A constitutive model for sheared dense fiber suspensions
Abstract
We propose a constitutive model to predict the viscosity of fiber suspensions, which undergoes shear thinning, at various volume fractions, aspect ratios, and shear stresses/rates. We calibrate the model using the data from direct numerical simulation and prove the accuracy by predicting experimental measurements from the literature. We use a friction coefficient decreasing with the normal load between the fibers to quantitatively reproduce the experimentally observed shear thinning in fiber suspensions. In this model, the effective normal contact force, which is directly proportional to the bulk shear stress, determines the effective friction coefficient. A rise in the shear stress reduces the effective friction coefficient in the suspension. As a result, the jamming volume fraction increases with the shear stress, resulting in a shear thinning in the suspension viscosity. Moreover, we extend the model to quantify the effects of fiber volume fraction and aspect ratio in the suspension. We calibrate this model using the data from numerical simulations for the rate-controlled shear flow. Once calibrated, we show that the model can be used to predict the relative viscosity for different volume fractions, shear stresses, and aspect ratios. The model predictions are in excellent agreement with the available experimental measurements from themore »
- Authors:
-
[1];
[2];
[1]
- Purdue Univ., West Lafayette, IN (United States)
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
- Publication Date:
- Research Org.:
- Purdue Univ., West Lafayette, IN (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 2283541
- Alternate Identifier(s):
- OSTI ID: 1914365
- Grant/Contract Number:
- EE0008910
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physics of Fluids
- Additional Journal Information:
- Journal Volume: 35; Journal Issue: 1; Journal ID: ISSN 1070-6631
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; friction; fiber suspension; computer simulation; computational fluid dynamics; fluid flows; rheology and fluid dynamics; rheological properties; shear thinning
Citation Formats
Khan, Monsurul, More, Rishabh V., and Ardekani, Arezoo M. A constitutive model for sheared dense fiber suspensions. United States: N. p., 2023.
Web. doi:10.1063/5.0134728.
Khan, Monsurul, More, Rishabh V., & Ardekani, Arezoo M. A constitutive model for sheared dense fiber suspensions. United States. https://doi.org/10.1063/5.0134728
Khan, Monsurul, More, Rishabh V., and Ardekani, Arezoo M. Mon .
"A constitutive model for sheared dense fiber suspensions". United States. https://doi.org/10.1063/5.0134728. https://www.osti.gov/servlets/purl/2283541.
@article{osti_2283541,
title = {A constitutive model for sheared dense fiber suspensions},
author = {Khan, Monsurul and More, Rishabh V. and Ardekani, Arezoo M.},
abstractNote = {We propose a constitutive model to predict the viscosity of fiber suspensions, which undergoes shear thinning, at various volume fractions, aspect ratios, and shear stresses/rates. We calibrate the model using the data from direct numerical simulation and prove the accuracy by predicting experimental measurements from the literature. We use a friction coefficient decreasing with the normal load between the fibers to quantitatively reproduce the experimentally observed shear thinning in fiber suspensions. In this model, the effective normal contact force, which is directly proportional to the bulk shear stress, determines the effective friction coefficient. A rise in the shear stress reduces the effective friction coefficient in the suspension. As a result, the jamming volume fraction increases with the shear stress, resulting in a shear thinning in the suspension viscosity. Moreover, we extend the model to quantify the effects of fiber volume fraction and aspect ratio in the suspension. We calibrate this model using the data from numerical simulations for the rate-controlled shear flow. Once calibrated, we show that the model can be used to predict the relative viscosity for different volume fractions, shear stresses, and aspect ratios. The model predictions are in excellent agreement with the available experimental measurements from the literature. The findings of this study can potentially be used to tune the fiber size and volume fraction for designing the suspension rheology in various applications.},
doi = {10.1063/5.0134728},
journal = {Physics of Fluids},
number = 1,
volume = 35,
place = {United States},
year = {Mon Jan 23 00:00:00 EST 2023},
month = {Mon Jan 23 00:00:00 EST 2023}
}
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Works referenced in this record:
Elastic–plastic spherical contact under combined normal and tangential loading in full stick
journal, November 2006
- Brizmer, V.; Kligerman, Y.; Etsion, I.
- Tribology Letters, Vol. 25, Issue 1
Study of semidilute fibre suspension rheology with lattice-Boltzmann method
journal, September 2013
- Salahuddin, Asif; Wu, Jingshu; Aidun, C. K.
- Rheologica Acta, Vol. 52, Issue 10-12
Rheological behavior of fiber-filled model suspensions: Effect of fiber flexibility
journal, May 2009
- Keshtkar, M.; Heuzey, M. C.; Carreau, P. J.
- Journal of Rheology, Vol. 53, Issue 3
Rheology of concentrated suspensions of non-colloidal rigid fibres
journal, August 2017
- Tapia, Franco; Shaikh, Saif; Butler, Jason E.
- Journal of Fluid Mechanics, Vol. 827
Rheology of non-Brownian rigid fiber suspensions with adhesive contacts
journal, March 2001
- Chaouche, Mohend; Koch, Donald L.
- Journal of Rheology, Vol. 45, Issue 2
Random packings of spheres and spherocylinders simulated by mechanical contraction
journal, May 2003
- Williams, S. R.; Philipse, A. P.
- Physical Review E, Vol. 67, Issue 5
The viscosity-volume fraction relation for suspensions of rod-like particles by falling-ball rheometry
journal, May 1989
- Milliken, William J.; Gottlieb, Moshe; Graham, Alan L.
- Journal of Fluid Mechanics, Vol. 202
The flow behavior of fiber suspensions in Newtonian fluids and polymer solutions.
journal, March 1986
- Goto, S.; Nagazono, H.; Kato, H.
- Rheologica Acta, Vol. 25, Issue 2
An objective model for slow orientation kinetics in concentrated fiber suspensions: Theory and rheological evidence
journal, September 2008
- Wang, Jin; O’Gara, John F.; Tucker, Charles L.
- Journal of Rheology, Vol. 52, Issue 5
Simulation of flexible filaments in a uniform flow by the immersed boundary method
journal, October 2007
- Huang, Wei-Xi; Shin, Soo Jai; Sung, Hyung Jin
- Journal of Computational Physics, Vol. 226, Issue 2
Simulation of semidilute suspensions of non-Brownian fibers in shear flow
journal, January 2008
- Lindström, Stefan B.; Uesaka, Tetsu
- The Journal of Chemical Physics, Vol. 128, Issue 2
Observations of fibre orientation in simple shear flow of semi-dilute suspensions
journal, May 1992
- Stover, Carl A.; Koch, Donald L.; Cohen, Claude
- Journal of Fluid Mechanics, Vol. 238
Apparent yield stress in rigid fibre suspensions: the role of attractive colloidal interactions
journal, August 2016
- Bounoua, S.; Lemaire, E.; Férec, J.
- Journal of Fluid Mechanics, Vol. 802
Using transient shear rheology to determine material parameters in fiber suspension theory
journal, May 2009
- Eberle, Aaron P. R.; Baird, Donald G.; Wapperom, Peter
- Journal of Rheology, Vol. 53, Issue 3
The rheology of suspensions of vinylon fibers in polymer liquids. I. Suspensions in silicone oil
journal, July 1981
- Kitano, T.; Kataoka, T.
- Rheologica Acta, Vol. 20, Issue 4
Constitutive equations for a nondilute dispersed fiber suspension
journal, January 1990
- Babkin, V. A.
- Fluid Dynamics, Vol. 24, Issue 6
A Constitutive Relation for the Viscous Flow of an Oriented Fiber Assembly
journal, September 1991
- Pipes, R. Byron; Hearle, J. W. S.; Beaussart, A. J.
- Journal of Composite Materials, Vol. 25, Issue 9
Normal stress differences in suspensions of rigid fibres
journal, October 2014
- Snook, Braden; Davidson, Levi M.; Butler, Jason E.
- Journal of Fluid Mechanics, Vol. 758
Dynamics of Flexible Fibers in Viscous Flows and Fluids
journal, January 2019
- du Roure, Olivia; Lindner, Anke; Nazockdast, Ehssan N.
- Annual Review of Fluid Mechanics, Vol. 51, Issue 1
Rheology of sheared suspensions of rough frictional particles
journal, September 2014
- Gallier, Stany; Lemaire, Elisabeth; Peters, François
- Journal of Fluid Mechanics, Vol. 757
Tensile stress contribution of flow-oriented slender particles in non-newtonian fluids
journal, January 1976
- Goddard, J. D.
- Journal of Non-Newtonian Fluid Mechanics, Vol. 1, Issue 1
A numerical study of the effect of fibre stiffness on the rheology of sheared flexible fibre suspensions
journal, September 2010
- Wu, Jingshu; Aidun, Cyrus K.
- Journal of Fluid Mechanics, Vol. 662
Flow patterns around heart valves: A numerical method
journal, October 1972
- Peskin, Charles S.
- Journal of Computational Physics, Vol. 10, Issue 2
The rheology of fibre suspensions
journal, November 1999
- Petrie, Christopher J. S.
- Journal of Non-Newtonian Fluid Mechanics, Vol. 87, Issue 2-3
Rheological properties of short fiber model suspensions
journal, September 2004
- Sepehr, M.; Carreau, P. J.; Moan, M.
- Journal of Rheology, Vol. 48, Issue 5
Simulations of sheared dense noncolloidal suspensions: Evaluation of the role of long-range hydrodynamics
journal, April 2018
- Gallier, Stany; Peters, François; Lobry, Laurent
- Physical Review Fluids, Vol. 3, Issue 4
Effect of roughness on the rheology of concentrated non-Brownian suspensions: A numerical study
journal, January 2020
- More, Rishabh V.; Ardekani, Arezoo M.
- Journal of Rheology, Vol. 64, Issue 1
The flow of a model suspension fluid past a sphere
journal, March 1991
- Phan-Thien, N.; Zheng, R.; Graham, A. L.
- Journal of Statistical Physics, Vol. 62, Issue 5-6
Discontinuous Shear Thickening without Inertia in Dense Non-Brownian Suspensions
journal, March 2014
- Wyart, M.; Cates, M. E.
- Physical Review Letters, Vol. 112, Issue 9
A rheological constitutive model for semiconcentrated rod suspensions in Bingham fluids
journal, July 2017
- Férec, J.; Bertevas, E.; Khoo, B. C.
- Physics of Fluids, Vol. 29, Issue 7
A novel approach to analyze beam-like composite structures using mechanics of structure genome
journal, October 2016
- Liu, Xin; Yu, Wenbin
- Advances in Engineering Software, Vol. 100
Rheology of sheared flexible fiber suspensions via fiber-level simulations
journal, May 2003
- Switzer, Leonard H.; Klingenberg, Daniel J.
- Journal of Rheology, Vol. 47, Issue 3
A constitutive model for sheared dense suspensions of rough particles
journal, September 2020
- More, R. V.; Ardekani, A. M.
- Journal of Rheology, Vol. 64, Issue 5
The PELskin project: part IV—control of bluff body wakes using hairy filaments
journal, September 2016
- Pinelli, Alfredo; Omidyeganeh, Mohammad; Brücker, Christoph
- Meccanica, Vol. 52, Issue 7
Lightweight aggregate concrete fiber reinforcement – A review
journal, December 2012
- Hassanpour, Mahmoud; Shafigh, Payam; Mahmud, Hilmi Bin
- Construction and Building Materials, Vol. 37
A constitutive model for simple shear of dense frictional suspensions
journal, March 2018
- Singh, Abhinendra; Mari, Romain; Denn, Morton M.
- Journal of Rheology, Vol. 62, Issue 2
Orientation Behavior of Fibers in Concentrated Suspensions
journal, April 1984
- Folgar, Fransisco; Tucker, Charles L.
- Journal of Reinforced Plastics and Composites, Vol. 3, Issue 2
Constitutive equations in suspension mechanics. Part 1. General formulation
journal, October 1975
- Hinch, E. J.; Leal, L. G.
- Journal of Fluid Mechanics, Vol. 71, Issue 3
Normal stress differences in non-Brownian fiber suspensions
journal, July 2016
- Bounoua, Sihem; Kuzhir, Pavel; Lemaire, Elisabeth
- Journal of Rheology, Vol. 60, Issue 4
Unifying disparate rate-dependent rheological regimes in non-Brownian suspensions
journal, June 2021
- More, R. V.; Ardekani, A. M.
- Physical Review E, Vol. 103, Issue 6
Time-dependent shear flows of a suspension of particles with weak Brownian rotations
journal, March 1973
- Hinch, E. J.; Leal, L. G.
- Journal of Fluid Mechanics, Vol. 57, Issue 4
Rheology of dense fiber suspensions: Origin of yield stress, shear thinning, and normal stress differences
journal, June 2023
- Khan, Monsurul; More, Rishabh V.; Brandt, Luca
- Physical Review Fluids, Vol. 8, Issue 6
A new constitutive model for fibre suspensions: flow past a sphere
journal, January 1991
- Phan-Thien, N.; Graham, A. L.
- Rheologica Acta, Vol. 30, Issue 1
Anisotropic Viscosities of an Oriented Fiber Composite with a Power-Law Matrix
journal, October 1992
- Pipes, R. Byron
- Journal of Composite Materials, Vol. 26, Issue 10
An experimental determination of the stress–microstructure relationship in semi-concentrated fiber suspensions
journal, December 2000
- Petrich, Michael P.; Koch, Donald L.; Cohen, Claude
- Journal of Non-Newtonian Fluid Mechanics, Vol. 95, Issue 2-3
A numerical simulation of short fiber orientation in compression molding
journal, June 1990
- Advani, Suresh G.; Tucker, Charles L.
- Polymer Composites, Vol. 11, Issue 3
Shear-thinning in concentrated rigid fiber suspensions: Aggregation induced by adhesive interactions
journal, November 2016
- Bounoua, S.; Lemaire, E.; Férec, J.
- Journal of Rheology, Vol. 60, Issue 6
Non-Newtonian Constitutive Relationships for Hyperconcentrated Fiber Suspensions
journal, February 1994
- Pipes, R. Byron; Coffin, Douglas W.; Shuler, Stephen F.
- Journal of Composite Materials, Vol. 28, Issue 4
The stress generated in a non-dilute suspension of elongated particles by pure straining motion
journal, April 1971
- Batchelor, G. K.
- Journal of Fluid Mechanics, Vol. 46, Issue 4
Rheology measurements of a biomass slurry: an inter-laboratory study
journal, September 2009
- Stickel, Jonathan J.; Knutsen, Jeffrey S.; Liberatore, Matthew W.
- Rheologica Acta, Vol. 48, Issue 9
Microscopic Mechanism for Shear Thickening of Non-Brownian Suspensions
journal, September 2013
- Fernandez, Nicolas; Mani, Roman; Rinaldi, David
- Physical Review Letters, Vol. 111, Issue 10
Constitutive equations in suspension mechanics. Part 2. Approximate forms for a suspension of rigid particles affected by Brownian rotations
journal, July 1976
- Hinch, E. J.; Leal, L. G.
- Journal of Fluid Mechanics, Vol. 76, Issue 1
A Rheological Equation of State for Semiconcentrated Fiber Suspensions
journal, June 1984
- Dinh, Steven M.; Armstrong, Robert C.
- Journal of Rheology, Vol. 28, Issue 3
Roughness induced shear thickening in frictional non-Brownian suspensions: A numerical study
journal, March 2020
- More, R. V.; Ardekani, A. M.
- Journal of Rheology, Vol. 64, Issue 2
Elasto-viskose Flüssigkeiten, für die in stationären Schichtströmungen sämtliche Normalspannungskomponenten verschieden groß sind
journal, March 1962
- Giesekus, Hanswalter
- Rheologica Acta, Vol. 2, Issue 1
Settling behavior of spherical particles in fiber-containing drilling fluids
journal, April 2012
- Elgaddafi, Rida; Ahmed, Ramadan; George, Matthew
- Journal of Petroleum Science and Engineering, Vol. 84-85
Shear thinning in non-Brownian suspensions explained by variable friction between particles
journal, December 2018
- Lobry, Laurent; Lemaire, Elisabeth; Blanc, Frédéric
- Journal of Fluid Mechanics, Vol. 860
The hydrodynamic stress in a suspension of rods
journal, January 1990
- Shaqfeh, Eric S. G.; Fredrickson, Glenn H.
- Physics of Fluids A: Fluid Dynamics, Vol. 2, Issue 1
Shear thickening, frictionless and frictional rheologies in non-Brownian suspensions
journal, November 2014
- Mari, Romain; Seto, Ryohei; Morris, Jeffrey F.
- Journal of Rheology, Vol. 58, Issue 6
Jamming of frictional spheres and random loose packing
journal, January 2010
- Silbert, Leonardo E.
- Soft Matter, Vol. 6, Issue 13
The stress field of slender particles oriented by a non-Newtonian extensional flow
journal, November 1976
- Goddard, J. D.
- Journal of Fluid Mechanics, Vol. 78, Issue 1
Modeling fiber interactions in semiconcentrated fiber suspensions
journal, January 2009
- Férec, J.; Ausias, G.; Heuzey, M. C.
- Journal of Rheology, Vol. 53, Issue 1
The effect of shear-thinning behaviour on rod orientation in filled fluids
journal, June 2016
- Férec, Julien; Bertevas, Erwan; Khoo, Boo Cheong
- Journal of Fluid Mechanics, Vol. 798
Fluid Mechanics of Papermaking
journal, January 2011
- Lundell, Fredrik; Söderberg, L. Daniel; Alfredsson, P. Henrik
- Annual Review of Fluid Mechanics, Vol. 43, Issue 1
Numerical study of filament suspensions at finite inertia
journal, November 2019
- Alizad Banaei, Arash; Rosti, Marco Edoardo; Brandt, Luca
- Journal of Fluid Mechanics, Vol. 882
Simulation of the motion of flexible fibers in viscous fluid flow
journal, November 2007
- Lindström, Stefan B.; Uesaka, Tetsu
- Physics of Fluids, Vol. 19, Issue 11
Structure and properties of sheared fiber suspensions with mechanical contacts
journal, December 1997
- Sundararajakumar, R. R.; Koch, Donald L.
- Journal of Non-Newtonian Fluid Mechanics, Vol. 73, Issue 3
The effect of weak Brownian rotations on particles in shear flow
journal, April 1971
- Leal, L. G.; Hinch, E. J.
- Journal of Fluid Mechanics, Vol. 46, Issue 4