidelberg
Published in: Rheologica Acta / Issue 12/2021
Print ISSN: 0035-4511
Electronic ISSN: 1435-1528
DOI: https://doi.org/10.1007/s00397-021-01290-4

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