Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-03T20:37:41.909Z Has data issue: false hasContentIssue false
  • English
  • Français

Onset of transition in the flow of polymer solutions through microtubes

Published online by Cambridge University Press:  16 April 2018

Bidhan Chandra ,
V. Shankar Open the ORCID record for V. Shankar [Opens in a new window]  and
Debopam Das Open the ORCID record for Debopam Das [Opens in a new window]
Bidhan Chandra
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology, Kanpur, 208016, India
V. Shankar*
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology, Kanpur, 208016, India
Debopam Das
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology, Kanpur, 208016, India
*
†Email address for correspondence: vshankar@iitk.ac.in
Get access Rights & Permissions [Opens in a new window]

Abstract

Experiments are performed to characterize the onset of laminar–turbulent transition in the flow of high-molecular-weight polymer solutions in rigid microtubes of diameters in the range $390~\unicode[STIX]{x03BC}\text{m}{-}470~\unicode[STIX]{x03BC}\text{m}$ using the micro-PIV technique. By considering flow in tubes of such small diameters, the present study probes higher values of elasticity numbers ($E\equiv \unicode[STIX]{x1D706}\unicode[STIX]{x1D708}/R^{2}$) compared to existing studies, where $\unicode[STIX]{x1D706}$ is the longest relaxation time of the polymer solution, $R$ is the tube radius and $\unicode[STIX]{x1D708}$ is the kinematic viscosity of the polymer solution. For the Newtonian case, our experiments indicate that the natural transition (without the aid of any forcing mechanism) occurs at Reynolds number ($Re$) $2000\pm 100$. As the concentration of polymer is increased, initially there is a delay in the onset of the transition and the transition Reynolds number increases to $2500$. Further increase in concentration of the polymer results in a decrease in the Reynolds number for transition. At sufficiently high concentrations, the added polymer tends to destabilize the flow and the transition is observed to happen at $Re$ as low as $800$. It is also observed that the addition of polymers, regardless of their concentration, reduces the magnitude of the velocity fluctuations after transition. Dye-stream visualization is further used to corroborate the onset of transition in the flow of polymer solutions. The present work thus shows that addition of polymer, at sufficiently high concentrations, destabilizes the flow when compared to that of a Newtonian fluid, thereby providing additional evidence for ‘early transition’ or ‘elasto-inertial turbulence’ in the flow of polymer solutions. The data for the transition Reynolds number $Re_{t}$ from our experiments (for tubes of different diameters, and for two different polymers at varying concentrations) collapse well according to the scaling relation $Re_{t}\propto 1/\sqrt{E(1-\unicode[STIX]{x1D6FD})}$, where $\unicode[STIX]{x1D6FD}$ is the ratio of solvent viscosity to the viscosity of the polymer solution.

JFM classification

Instability: Instability Non-Newtonian Flows: Non-Newtonian Flows Instability: Transition to turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 844 , 10 June 2018 , pp. 1052 - 1083
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Avila, K., Moxey, D., Lozar, A., Avila, M., Barkley, D. & Hof, B. 2011 The onset of turbulence in pipe flow. Science 333, 192–196.10.1126/science.1203223Google Scholar
Bodiguel, H., Beaumont, J., Machado, A., Martinie, L., Kellay, H. & Colin, A. 2015 Flow enhancement due to elastic turbulence in channel flows of shear thinning fluids. Phys. Rev. Lett. 114, 028302.10.1103/PhysRevLett.114.028302Google Scholar
Bonn, D., Ingremeau, F., Amarouchene, Y. & Kellay, H. 2011 Large velocity fluctuations in small-Reynolds-number pipe flow of polymer solutions. Phys. Rev. E 84, 045301.Google Scholar
Clasen, C., Plog, J. P., Kulicke, W.-M., Owens, M., Macosko, C., Scriven, L. E., Verani, M. & McKinley, G. H. 2006 How dilute are dilute solutions in extensional flows? J. Rheol. 50, 849–881.10.1122/1.2357595Google Scholar
Dinic, J., Zhang, Y., Jimenez, L. N. & Sharma, V. 2015 Extensional relaxation times of dilute, aqueous polymer solutions. ACS Macro Lett. 4, 804–808.10.1021/acsmacrolett.5b00393Google Scholar
Doi, M. & Edwards, S. F. 1988 The Theory of Polymer Dynamics. Oxford Science Publications.Google Scholar
Draad, A. A., Kuiken, G. D. C. & Nieuwstadt, F. T. M. 1998 Laminar–turbulent transition in pipe flow for Newtonian and non-Newtonian fluids. J. Fluid Mech. 377, 267–312.10.1017/S0022112098003139Google Scholar
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.Google Scholar
Dubief, Y., Terrapon, V. E. & Soria, J. 2013 On the mechanism of elasto-inertial turbulence. Phys. Fluids 25 (11), 110817.10.1063/1.4820142Google Scholar
Ebagninin, K. W., Benchabane, A. & Bekkour, K. 2009 Rheological characterization of poly(ethylene oxide) solutions of different molecular weights. J. Colloid Interface Sci. 336, 360–397.10.1016/j.jcis.2009.03.014Google Scholar
Eckhardt, B., Schneider, T. M., Hof, B. & Westerweel, J. 2007 Turbulence transition in pipe flow. Annu. Rev. Fluid Mech. 39 (1), 447–468.10.1146/annurev.fluid.39.050905.110308Google Scholar
Escudier, M. P., Poole, R. J., Presti, F., Dales, C., Nouar, C., Desaubry, C., Graham, L. & Pullum, L. 2005 Observations of asymmetrical flow behaviour in transitional pipe flow of yield-stress and other shear-thinning liquids. J. Non-Newtonian Fluid Mech. 127 (2), 143–155.10.1016/j.jnnfm.2005.02.006Google Scholar
Fang, L., Brown, W. & Hvidt, S. 1992 Static and dynamic properties of polyacrylamide gels and solutions in mixtures of water and glycerol: a comparison of the application of mean-field and scaling theories. Macromolecules 25, 3137–3142.10.1021/ma00038a018Google Scholar
Forame, P. C., Hansen, R. J. & Little, R. C. 1972 Observations of early turbulence in the pipe flow of drag reducing polymer solutions. AIChE J. 18 (1), 213–217.10.1002/aic.690180139Google Scholar
Goldstein, R. J., Adrian, R. J. & Kreid, D. K. 1969 Turbulent and transition pipe flow of dilute aqueous polymer solutions. Ind. Engng Chem. Fundam. 8, 498–502.10.1021/i160031a021Google Scholar
Graham, M. D. 2014 Drag reduction and the dynamics of turbulence in simple and complex fluids. Phys. Fluids 26, 101301.10.1063/1.4895780Google Scholar
Groisman, A. & Steinberg, V. 2000 Elastic turbulence in a polymer solution flow. Nature 405, 53–55.10.1038/35011019Google Scholar
Hansen, R. J. & Little, R. C. 1974 Early turbulence and drag reduction phenomena in larger pipes. Nature 252, 690.10.1038/252690a0Google Scholar
Hansen, R. J., Little, R. C. & Forame, P. G. 1973 Experimental and theoretical studies of early turbulence. J. Chem. Engng Japan 6 (4), 310–314.10.1252/jcej.6.310Google Scholar
Hof, B. & Lozar, A. D. 2009 An experimental study of the decay of turbulent puffs in pipe flow. Phil. Trans. R. Soc. Lond. A 367, 589–599.Google Scholar
Hoyt, J. W. 1977 Laminar–turbulent transition in polymer solutions. Nature 270, 508–509.10.1038/270508a0Google Scholar
Jackson, D. & Launder, B. 2007 Osborne Reynolds and the publication of his papers on turbulent flow. Annu. Rev. Fluid Mech. 39, 19–35.10.1146/annurev.fluid.39.050905.110241Google Scholar
Kulicke, W. M., Kniewske, R. & Klein, J. 1982 Preparation, characterization, solution properties and rheological behaviour of polyacrylamide. Prog. Polym. Sci. 8, 373–468.10.1016/0079-6700(82)90004-1Google Scholar
Larson, R. G. 1992 Instabilities in viscoelastic flows. Rheol. Acta 31, 213–263.10.1007/BF00366504Google Scholar
Larson, R. G., Shaqfeh, E. S. G. & Muller, S. J. 1990 A purely elastic instability in Taylor–Couette flow. J. Fluid Mech. 218, 573–600.10.1017/S0022112090001124Google Scholar
Little, C. R., Hansen, R. J., Hunston, D. L., Kim, O., Patterson, R. L. & Ting, R. Y. 1975 The drag reduction phenomenon: observed characteristics, improved agents, and proposed mechanisms. Ind. Engng Chem. Fundam. 14 (4), 283–296.10.1021/i160056a001Google Scholar
Mullin, T. 2011 Experimental studies of transition to turbulence in a pipe. Annu. Rev. Fluid Mech. 43 (1), 1–24.10.1146/annurev-fluid-122109-160652Google Scholar
Neelamegam, R. & Shankar, V. 2015 Experimental study of the instability of laminar flow in a tube with deformable walls. Phys. Fluids 27, 043305.10.1063/1.4907246Google Scholar
Neelamegam, R., Shankar, V. & Das, D. 2013 Suppression of purely elastic instabilities in the torsional flow of viscoelastic fluid past a soft solid. Phys. Fluids 25, 124102.10.1063/1.4840195Google Scholar
Pan, L., Morozov, A., Wagner, C. & Arratia, P. E. 2013 Nonlinear elastic instability in channel flows at low Reynolds numbers. Phys. Rev. Lett. 110, 174502.10.1103/PhysRevLett.110.174502Google Scholar
Patel, V. C. & Head, M. R. 1969 Some observations on skin friction and velocity profiles in fully developed pipe and channel flows. J. Fluid Mech. 38, 181–201.10.1017/S0022112069000115Google Scholar
Pfenninger, W. 1961 Boundary layer suction experiments with laminar flow at high Reynolds numbers in the inlet length of a tube by various suction methods. In Boundary Layer and Flow Control (ed. Lachmann, G. V.), pp. 961–980. Pergamon.10.1016/B978-1-4832-1323-1.50013-0Google Scholar
Pinho, F. T. & Whitelaw, J. H. 1990 Flow of non-Newtonian fluids in a pipe. J. Non-Newtonian Fluid Mech. 34, 129–144.10.1016/0377-0257(90)80015-RGoogle Scholar
Poole, R. J. 2012 The Deborah and Weissenberg numbers. Brit. Soc. Rheol. 53, 32–39.Google Scholar
Poole, R. J. 2016 Elastic instabilities in parallel shear flows of a viscoelastic shear-thinning liquid. Phys. Rev. Fluids 1, 041301.10.1103/PhysRevFluids.1.041301Google Scholar
Reynolds, O. 1883 An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels. Proc. R. Soc. Lond. 35, 84–99.Google Scholar
Samanta, D., Dubief, Y., Holzner, M., Schäfer, C., Morozov, A. N., Wagner, C. & Hof, B. 2013 Elasto-inertial turbulence. Proc. Natl Acad. Sci. USA 110, 10557–10562.10.1073/pnas.1219666110Google Scholar
Schiamberg, B. A., Shereda, L. T., Hu, H. & Larson, R. G. 2006 Transitional pathway to elastic turbulence in torsional, parallel-plate flow of a polymer solution. J. Fluid Mech. 554, 191–216.10.1017/S0022112006009426Google Scholar
Schmid, P. J. & Henningson, D. S. 2001 Stability and Transition in Shear Flows. Springer.10.1007/978-1-4613-0185-1Google Scholar
Shaqfeh, E. S. G. 1996 Purely elastic instabilities in viscometric flows. Annu. Rev. Fluid Mech. 28, 129–185.10.1146/annurev.fl.28.010196.001021Google Scholar
Sharp, K. V. & Adrian, R. J. 2004 Transition from laminar to turbulent flow in liquid filled microtubes. Exp. Fluids 36, 741–747.10.1007/s00348-003-0753-3Google Scholar
Sid, S., Terrapon, V. E. & Dubief, Y. 2018 Two-dimensional dynamics of elasto-inertial turbulence and its role in polymer drag reduction. Phys. Rev. F 3, 011301(R).Google Scholar
Srinivas, S. S. & Kumaran, V. 2015 After transition in a soft-walled microchannel. J. Fluid Mech. 780, 649–686.10.1017/jfm.2015.476Google Scholar
Srinivas, S. S. & Kumaran, V. 2017 Effect of viscoelasticity on the soft-wall transition and turbulence in a microchannel. J. Fluid Mech. 812, 1076–1118.10.1017/jfm.2016.839Google Scholar
Terrapon, V. E., Dubief, Y. & Soria, J. 2013 On the role of pressure in elasto-inertial turbulence. J. Turbul. 16 (1), 26–43.10.1080/14685248.2014.952430Google Scholar
Toms, B. 1949 Observation on the flow of linear polymer solutions through straight tubes at large Reynolds numbers. In Proceedings of the 1st International Congress on Rheology (ed. Burgers, J. M.), vol. 2, pp. 135–141. North-Holland.Google Scholar
Verma, M. K. S. & Kumaran, V. 2012 A dynamical instability due to fluid wall coupling lowers the transition Reynolds number in the flow through a flexible tube. J. Fluid Mech. 705, 322–347.10.1017/jfm.2011.55Google Scholar
Virk, P. S. 1975 Drag reduction fundamentals. AIChE J. 21, 625–656.10.1002/aic.690210402Google Scholar
Virk, P. S., Merril, E. W., Mickly, H. S., Smith, K. A. & Christensen, E. 1967 The Toms phenomenon: turbulent pipe flow of dilute polymer solutions. J. Fluid Mech. 30, 305–328.10.1017/S0022112067001442Google Scholar
Wen, C., Poole, R. J., Willis, A. P. & Dennis, D. J. C. 2017 Experimental evidence of symmetry-breaking supercritical transition in pipe flow of shear-thinning fluids. Phys. Rev. Fluids 2, 031901.10.1103/PhysRevFluids.2.031901Google Scholar
White, M. C. & Mungal, M. G. 2008 Mechanics and prediction of turbulent drag reduction with polymer additives. Annu. Rev. Fluid Mech. 40, 235–256.10.1146/annurev.fluid.40.111406.102156Google Scholar
Zakin, J. L., Ni, C. C., Hansen, R. J. & Reischman, M. M. 1977 Laser Doppler velocimetry studies of early turbulence. Phys. Fluids 20 (10), S85–S88.10.1063/1.861763Google Scholar