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Mapping thixo-elasto-visco-plastic behavior

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Abstract

A century ago, and more than a decade before the term rheology was formally coined, Bingham introduced the concept of plastic flow above a critical stress to describe steady flow curves observed in English china clay dispersions. However, in many complex fluids and soft solids, the manifestation of a yield stress is also accompanied by other complex rheological phenomena such as thixotropy and viscoelastic transient responses, both above and below the critical stress. In this perspective article, we discuss efforts to map out the different limiting forms of the general rheological response of such materials by considering higher dimensional extensions of the familiar Pipkin map. Based on transient and nonlinear concepts, the maps first help organize the conditions of canonical flow protocols. These conditions can then be normalized with relevant material properties to form dimensionless groups that define a 3D state space to represent the spectrum of thixotropic elastoviscoplastic (TEVP) material responses.

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References

  • Ames N M, Srivastava V, Chester S A, Anand L (2009) A thermo-mechanically coupled theory for large deformations of amorphous polymers. Part II: applications. Int J Plast 25:1495–1539. doi:10.1016/j.ijplas.2008.11.005

  • Ashby M F (1999) Materials selection in mechanical design. Butterworth-Heinemann, Boston, MA

    Google Scholar 

  • Astarita G, Jongschaap R J J (1978) The maximum amplitude of strain for the validity of linear viscoelasticity. J Non-Newtonian Fluid Mech 3:281–287. doi:10.1016/0377-0257(78)87005-0

    Article  Google Scholar 

  • Balmforth N J, Frigaard I A, Ovarlez G (2013) Yielding to stress: recent developments in viscoplastic fluid mechanics. Annu Rev Fluid Mech 46:130819114955006. doi:10.1146/annurev-fluid-010313-141424

    Google Scholar 

  • Barnes H A (1997) Thixotropy—a review. J Non-Newton Fluid Mech 70:1–33. doi:10.1016/S0377-0257(97)00004-9

    Article  Google Scholar 

  • Bharadwaj N A, Ewoldt R H (2014) The general low-frequency prediction for asymptotically-nonlinear material functions in oscillatory shear. J Rheol (NY, NY) 58:891–910. doi:10.1122/1.4874344

    Article  Google Scholar 

  • Bharadwaj N A, Ewoldt R H (2015) Constitutive model fingerprints in medium-amplitude oscillatory shear. J Rheol (NY, NY) 59:557–592. doi:10.1122/1.4903346

    Article  Google Scholar 

  • Bingham E C (1916) An investigation of the laws of plastic flow. In: Bulletin of the bureau of standards. doi:10.6028/bulletin.304, vol 13, No 2. Govt. Print. Off., Washington, pp 309–353

  • Bird R B, Armstrong R C, Hassager O (1987) Dynamics of polymeric liquids: volume 1 fluid mechanics, 2nd edn. Wiley, New York

    Google Scholar 

  • Bird R B, Dai G, Yarusoo B J (1983) The rheology and flow of viscoplastic materials. Rev Chem Eng 1:1–70. doi:10.1515/revce-1983-0102

    Article  Google Scholar 

  • Blackwell B C, Ewoldt R H (2014) A simple thixotropic-viscoelastic constitutive model produces unique signatures in large-amplitude oscillatory shear (LAOS). J Non-Newton Fluid Mech 208:27–41. doi:10.1016/j.jnnfm.2014.03.006

  • Bonn D, Paredes J, Denn M M, Berthier L, Divoux T, Manneville S (2015) Yield stress materials in soft condensed matter. arXiv:1502.05281

  • Boromand A, Jamali S, Maia M (2017) Structural fingerprints of yielding mechanisms in attractive colloidal gels. Soft Matter 13:458–473. doi:10.1039/c6sm00750c

    Article  Google Scholar 

  • Carter K A, Girkin J M, Fielding S M (2016) Shear banding in large amplitude oscillatory shear (LAOStrain and LAOStress) of polymers and wormlike micelles. J Rheol (NY, NY) 60:883–904. doi:10.1122/1.4960512

    Article  Google Scholar 

  • Chung C, Chun J, Um W, Sundaram SK, Westik Jr JH (2013) Setting and stiffening of cementitious components in Cast Stone waste form for disposal of secondary wastes from the Hanford waste treatment and immobilization plant. Cem Concr Res 46:14–22. doi:10.1016/j.cemconres.2013.01.003

    Article  Google Scholar 

  • Coussot P, Tabuteau H, Chateau X, Tocquer L, Ovarlez G (2006) Aging and solid or liquid behavior in pastes. J Rheol (NY, NY) 50:975. doi:10.1122/1.2337259

    Article  Google Scholar 

  • Davis JG (1937) The rheology of cheese, butter and other milk products (the measurement of “body” and “texture”). J Dairy Res 8:245–264. doi:10.1017/S0022029900002090

    Article  Google Scholar 

  • Davis W M, Macosko C W (1978) Nonlinear dynamic mechanical moduli for polycarbonate and PMMA. J Rheol (NY, NY) 22:53–71. doi:10.1122/1.549500

    Article  Google Scholar 

  • Dealy J M (2010) Weissenberg and Deborah numbers—their definition and use. Rheol Bull 79:14–18

    Google Scholar 

  • Dealy J M, Wissbrun K F (1990) Melt rheology and its role in plastics processing: theory and applications. Van Nostrand Reinhold, New York

    Book  Google Scholar 

  • de Souza Mendes P R, Thompson R L (2012) A critical overview of elasto-viscoplastic thixotropic modeling. J Non-Newton Fluid Mech 187–188:8–15. doi:10.1016/j.jnnfm.2012.08.006

  • de Souza Mendes P R, Thompson R L (2013) A unified approach to model elasto-viscoplastic thixotropic yield-stress materials and apparent yield-stress fluids. Rheol Acta 52:673–694. doi:10.1007/s00397-013-0699-1

  • Denn M M, Bonn D (2011) Issues in the flow of yield-stress liquids. Rheol Acta 50:307–315. doi:10.1007/s00397-010-0504-3

    Article  Google Scholar 

  • Dimitriou C J, McKinley G H (2014) A comprehensive constitutive law for waxy crude oil: a thixotropic yield stress fluid. Soft Matter 10:6619–44. doi:10.1039/c4sm00578c

    Article  Google Scholar 

  • Dimitriou C J, Ewoldt R H, McKinley G H (2013) Describing and prescribing the constitutive response of yield stress fluids using large amplitude oscillatory stress (LAOStress). J Rheol (NY, NY) 57:27–70. doi:10.1122/1.3684751

    Article  Google Scholar 

  • Dinkgreve M, Paredes J, Denn MM, Bonn D (2016) On different ways of measuring “the” yield stress. J Non-Newton Fluid Mech. doi:10.1016/j.jnnfm.2016.11.001

  • Dinkgreve M, Bonn D, Denn MM (2017) “Everything flows?”: Elastic effects on start-up flows of yield stress fluids. Rheol Acta. doi:10.1007/s00397-017-0998-z

  • Divoux T, Barentin C, Manneville S (2011) From stress-induced fluidization processes to Herschel-Bulkley behaviour in simple yield stress fluids. Soft Matter 7:8409–8418. doi:10.1039/c1sm05607g

    Article  Google Scholar 

  • Ewoldt R H (2014) Extremely soft: design with rheologically complex fluids. Soft Robot 1:12–20. doi:10.1089/soro.2013.1508

    Article  Google Scholar 

  • Ewoldt R H (2016) Predictions for the northern coast of the shear rheology map: XXLAOS. J Fluid Mech 798:1–4. doi:10.1017/jfm.2016.265

    Article  Google Scholar 

  • Ewoldt R H, Bharadwaj N A (2013) Low-dimensional intrinsic material functions for nonlinear viscoelasticity. Rheol Acta 52:201–219. doi:10.1007/s00397-013-0686-6

    Article  Google Scholar 

  • Ewoldt R H, Clasen C, Hosoi A E, McKinley G H (2007) Rheological fingerprinting of gastropod pedal mucus and synthetic complex fluids for biomimicking adhesive locomotion. Soft Matter 3:634–643. doi:10.1039/b615546d

    Article  Google Scholar 

  • Ewoldt R H, Hosoi A E, McKinley G H (2008) New measures for characterizing nonlinear viscoelasticity in large amplitude oscillatory shear. J Rheol (NY, NY) 52:1427–1458. doi:10.1122/1.2970095

    Article  Google Scholar 

  • Ewoldt R H, Winter P, Maxey J, McKinley G H (2010) Large amplitude oscillatory shear of pseudoplastic and elastoviscoplastic materials. Rheol Acta 49:191–212. doi:10.1007/s00397-009-0403-7

    Article  Google Scholar 

  • Ewoldt R H, Gurnon A K, López-Barrón C, McKinley G H, Swan J, Wagner N J (2012) A report on “LAOS Rheology Day,” held Friday the 13th at the Colburn Laboratory, University of Delaware. Rheol Bull 81:12–19

    Google Scholar 

  • Faber T J, Jaishankar A, McKinley G H (2017) Describing the firmness, springiness and rubberiness of food gels using fractional calculus. Part I: theoretical framework. Food Hydrocoll 62:311–324. doi:10.1016/j.foodhyd.2016.05.041

    Article  Google Scholar 

  • Fielding S M, Sollich P, Cates M E (2000) Aging and rheology in soft materials. J Rheol (NY, NY) 44:323–369. doi:10.1122/1.551088

    Article  Google Scholar 

  • Fraggedakis D, Dimakopoulos Y, Tsamopoulos J (2016a) Yielding the yield stress analysis: a thorough comparison of recently proposed elasto-visco-plastic (EVP) fluid models. J Non-Newton Fluid Mech 236:104–122. doi:10.1016/j.jnnfm.2016.09.001

  • Fraggedakis D, Dimakopoulos Y, Tsamopoulos J (2016b) Yielding the yield-stress analysis: a study focused on the effects of elasticity on the settling of a single spherical particle in simple yield-stress fluids. Soft Matter 12:5378–5401. doi:10.1039/C6SM00480F

  • Galindo-Rosales F J, Alves M A, Oliveira M S N (2013) Microdevices for extensional rheometry of low viscosity elastic liquids: a review. Microfluid Nanofluidics 14:1–19. doi:10.1007/s10404-012-1028-1

    Article  Google Scholar 

  • Geri M, McKinley GH, Venkatesan R, Sambath K (2017) Thermo-kinematic memory and the thixotropic elasto-visco-plasticity of waxy crude oils. J Rheol (NY, NY) 61(2). (in press)

  • Giacomin A J, Bird R B, Johnson L M, Mix A W (2011) Large-amplitude oscillatory shear flow from the corotational Maxwell model. J Non-Newton Fluid Mech 166:1081–1099. doi:10.1016/j.jnnfm.2011.04.002

    Article  Google Scholar 

  • Goodeve C F, Whitfield G W (1938) The measurement of thixotropy in absolute units. Trans Faraday Soc 34:511–520. doi:10.1039/TF9383400511

    Article  Google Scholar 

  • Hoyle D M, Fielding S M (2015) Age-dependent modes of extensional necking instability in soft glassy materials. Phys Rev Lett 114:158301. doi:10.1103/PhysRevLett.114.158301

    Article  Google Scholar 

  • Hyun K, Wilhelm M, Klein C O, Cho K S, Nam J G, Ahn K H, Lee S L J, Ewoldt R H, McKinley G H (2011) A review of nonlinear oscillatory shear tests: analysis and application of large amplitude oscillatory shear (LAOS). Prog Polym Sci 36:1697–1753. doi:10.1016/j.progpolymsci.2011.02.002

    Article  Google Scholar 

  • Jamali S, McKinley G H, Armstrong R C (2017) Microstructural rearrangements and their rheological implications in a model thixotropic elastoviscoplastic fluid. Phys Rev Lett 118:48003. doi:10.1103/PhysRevLett.118.048003

    Article  Google Scholar 

  • Khair A S (2016a) On a suspension of nearly spherical colloidal particles under large-amplitude oscillatory shear flow. J Fluid Mech 791:R5. doi:10.1017/jfm.2016.77

  • Khair A S (2016b) Large amplitude oscillatory shear of the Giesekus model. J Rheol (NY, NY) 60:257–266. doi:10.1122/1.4941423

  • Larson R G (2015) Constitutive equations for thixotropic fluids. J Rheol (NY, NY) 59:595–611. doi:10.1122/1.4913584

    Article  Google Scholar 

  • Macosko C W (1994) Rheology: principles, measurements and applications. Wiley-VCH, New York

    Google Scholar 

  • Maki K L, Renardy Y (2010) The dynamics of a simple model for a thixotropic yield stress fluid. J Non-Newton Fluid Mech 165:1373–1385. doi:10.1016/j.jnnfm.2010.07.002

    Article  Google Scholar 

  • McKinley G H (2005) Visco-elasto-capillary thinning and break-up of complex fluids. In: Binding D M, Walters K (eds) Annual rheology reviews. British Society of Rheology, pp 1–48

  • Mewis J, Wagner N J (2009) Thixotropy. Adv Colloid Interface Sci 147–148:214–27. doi:10.1016/j.cis.2008.09.005

  • Mitsoulis E, Tsamopoulos JA (2017) Numerical simulations of complex yield-stress fluid flows. Rheol Acta. doi:10.1007/s00397-016-0981-0

  • Mohraz A, Solomon M J (2005) Orientation and rupture of fractal colloidal gels during start-up of steady shear flow. J Rheol (NY, NY) 49:657–681. doi:10.1122/1.1895799

    Article  Google Scholar 

  • Møller P, Fall A, Chikkadi V, Derks D, Bonn D (2009) An attempt to categorize yield stress fluid behaviour. Philos Trans A Math Phys Eng Sci 367:5139–55. doi:10.1098/rsta.2009.0194

    Article  Google Scholar 

  • Moore F (1959) The rheology of ceramic slips and bodies. Trans Br Ceram Soc 58:470–494

    Google Scholar 

  • Mours M, Winter H H (1994) Time-resolved rheometry. Rheol Acta 33:385–397. doi:10.1007/BF00366581

    Article  Google Scholar 

  • Nelson AZ (2015) Extending yield-stress fluid paradigms. MS Thesis, Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign

  • Osswald T A, Rudolph N (2015) Polymer rheology: fundamentals and applications. Hanser Publications, Cincinnati

    Google Scholar 

  • Papanastasiou T C (1987) Flows of materials with yield. J Rheol (NY, NY) 31:385–404. doi:10.1122/1.549926

    Article  Google Scholar 

  • Pipkin A C (1972) Lectures on viscoelasticity theory. Springer, New York. doi:10.1007/978-1-4612-1078-8

    Book  Google Scholar 

  • Poumaere A, Moyers-González M, Castelain C, Burghelea T (2014) Unsteady laminar flows of a Carbopol gel in the presence of wall slip. J Non-Newton Fluid Mech 205:28–40. doi:10.1016/j.jnnfm.2014.01.003

    Article  Google Scholar 

  • Reimers M J, Dealy J M (1996) Sliding plate rheometer studies of concentrated polystyrene solutions: large amplitude oscillatory shear of a very high molecular weight polymer in diethyl phthalate. J Rheol (NY, NY) 40:167–186. doi:10.1122/1.550738

    Article  Google Scholar 

  • Reimers M J, Dealy J M (1998) Sliding plate rheometer studies of concentrated polystyrene solutions: nonlinear viscoelasticity and wall slip of two high molecular weight polymers in tricresyl phosphate. J Rheol (NY, NY) 42:527–548. doi:10.1122/1.550958

    Article  Google Scholar 

  • Reiner M (1971) Advanced Rheology. H. K. Lewis, London

    Google Scholar 

  • Reiner M, Scott Blair G W (1967) Chapter 9 - rheological terminology. In: Eirich F R (ed) Rheology. doi:10.1016/B978-1-4832-2941-6.50015-5, vol 4. Academic Press, New York, pp 461–488

  • Renardy M (2010) The mathematics of myth: yield stress behavior as a limit of non-monotone constitutive theories. J Non-Newton Fluid Mech 165:519–521. doi:10.1016/j.jnnfm.2010.02.010

    Article  Google Scholar 

  • Renardy M, Renardy Y (2016) Thixotropy in yield stress fluids as a limit of viscoelasticity. IMA J Appl Math 81:522–537. doi:10.1093/imamat/hxw031

    Article  Google Scholar 

  • Rogers S A (2012) A sequence of physical processes determined and quantified in LAOS: An instantaneous local 2D/3D approach. J Rheol (NY, NY) 6:1129–1151. doi:10.1122/1.4726083

    Article  Google Scholar 

  • Saramito P (2009) A new elastoviscoplastic model based on the Herschel-Bulkley viscoplastic model. J Non-Newton Fluid Mech 158:154–161. doi:10.1016/j.jnnfm.2008.12.001

    Article  Google Scholar 

  • Saramito P, Wachs A (2017) Progress in numerical simulation of yield stress fluid flows. Rheol Acta. doi:10.1007/s00397-016-0985-9

  • Swan J W, Zia R N, Brady J F (2014) Large amplitude oscillatory microrheology. J Rheol (NY, NY) 58:1. doi:10.1122/1.4826939

    Article  Google Scholar 

  • Thurston G B, Pope G A (1981) Shear rate dependence of the viscoelasticity of polymer-solutions. 2. Xanthan gum. J Non-Newton Fluid Mech 9:69–78

    Article  Google Scholar 

  • Tracey E M, Smith P A, Morrey E V (1996) Rheology of concentrated, heterogeneous slurries containing >1M electrolyte—a case study in nuclear waste suspensions. J Nucl Mater 230:19–35. doi:10.1016/0022-3115(96)00025-6

    Article  Google Scholar 

  • Wagner M H, Rolón-Garrido V H, Hyun K, Wilhelm M (2011) Analysis of medium amplitude oscillatory shear data of entangled linear and model comb polymers. J Rheol (NY, NY) 55:495–516. doi:10.1122/1.3553031

    Article  Google Scholar 

  • Weber E, Moyers-González M, Burghelea T I (2012) Thermorheological properties of a Carbopol gel under shear. J Non-Newton Fluid Mech 183–184:14–24. doi:10.1016/j.jnnfm.2012.07.005

    Article  Google Scholar 

  • Zhou Y, Schroeder C M (2016) Transient and average unsteady dynamics of single polymers in large-amplitude oscillatory extension. Macromolecules 49:8018–8030. doi:10.1021/acs.macromol.6b01606

    Article  Google Scholar 

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Acknowledgements

R.H.E. acknowledges Ms. Rebecca E. Corman, Mr. Brendan C. Blackwell, Dr. N. Ashwin K. Bharadwaj, Prof. Simon A. Rogers, and Mr. Victor Cortez for fruitful discussions, and support from the National Science Foundation under grant no. CBET-1351342. G.H.M. acknowledges stimulating discussions with Dr. C. Dimitriou, Ms. M. Geri, Ms. S. Shahsavari, and Dr. S. Jamali, plus support from the Chevron-MIT University Partnership and the Chevron Flow Assurance group. Both authors would also like to thank the organizers and participants at the workshop “Viscoplastic Fluids: From Theory to Application VI” in Banff, Canada, October 2015, where many of these ideas first began to gel.

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  1. Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    Randy H. Ewoldt

  2. Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Gareth H. McKinley

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  1. Randy H. Ewoldt
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  2. Gareth H. McKinley
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Correspondence to Randy H. Ewoldt or Gareth H. McKinley.

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Special Issue to celebrate the centennial anniversary of the seminal Bingham paper.

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Ewoldt, R.H., McKinley, G.H. Mapping thixo-elasto-visco-plastic behavior. Rheol Acta 56, 195–210 (2017). https://doi.org/10.1007/s00397-017-1001-8

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