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Rheologica Acta

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21.05.2019 | Original Contribution

Instantaneous dimensionless numbers for transient nonlinear rheology

verfasst von: Simon A. Rogers, Jun Dong Park, Ching-Wei Johnny Lee

Erschienen in: Rheologica Acta | Ausgabe 8/2019

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Abstract

Two instantaneous dimensionless numbers that act as Deborah and Weissenberg numbers are introduced to diagnose flow conditions for transient nonlinear rheology. The utility of the new numbers is demonstrated on the steady alternating large amplitude oscillatory shear response of a colloidal Ludox glass, the soft glassy rheology model, and a viscoelastic wormlike micelle solution. Complex nonlinear trajectories through Pipkin space are observed, from which it is concluded that large amplitude oscillatory shear represents a range of distinct flow types. These results indicate that the observation time may change significantly during a period of oscillation. The complex trajectories observed for all three systems go from close to one axis to close to the other and back in quick succession. Rather than existing in the dominant central area that Pipkin originally marked as “?”, LAOS may simply be the way by which the axes of Pipkin space are dynamically linked.

Vorheriger Artikel Quantifying the errors due to overfilling for Newtonian fluids in rotational rheometry

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Anvari M, Joyner (Melito) HS (2017) Effect of formulation on structure-function relationships of concentrated emulsions: rheological, tribological, and microstructural characterization. Food Hydrocoll 72:11–26CrossRef

Astarita G, Jongschaap RJJ (1978) The maximum amplitude of strain for the validity of linear viscoelasticity. J Non-Newtonian Fluid Mech 3(3):281–287CrossRef

Auer S, Frenkel D (2001) Suppression of crystal nucleation in polydisperse colloids due to increase of the surface free energy. Nature 413(6857):711–713CrossRef

Augusto PED, Falguera V, Cristianini M, Ibarz A (2013a) Viscoelastic properties of tomato juice: applicability of the Cox-Merz rule. Food Bioprocess Technol 6(3):839–843CrossRef

Augusto PED, Ibarz A, Cristianini M (2013b) Effect of high pressure homogenization (HPH) on the rheological properties of tomato juice: viscoelastic properties and the Cox-Merz rule. J Food Eng 114(1):57–63CrossRef

Berg RF (2004) Fluids near a critical point obey a generalized Cox–Merz rule. J Rheol 48(6):1365–1373CrossRef

Calabrese MA, Rogers SA, Porcar L, Wagner NJ (2016) Understanding steady and dynamic shear banding in a model wormlike micellar solution. J Rheol 60:1001CrossRef

Cates ME, Candau SJ (1990) Statics and dynamics of worm-like surfactant micelles. J Phys Condens Matter 2(33):6869–6892CrossRef

Chan RW (2018) Nonlinear viscoelastic characterization of human vocal fold tissues under large-amplitude oscillatory shear (LAOS). J Rheol 62(3):695–712CrossRef

Cho KS, Hyun K, Ahn KH, Lee SJ (2005) A geometrical interpretation of large amplitude oscillatory shear response. J Rheol 49(3):747–758CrossRef

Conte T, Chaouche M (2016) Rheological behavior of cement pastes under large amplitude oscillatory shear. Cem Concr Res 89:332–344CrossRef

Cox WP, Merz EH (1958) Correlation of dynamic and steady flow viscosities. J Polym Sci 28(118):619–622CrossRef

de Souza Mendes PR, Thompson RL, Alicke AA, Leite RT (2014) The quasilinear large-amplitude viscoelastic regime and its significance in the rheological characterization of soft matter. J Rheol 58(2):537–561CrossRef

Dealy JM (2010) Weissenberg and Deborah numbers—their definition and use. Rheology Bulletin 79(2):14–18

Dimitriou CJ, Ewoldt RH, Mckinley GH (2013) Describing and prescribing the constitutive response of yield stress fluids using large amplitude oscillatory shear stress (LAOStress). J Rheol 57:1CrossRef

Dinkgreve M, Denn MM, Bonn D (2017) “Everything flows?”: elastic effects on startup flows of yield-stress fluids. Rheol Acta 56(3):189–194CrossRef

Donley GJ, de Bruyn JR, McKinley GH, Rogers SA (2018) Time-resolved dynamics of the yielding transition in soft materials. Journal of Non-Newtonian Fluid Mechanics 264 (2019) 117–134

Doraiswamy D, Mujumdar AN, Tsao I, Beris AN, Danforth SC, Metzner AB (1991) The Cox–Merz rule extended: a rheological model for concentrated suspensions and other materials with a yield stress. J Rheol 35(4):647–685CrossRef

Duvarci OC, Yazar G, Kokini JL (2017) The SAOS, MAOS and LAOS behavior of a concentrated suspension of tomato paste and its prediction using the Bird-Carreau (SAOS) and Giesekus models (MAOS-LAOS). J Food Eng 208:77–88CrossRef

Ewoldt RH, McKinley GH (2017) Mapping thixo-elasto-visco-plastic behavior. Rheol Acta 56(3):195–210CrossRef

Ewoldt RH, McKinley GH, Hosoi AE (2008) Fingerprinting soft materials: a framework for characterizing nonlinear viscoelasticity. J Rheol 52:1CrossRef

Ewoldt RH, Winter P, Maxey J, Mckinley GH, Ewoldt RH, Winter P et al (2010) Large amplitude oscillatory shear of pseudoplastic and elastoviscoplastic materials. Rheol Acta 49:191–212CrossRef

Ewoldt RH, Bharadwaj, Ashwin N, Ewoldt RH, Bharadwaj NA (2013) Low-dimensional intrinsic material functions for nonlinear viscoelasticity. Rheol Acta 52:201–219CrossRef

Ferry JD, Sawyer WM, Ashworth JN (1947) Behavior of concentrated polymer solutions under periodic stresses. J Polym Sci 2(6):593–611CrossRef

Garinei A, Pucci E, Marconi G, Pucci IE (2016) New measures for characterizing nonlinear viscoelasticity in large amplitude oscillatory shear. J Rheol 60:333CrossRef

Gemant A (1935) The conception of a complex viscosity and its application to dielectrics. Trans Faraday Soc 31(0):1582CrossRef

Ghosh S, Holwerda EK, Worthen RS, Lynd LR, Epps BP (2018) Rheological properties of corn tover slurries during fermentation by Clostridium thermocellum. Biotechnol Biofuels 11:246CrossRef

Giacomin AJ, Oakley JG (1992) Structural network models for molten plastics evaluated in large amplitude oscillatory shear. J Rheol 36(8):1529–1546CrossRef

Gleissle W, Hochstein B (2003) Analysis of linear viscoelasticity of a crosslinking polymer at the gel point journal of rheology. Trans Soc Rheol 47:137CrossRef

González E, Costa LMB, Silva HMRD, Hilliou L (2016) Rheological characterization of EVA and HDPE polymer modified bitumens under large deformation at 20 °C. Constr Build Mater 112:756–764CrossRef

Harris J, Bogie K (1967) The experimental analysis of non-linear waves in mechanical systems. Rheol Acta 6(1):3–5CrossRef

Hiemenz PC, Lodge T (2007) Polymer chemistry. CRC Press, Boca Raton

Holroyd GAJ, Martin SJ, Graham RS (2017) Analytic solutions of the Rolie Poly model in time-dependent shear. J Rheol 61(5):859–870CrossRef

Horner JS, Armstrong MJ, Wagner NJ, Beris AN (2018) Investigation of blood rheology under steady and unidirectional large amplitude oscillatory shear. J Rheol 62:577CrossRef

Huilgol RR (1975) On the concept of the Deborah number. Trans Soc Rheol 19(2):297–306CrossRef

Hyun, K., Wilhelm, M., Klein, C. O., Soo Cho, K., Gun Nam, J., Hyun Ahn, K., … McKinley, G. H. (2011). A review of nonlinear oscillatory shear tests: analysis and application of large amplitude oscillatory shear (LAOS). Prog Polym Sci, 36, 1697–1753CrossRef

Ianniruberto G, Marrucci G (1996) On compatibility of the Cox-Merz rule with the model of Doi and Edwards. J Non-Newtonian Fluid Mech 65(2–3):241–246CrossRef

Jeyaseelan RS, Giacomin AJ (1994) Predicting polymer melt behavior near the inception of wall slip in oscillatory shear. J Non-Newtonian Fluid Mech 53. https://doi.org/10.1016/0377-0257(94)85043-7

Joyner (Melito) HS (2018) Explaining food texture through rheology. Curr Opin Food Sci 21:7–14CrossRef

Kim J, Merger D, Wilhelm M, Helgeson ME (2014) New measures for characterizing nonlinear viscoelasticity in large amplitude oscillatory shear. J Rheol 58(5):1359CrossRef

Laun HM (1986) Prediction of elastic strains of polymer melts in shear and elongation. J Rheol 30(3):459–501CrossRef

Lee C-W, Rogers SA (2017) A sequence of physical processes quantified in LAOS by continuous local measures. Korea-Australia Rheology Journal, 29(4), 269–279 November 2017

Lin NYC, Goyal S, Cheng X, Zia RN, Escobedo FA, Cohen I (2013) Far-from-equilibrium sheared colloidal liquids: disentangling relaxation, advection, and shear-induced diffusion. Phys Rev E 88:62309CrossRef

Lodge AS (1964) Elastic Liquids. Academic Press, Cambridge

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):1–15CrossRef

Marenne S, Morris JF (2017) Nonlinear rheology of colloidal suspensions probed by oscillatory shear. J Rheol 61:797CrossRef

Marrucci G (1996) Dynamics of entanglements: a nonlinear model consistent with the Cox-Merz rule. J Non-Newtonian Fluid Mech 62(2–3):279–289CrossRef

Park JD, Rogers SA (2018) The transient behavior of soft glassy materials far from equilibrium. Journal of Rheology 62, 869

Philippoff W (1966) Vibrational measurements with large amplitudes. Trans Soc Rheol 10(1):317–334CrossRef

Philippoff W, Gaskins FH (1958) The capillary experiment in rheology. Trans Soc Rheol 2(1):263–284CrossRef

Pipkin AC (1972) Lectures on viscoelasticity theory. Springer New York, New York, NYCrossRef

Poole R (2012) The Deborah and Weissenberg numbers. Rheol Bull 53:32–39

Poulos AS, Renou F, Jacob AR, Koumakis N, Petekidis G (2015) Large amplitude oscillatory shear (LAOS) in model colloidal suspensions and glasses: frequency dependence. Rheol Acta 54(8):715–724CrossRef

Pusey PN (1991) Liquids, freezing and the glass transition. In: Les Houches Summer Schools of Theoretical Physics Session LI (1989). North-Holland, Amsterdam

Pusey PN, van Megen W (1986) Phase behaviour of concentrated suspensions of nearly hard colloidal spheres. Nature 320(6060):340–342CrossRef

Radhakrishnan, R., & Fielding, S. M. (2016). Shear banding of soft glassy materials in large amplitude oscillatory shearCrossRef

Ravindranath S, Wang S-Q (2008) Universal scaling characteristics of stress overshoot in startup shear of entangled polymer solutions. J Rheol 52(3):681–695CrossRef

Reimers MJ, Dealy JM (1996) Rheology of xanthan gum: salt, temperature, and strain effects in oscillatory and steady shear experiments. J Rheol 40:1155CrossRef

Reiner M (1964) Citation. Trans Soc Rheol 17:297

Rogers SA (2012) A sequence of physical processes determined and quantified in LAOS: an instantaneous local 2D/3D approach. Journal of Rheology 56(5), 1129-1151 September/October 2012

Rogers SA (2017) In search of physical meaning: defining transient parameters for nonlinear viscoelasticity. Rheol Acta 56: 501

Rogers S (2018) Large amplitude oscillatory shear: simple to describe, hard to interpret. Physics Today 71, 7, 34

Rogers SA, Lettinga MP (2012) A sequence of physical processes determined and quantified in large-amplitude oscillatory shear (LAOS): application to theoretical nonlinear models. J. Rheol. 56(1), 1–25 January/February 2012

Rogers SA, Erwin BM, Vlassopoulos D, Cloitre M (2011a) A sequence of physical processes determined and quantified in LAOS: application to a yield stress fluid. J. Rheol. 55(2), 435–458 March/April 2011

Rogers SA, Erwin BM, Vlassopoulos D, Cloitre M (2011b) Oscillatory yielding of a colloidal star glass. J. Rheol. 55(4), 733–752 July/August 2011

Sharma V, McKinley GH (2012) An intriguing empirical rule for computing the first normal stress difference from steady shear viscosity data for concentrated polymer solutions and melts the Cox-Merz rule and Laun’s rule. Rheol Acta 51:487–495CrossRef

Stickel JJ, Knutsen JS, Liberatore MW (2013) Extending yield-stress fluid paradigms. J Rheol 57:357CrossRef

Szopinski D, Luinstra GA (2016) Viscoelastic properties of aqueous guar gum derivative solutions under large amplitude oscillatory shear (LAOS). Carbohydr Polym 153:312–319CrossRef

Tan, K., Cheng, S., Jugé, L., & Bilston, L. E. (2013). Characterising soft tissues under large amplitude oscillatory shear and combined loadingCrossRef

Tariq S, Giacomin AJ, Gunasekaran S (1998) Nonlinear viscoelasticity of cheese. Biorheology 35:3 171–191

van der Vaart K, Rahmani Y, Zargar R, Hu Z, Bonn D, Schall P (2013) Rheology of concentrated soft and hard-sphere suspensions. J Rheol 57(4):1195–1209CrossRef

Vananroye, A., Leen, P., Peter, ·, Puyvelde, V., Clasen, C., Vananroye, A., …, Clasen, C. (2011). TTS in LAOS: validation of time-temperature superposition under large amplitude oscillatory shear. Rheol Acta, 50, 795–807CrossRef

Vasquez, P. A., Jin, Y., Vuong, K., Hill, D. B., & Forest, M. G. (2013). A new twist on Stokesâ€™ second problem: Partial penetration of nonlinearity in sheared viscoelastic layers

Venkatraman S, Okano M (1990) A comparison of torsional and capillary rheometry for polymer melts: the Cox-Merz rule revisited. Polym Eng Sci 30(5):308–313CrossRef

Wang Y, Wang S-Q (2008) From elastic deformation to terminal flow of a monodisperse entangled melt in uniaxial extension. J Rheol 52(6):1275–1290CrossRef

Wang Y, Li X, Zhu X, Wang S-Q (2012) Characterizing state of chain entanglement in entangled polymer solutions during and after large shear deformation. Macromolecules 45(5):2514–2521CrossRef

Wang S-Q, Wang Y, Cheng S, Li X, Zhu X, Sun H (2013) New experiments for improved theoretical description of nonlinear rheology of entangled polymers. Macromolecules 46(8):3147–3159CrossRef

Weissenberg K (1947) A continuum theory of rheological phenomena. Nature 159(4035):310CrossRef

Wen YH, Lin HC, Li CH, Hua CC (2004) An experimental appraisal of the Cox-Merz rule and Laun’s rule based on bidisperse entangled polystyrene solutions. Polymer 45(25):8551–8559CrossRef

White JL (1964) Dynamics of viscoelastic fluids, melt fracture, and the rheology of fiber spinning. J Appl Polym Sci 8(5):2339–2357CrossRef

Winter HH (2009) Three views of viscoelasticity for Cox-Merz materials. Rheol Acta 48(3):241–243CrossRef

Wood-Adams PM (2001) The effect of long chain branches on the shear flow behavior of polyethylene. J Rheol 45(1):203–210CrossRef

Zhang Z, Christopher GF (2015) The nonlinear viscoelasticity of hyaluronic acid and its role in joint lubrication. Soft Matter 11(13):2596–2603CrossRef

Zhou Y, Schroeder CM (2016) Single polymer dynamics under large amplitude oscillatory extension. Phys Rev Fluids 1:53301CrossRef

Zhou L, Cook LP, Mckinley GH (2010) Probing shear-banding transitions of the VCM model for entangled wormlike micellar solutions using large amplitude oscillatory shear (LAOS) deformations. J Non-Newtonian Fluid Mech 165:1462–1472CrossRef

Titel: Instantaneous dimensionless numbers for transient nonlinear rheology
verfasst von: Simon A. Rogers
Jun Dong Park
Ching-Wei Johnny Lee
Publikationsdatum: 21.05.2019
Verlag: Springer Berlin Heidelberg
Erschienen in: Rheologica Acta / Ausgabe 8/2019
Print ISSN: 0035-4511
Elektronische ISSN: 1435-1528
DOI: https://doi.org/10.1007/s00397-019-01150-2

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