Abstract
A filament-stretching rheometer is used to measure the extensional viscosity of a shear-thickening suspension of cornstarch in water. The experiments are performed at a concentration of 55 wt.%. The shear rheology of these suspensions demonstrates a strong shear-thickening behavior. The extensional rheology of the suspensions demonstrates a Newtonian response at low extension rates. At moderate strain rates, the fluid strain hardens. The speed of the strain hardening and the extensional viscosity achieved increase quickly with increasing extension rate. Above a critical extension rate, the extensional viscosity goes through a maximum and the fluid filaments fail through a brittle fracture at a constant tensile stress. The glassy response of the suspension is likely the result of jamming of particles or clusters of particles at these high extension rates. This same mechanism is responsible for the shear thickening of these suspensions. In capillary breakup extensional rheometry, measurement of these suspensions demonstrates a divergence in the extensional viscosity as the fluid stops draining after a modest strain is accumulated.
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Anna SL, McKinley GH (2001) Elasto-capillary thinning and breakup of model elastic liquids. J Rheol 45:115–138
Anna SL, McKinley GH, Nguyen DA, Sridhar T, Muller SJ, Huang J, James DF (2001) An inter-laboratory comparison of measurements from filament stretching rheometers using common test fluids. J Rheol 45:83–114
Bach A, Almdal K, Rasmussen HK, Hassager O (2003) Elongational viscosity of narrow molar mass distribution polystyrene. Macromolecules 36:5174–5179
Barnes HA (1989) Shear-thickening in suspensions of nonaggregrating solid particles dispersed in Newtonian liquids. J Rheol 33:329–366
Batchelor GK (1971) The stress generated in a non-dilute suspension of elongated particles by pure straining motion. J Fluid Mech 46:813–829
Bazilevsky AV, Entov VM, Rozhkov AN (1990) Liquid filament microrheometer and some of its applications. Proceedings of the Third European Rheology Conference, Edinburgh
Bender J, Wagner NJ (1996) Reversible shear thickening in monodisperse and bidisperse colloidal dispersions. J Rheol 40:899–916
Bossis G, Brady JF (1984) Dynamic simulation of sheared suspensions. 1. General method. J Chem Phys 80:5141–5154
Bossis G, Brady JF (1989) The rheology of Brownian suspensions. J Chem Phys 91:1866–1874
Cates ME, Wittmer JP, Bouchaud JP, Claudin P (1998) Jamming, force chains, and fragile matter. Phys Rev Lett 81:1841–1844
Catherall AA, Melrose JR, Ball RC (2000) Shear thickening and order-disorder effects in concentrated colloids at high shear rates. J Rheol 44:1–25
Chellamuthu M, Arndt EM, Rothstein JP (2009) Extensional rheology of shear-thickening nanoparticle suspensions. Soft Matter 5:2117–2124
Chen S, Rothstein JP (2004) Flow of a wormlike micelle solution past a falling sphere. J Non-Newton Fluid Mech 116:205–234
Clasen C, Plog JP, Kulicke WM, Owens M, Macosko C, Scriven LE, Verani M, McKinley GH (2006) How dilute are dilute solutions in extensional flows? J Rheol 50:849–881
Enstein A (1906) Eine neue Bestimmung der Moleküldimensionen. Ann Phys 19:289–306
Einstein A (1911) Berichtigung zu meiner Arbeit: Eine neue Bestimmung der Moleküldimensionen. Ann Phys 34:591–592
Entov VM, Hinch EJ (1997) Effect of a spectrum of relaxation times on the capillary thinning of a filament of elastic liquid. J Non-Newton Fluid Mech 72:31–53
Fagan ME, Zukoski CF (1997) The rheology of charge stabilized silica suspensions. J Rheol 41:373–397
Fall A, Huang N, Bertrand F, Ovarlez G, Bonn D (2008) Shear thickening of cornstarch suspensions as a reentrant jamming transition. Phys Rev Lett 100:018301
Farr RS, Melrose JR, Ball RC (1997) Kinetic theory of jamming in hard-sphere startup flows. Phys Rev E 55:7203–7211
Férec J, Heuzey M-C, Pérez-González J, Vargas Ld, Ausias G, Carreau PJ (2009) Investigation of the rheological properties of short glass fiber-filled polypropylene in extensional flow. Rheol Acta 48:59–72
Happel J, Brenner H (1965) Low Reynolds number hydrodynamics. Prentice-Hall, Englewood Cliffs
Helber R, Doncker F, Bung R (1990) Vibration attenuation by passive stiffness switching mounts. J Sound Vib 138:47–57
Hoffman RL (1972) Discontinuous and dilatant viscosity behavior in concentrated suspensions. I. Observation of a flow instability. J Rheol 16:155–173
Hoffman RL (1974) Discontinuous and dilatant viscosity behavior in concentrated suspensions. II. Theory and experimental tests. J Colloid Interface Sci 46:491–506
Jeffreys DJ, Acrivos A (1976) The rheological properties of suspensions of rigid particles. AIChE J 22:417–432
Joshi YM, Denn MM (2004) Failure and recovery of entangled polymer melts in elongational flow. In: Binding DM, Walters K (eds) Rheology reviews. British Society of Rheology, Aberystwyth
Kizior TE, Seyer FA (1974) Axial stress in elongational flow of fiber suspension. J Rheol 18:271–285
Kojic N, Bico J, Clasen C, McKinley GH (2006) Ex vivo rheology of spider silk. J Exp Biol 209:4355–4362
Larson RG (1999) The structure and rheology of complex fluids. Oxford University Press, New York
Laun HM, Bung R, Hess S, Loose W, Hess O, Hahn K, Hadicke E, Hingmann R, Schmidt F, Lindner P (1992) Rheological and small-angle neutron-scattering investigation of shear-induced particle structures of concentrated polymer dispersions submitted to plane Poiseuille and Couette-flow. J Rheol 36:743–787
Laun HM, Bung R, Schmidt F (1991) Rheology of extremely shear thickening polymer dispersions (passively viscosity switching fluids). J Rheol 35:999–1034
Lee YS, Wetzel ED, Wagner NJ (2003) The ballistic impact characteristics of Kevlar woven fabrics impregnated with a colloidal shear thickening fluid. J Mater Sci 38:2825–2833
Ma AWK, Chinesta F, Tuladhar T, Mackley MR (2008) Filament stretching of carbon nanotube suspensions. Rheol Acta 47:447–457
Malkin AY, Petrie CJS (1997) Some conditions for rupture of polymer liquids in extension. J Rheol 41:1–25
Maranzano BJ, Wagner NJ (2001) The effects of interparticle interactions and particle size on reversible shear thickening: hard-sphere colloidal dispersions. J Rheol 45:1205–1222
McKinley GH, Sridhar T (2002) Filament stretching rheometry. Annu Rev Fluid Mech 34:375–415
McKinley GH, Tripathi A (2000) How to extract the Newtonian viscosity from capilary breakup measurements in a filament rheometer. J Rheol 44:653–670
Merkt FS, Deegan RD, Goldman DI, Rericha EC, Swinney HL (2004) Persistent holes in a fluid. Phys Rev Lett 92:184501
Metzner AB (1985) Rheology of suspensions in polymeric liquids. J Rheol 29:739–775
Mewis J, Metzner AB (1974) The rheological properties of suspensions of fibres in Newtonian fluids subjected to extensional deformations. J Fluid Mech 62:593–600
Miller E (2007) The dynamics and rheology of shear-banding wormlike micelles and other non-Newtonian fluids. Thesis, University of Massachusetts
Miller E, Clasen C, Rothstein JP (2009) The effect of step-stretch parameters on capillary breakup extensional rheology (CaBER) measurements. Rheol Acta 48:625–639
Orr NV, Sridhar T (1999) Probing the dynamics of polymer solutions in extensional flow using step strain rate experiments. J Non-Newton Fluid Mech 82:203–232
Papageorgiou DT (1995) On the breakup of viscous liquid threads. Phys Fluids 7:1529–1544
Plog JP, Kulicke WM, Clasen C (2005) Influence of the molar mass distribution on the elongational behaviour of polymer solutions in capillary breakup. Appl Rheol 15:28–37
Pryce-Jones J (1941) Experiments on thixotropic and other anomalous fluids with a new rotation viscometer. J Sci Instrum 18:39–48
Raghavan SR, Khan SA (1997) Shear-thickening response of fumed silica suspensions under steady and oscillatory shear. J Colloid Interface Sci 185:57–67
Rasmussen HK, Nielsen JK, Bach A, Hassager O (2005) Viscosity overshoot in the start-up of uniaxial elongation of LDPE melts. J Rheol 49:369–381
Reiner M (1949) Deformation and flow. Lewis, London
Renardy M (2004) Self-similar breakup of non-Newtonian fluid jets. In: Binding DM, Walters K (eds) Rheology reviews. The British Society of Rheology, Aberystwyth
Rodd LE, Scott TP, Cooper-White JJ, McKinley GH (2005) Capillary break-up rheometry of low-viscosity elastic fluids. Appl Rheol 15:12–27
Rothstein JP (2003) Transient extensional rheology of wormlike micelle solutions. J Rheol 47:1227–1247
Rothstein JP, McKinley GH (2002a) A comparison of the stress and birefringence growth of dilute, semi-dilute and concentrated polymer solutions in uniaxial extensional flows. J Non-Newton Fluid Mech 108:275–290
Rothstein JP, McKinley GH (2002b) Inhomogeneous transient uniaxial extensional rheometry. J Rheol 46:1419–1443
Smith TL (1958) Dependence of the ultimate properties of a GR-S rubber on strain rate and temperature. J Polym Sci 32:99–113
Spiegelberg SH, McKinley GH (1996) Stress relaxation and elastic decohesion of viscoelastic polymer solutions in extensional flow. J Non-Newton Fluid Mech 67:49–76
Sridhar T, Nguyen DA, Fuller GG (2000) Birefringence and stress growth in uniaxial extension of polymer solutions. J Non-Newton Fluid Mech 90:299–315
Stelter M, Brenn G, Yarin AL, Singh RP, Durst F (2000) Validation and application of a novel elongational device for polymer solutions. J Rheol 44:595–616
Szabo P (1997) Transient filament stretching rheometry I: force balance analysis. Rheol Acta 36:277–284
Takserman-Krozer R, Ziabicki A (1963) Behavior of polymer solutions in a velocity field with parallel gradient. I. Orientation of rigid ellipsoids in a dilute solution. J Polym Sci Part A 1:491–506
Tirtaatmadja V, Sridhar T (1993) A filament stretching device for measurement of extensional viscosity. J Rheol 37:1133–1160
Tripathi A, Whitingstall P, McKinley GH (2000) Using filament stretching rheometry to predict stand formations and processability in adhesives and other non-Newtonian fluids. Rheol Acta 39:321–337
Vinogradov GV, Malkin AY, Volosevitch VV, Shatalov VP, Yudin VP (1975) Flow, high-elastic (recoverable) deformations and rupture of uncured high molecular weight linear polymers in uniaxial extension. J Polym Sci Polym Phys Ed 13:1721–1735
Xu J, Chatterjee S, Koelling KW, Wang Y, Bechtel SE (2005) Shear and extensional rheology of carbon nanofiber suspensions. Rheol Acta 44:537–562
Yang J, Sliva A, Banerjee A, Dave RN, Pfeffe R (2005) Dry particle coating for improving the flowability of cohesive powders. Powder Technol 158:21–33
Yao M, Spiegelberg SH (2000) Dynamics of weakly strain hardening fluids in filament stretching devices. J Non-Newton Fluid Mech 89:1–43
Yesilata B, Clasen C, McKinley GH (2006) Nonlinear shear and extensional flow dynamics of wormlike surfactant solutions. J Non-Newton Fluid Mech 133:73–90
Acknowledgements
The authors would like to thank the National Science Foundation for the generous support of this research under grant CBET-0547150 and through the MRSEC and the CHM at the University of Massachusetts, Amherst.
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Bischoff White, E.E., Chellamuthu, M. & Rothstein, J.P. Extensional rheology of a shear-thickening cornstarch and water suspension. Rheol Acta 49, 119–129 (2010). https://doi.org/10.1007/s00397-009-0415-3
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DOI: https://doi.org/10.1007/s00397-009-0415-3