Abstract
In recent years, large amplitude oscillatory shear (LAOS) has become a prime tool to investigate the nonlinear rheology of complex fluids. More specifically, most studies use LAOS data as a macroscopic probe for hypothetical microscopic changes, sometimes successfully. Nevertheless, we would like to raise awareness on the potential impact of secondary flows triggered by instabilities in LAOS performed in curved shear flows exemplified by the Taylor–Couette geometry. First, we show that even for Newtonian fluids, where no micro-structural changes are expected, complex flow patterns can emerge in the LAOS data. Second, we stress the potential impact of similar effects in complex fluids by studying LAOS flows of a well-known shear-banding surfactant solution. Our hope is that our thorough study of the Newtonian case together with preliminary experiments on a complex fluid will reinforce the already successful analogy existing between inertial and elastic instabilities, suggest caution for future LAOS studies focused solely on a structural perspective, and open new research avenues combining flow instabilities and unsteady flows in complex fluids.
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References
Adler F, Sawyer W, Ferry JD (1949) Propagation of transverse waves in viscoelastic media. J Appl Phys 20(11):1036–1041
Akhavan R, Kamm R, Shapiro A (1991) An investigation of transition to turbulence in bounded oscillatory stokes flows part 1. experiments. J Fluid Mech 225:395–422
Aouidef A, Normand C, Stegner A, Wesfreid J (1994) Centrifugal instability of pulsed flow. Phys Fluids 6(11):3665–3676
Bird R, Armstrong R, Hassager O (1987) Dynamics of polymeric liquids. Vol. 1: Fluid mechanics. Wiley, New York
Bird R, Armstrong R, Curtiss C (1987) Dynamics of polymeric liquids Kinetic theory, vol 2. Wiley, New York
Casanellas L, Ortín J (2012) Experiments on the laminar oscillatory flow of wormlike micellar solutions. Rheol Acta 51(6):545–557
Casanellas L, Ortín J (2014) Vortex ring formation in oscillatory pipe flow of wormlike micellar solutions. J Rheol 58:149
Casanellas L et al (2011) Laminar oscillatory flow of maxwell and oldroyd-b fluids: Theoretical analysis. J Non-Newtonian Fluid Mech 166(23):1315–1326
Couette M (1888) Comptes Rendus 107:388–390
Crandall IB (1926) Theory of vibrating systems and sound. D Van Nostrand Company Princeton
Dealy J (2010) Weissenberg and deborah numbers—their definition and use. Rheol Bulletin 79:2
Didden N (1979) On the formation of vortex rings: Rolling-up and production of circulation. ZAMP 30(1):101–116
Dimitriou CJ, Ewoldt RH, McKinley GH (2012a) Describing and prescribing the constitutive response of yield stress fluids using large amplitude oscillatory shear stress (laostress). J Rheol 57(1):27–70
Dimitriou CJ, Casanellas L, Ober TJ, McKinley GH (2012b) Rheo-piv of a shear-banding wormlike micellar solution under large amplitude oscillatory shear. Rheol acta 51(5):395–411
Donnelly R (1964) Experiments on the stability of viscous flow between rotating cylinder. iii. enhancement of stability by modulation. Proceedings of the Royal Society of London. Ser A Math Phys Sci 281(1384):130–139
Donnelly R, Fultz D (1960) Experiments on the stability of viscous flow between rotating cylinders. ii. visual observations. Proceedings of the Royal Society of London. Ser A MMath Phys Sci 258(1292):101–123
Donnelly RJ (1958) Experiments on the stability of viscous flow between rotating cylinders. i. torque measurements. Proceedings of the Royal Society of London. Ser A A MMath Phys Sci 246:312–325
Eckmann DM, Grotberg JB (1991) Experiments on transition to turbulence in oscillatory pipe flow. J Fluid Mech 222:329–350
Ewoldt RH, Clasen C, Hosoi A, McKinley GH (2007) Rheological fingerprinting of gastropod pedal mucus and synthetic complex fluids for biomimicking adhesive locomotion. Soft Matter 3(5):634–643
Ewoldt RH, Hosoi A, McKinley GH (2008) New measures for characterizing nonlinear viscoelasticity in large amplitude oscillatory shear. J Rheol 52(6):1427–1458
Fardin MA, Lasne B, Cardoso O, régoire G, Argentina M, Decruppe JP, Lerouge S (2009) Taylor-like vortices in shear-banding flow of giant micelles. Phys Rev Lett 028(2):302
Fardin MA, Lopez D, Croso J, Grégoire G, Cardoso O, McKinley G, Lerouge S (2010) Elastic turbulence in shear banding wormlike micelles. Phys Rev Lett 178(17):303
Fardin MA, Ober T, Gay C, Grégoire G, McKinley G, Lerouge S (2011) Criterion for purely elastic taylor-couette instability in the flows of shear-banding fluids. Eur Phys Lett 96:44,004
Fardin MA, Lerouge S (2012a) Instabilities in wormlike micelle systems. Eur Phys J E 35(9):1–29
Fardin MA, Divoux T, Guedeau-Boudeville M, Buchet-Maulien I, Browaeys J, McKinley G, Manneville S, Lerouge S (2012b) Shear-banding in surfactant wormlike micelles: Elastic instabilities and wall slip. Soft Matter 8(8):2535–2553
Fardin MA, Ober T, Grenard V, Divoux T, Manneville S, McKinley G, Lerouge S (2012c) Interplay between elastic instabilities and shear-banding: Three categories of taylor–couette flows and beyond. Soft Matter 8(39):10,072–10,089
Fardin MA, Perge C, Taberlet N (2014a) “The hydrogen atom of fluid dynamics”—Introduction to the taylor-couette flow for soft matter scientists. Soft Matter 10:3523–3535
Fardin MA, Perge C, Taberlet N, Manneville S (2014b) Flow-induced structures versus flow instabilities. Phys Rev E 89(1): 011001
Ferry JD (1942) Mechanical properties of substances of high molecular weight. ii. rigidities of the system polystyrene-xylene and their dependence upon temperature and frequency. J Am Chem Soc 64(6):1323–1329
Gallot T, Perge C, Grenard V, Fardin MA, Taberlet N, Manneville S (2013) Ultrafast ultrasonic imaging coupled to rheometry: Principle and illustration. Rev Sci Instrum 84:045,107
Gharib M, Rambod E, Shariff K (1998) A universal time scale for vortex ring formation. J Fluid Mech 360:121–140
Giacomin AJ, Dealy JM (1993) Large-amplitude oscillatory shear. In: Techniques in rheological measurement:99–121
Glezer A (1988) The formation of vortex rings. Phys Fluids 31(12):3532–3542
Groisman A, Steinberg V (2000) Elastic turbulence in a polymer solution flow. Nature 405(6782):53–55
Gurnon AK, Lopez-Barron CR, Eberle APR, Porcar L, Wagner NJ (2014) Spatiotemporal stress and structure evolution in dynamically sheared polymer-like micellar solutions. Soft Matter 10:2889–2898
Hall P (1975) The stability of unsteady cylinder flows. J Fluid Mech 67(01):29–63
Hino M, Sawamoto M, Takasu S (1976) Experiments on transition to turbulence in an oscillatory pipe flow. J Fluid Mech 75(02):193–207
Hyun K, Wilhelm M, Klein CO, Cho KS, Nam JG, Ahn KH, Lee SJ, Ewoldt RH, McKinley GH (2011) A review of nonlinear oscillatory shear tests: Analysis and application of large amplitude oscillatory shear (laos). Prog Polym Sci 36(12):1697– 1753
Larson R, Shaqfeh ES, Muller S (1990) A purely elastic instability in taylor-couette flow. J Fluid Mech 218:573–600
Larson R (1992) Instabilities in viscoelastic flows. Rheol Acta 31(3):213–263
Larson R (1999) The structure and rheology of complex fluids. Oxford University Press
Lerouge S, Fardin MA, Argentina M, Grégoire G, Cardoso O (2008) Interface dynamics in shear-banding flow of giant micelles. Soft Matter 4(9):1808–1819
Lerouge S, Berret JF (2010) Shear-induced transitions and instabilities in surfactant wormlike micelles. Adv Polym Sci 230:1–71
Mallock A (1888) Proc R Soc London A 45:126–132
McKinley G, Pakdel P, Öztekin A (1996) Rheological and geometric scaling of purely elastic flow instabilities. J non-Newt Fluid mech 67:19–47
Merkli P, Thomann H (1975) Transition to turbulence in oscillating pipe flow. J Fluid Mech 68(03):567–576
Morozov AN, van Saarloos W (2007) An introductory essay on subcritical instabilities and the transition to turbulence in visco-elastic parallel shear flows. Phys Rep 447(3):112–143
Muller SJ (2008) Elastically-influenced instabilities in taylor-couette and other flows with curved streamlines: a review. Korea-Australia Rheol J 20(3):117–125
Ohmi M, Iguchi M, Kakehashi K, Masuda T (1982) Transition to turbulence and velocity distribution in an oscillating pipe flow. Bull JSME 25(201):365–371
Perge C, Fardin M, Manneville S (2014a) Surfactant micelles: Model systems for flow instabilities of complex fluids. Eur Phys J E 37:23
Perge C, Fardin MA, Manneville S (2014b) Inertio-elastic instability of non shear-banding wormlike micelles. Soft Matter 10:1450
Phan-Thien N (1985) Cone-and-plate flow of the oldroyd-b fluid is unstable. J Non-Newtonian Fluid Mech 17(1):37–44
Rogers S, Kohlbrecher J, Lettinga MP (2012) The molecular origin of stress generation in worm-like micelles, using a rheo-sans laos approach. Soft Matter 8:7831–7839
Sakiadis B (1961) Boundary-layer behavior on continuous solid surfaces: I. boundary-layer equations for two-dimensional and axisymmetric flow. AIChE J 7(1):26–28
Schlichting H, Gersten K (2000) Boundary-layer theory. Springer Verlag
Sergeev S (1966) Fluid oscillations in pipes at moderate reynolds numbers. Fluid Dyn 1(1):121–122
Taylor G (1923) Stability of a viscous liquid contained between two rotating cylinders. Philos Trans R Soc London A 223:289–343
Torralba M, Castrejón-Pita J, Castrejón-Pita A, Huelsz G, Del Río J, Ortín J (2005) Measurements of the bulk and interfacial velocity profiles in oscillating newtonian and maxwellian fluids. Phys Rev E 72(1):016,308
Torralba M, Castrejón-Pita A, Hernández G, Huelsz G, Del Rio J, Ortín J (2007) Instabilities in the oscillatory flow of a complex fluid. Phys Rev E 75(5):056,307
Vasquez PA, Jin Y, Vuong K, Hill DB, Gregory Forest M (2013) A new twist on stokes second problem: Partial penetration of nonlinearity in sheared viscoelastic layers. J Non-Newtonian Fluid Mech 196:36–50
Yosick JA, Giacomin JA, Stewart WE, Ding F (1998) Fluid inertia in large amplitude oscillatory shear. Rheol acta 37(4):365–373
Zhou L, Cook LP, McKinley GH (2012) Multiple shear-banding transitions for a model of wormlike micellar solutions. SIAM J Appl Math 72(4):1192–1212
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This work was funded by the Institut Universitaire de France and by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement No. 258803.
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Fardin, M.A., Perge, C., Casanellas, L. et al. Flow instabilities in large amplitude oscillatory shear: a cautionary tale. Rheol Acta 53, 885–898 (2014). https://doi.org/10.1007/s00397-014-0818-7
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DOI: https://doi.org/10.1007/s00397-014-0818-7