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Early transition, relaminarization and drag reduction in the flow of polymer solutions through microtubes

  • Bidhan Chandra (a1), V. Shankar (a1) and Debopam Das (a2)


Experiments are performed to investigate the onset of early transition and drag reduction in the flow of polymer (polyacrylamide and polyethylene oxide) solutions through rigid microtubes of diameters in the range 0.49–2.84 mm. We measure friction factor variation with Reynolds number for varying polymer concentrations and tube diameters, and the Reynolds number, $Re_{t}$ , at which the experimental data deviate from the laminar value represents the onset of transition. Crucially, owing to the high shear rates encountered in our experiments, we show that it is important to account for shear thinning of the fluid in the theoretical estimation of the friction factor in the laminar regime. We accomplish this using a Carreau model, and show that the use of laminar friction factor calculated without shear thinning leads to an erroneous overestimation of $Re_{t}$ . The $Re_{t}$ obtained from friction factor data in the present study is in good agreement with that inferred using micro particle image velocimetry analysis in Chandra et al. (J. Fluid Mech., vol. 844, 2018, pp. 1052–1083). For smaller concentrations of the added polymer, there is a marginal delay in the onset of turbulence, but as the concentration is increased further, the transition Reynolds number decreases much below $2000$ , the usual value at which transition occurs in Newtonian pipe flows. Thus, the present study further corroborates the phenomenon of early transition leading to an ‘elasto-inertial’ turbulent state in the flow of polymer solutions. For concentrations such that there is a delay in transition, if $Re$ is maintained above the $Re_{t}$ for Newtonian fluids, the flow is transitional or turbulent in the absence of polymers. At such a fixed $Re$ , if the concentration of the polymer is increased gradually, the friction factor decreases and the flow relaminarizes. With further increase in polymer concentration, the flow undergoes a transition due to elasto-inertial instability. The effect of addition of small amounts of polymer on turbulent drag reduction in the flow of water through microtubes is also investigated. Increase in polymer concentration, molecular weight and decrease in tube diameter causes an increase in drag reduction. The friction factor data for different polymer concentrations, molecular weights, tube diameters and $Re$ , when plotted with $Wi(1-\unicode[STIX]{x1D6FD})$ , show a reasonable collapse, where $Wi$ is the Weissenberg number defined as the product of the longest relaxation time of the polymer solution and the average shear rate in the tube and $\unicode[STIX]{x1D6FD}$ is the ratio of solvent to total solution viscosity. Interestingly, the onset of the maximum drag reduction asymptote, for experiments using varying tube diameters and polymer concentrations, appears to occur at $Wi(1-\unicode[STIX]{x1D6FD})\sim O(1)$ .


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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.
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.
Chandra, B., Shankar, V. & Das, D. 2018 Onset of transition in the flow of polymer solutions through microtubes. J. Fluid Mech. 844, 10521083.
Choueiri, G. H., Lopez, J. M. & Hof, B. 2018 Exceeding the asymptotic limit of polymer drag reduction. Phys. Rev. Lett. 120, 124501.
Dinic, J., Zhang, Y., Jimenez, L. N. & Sharma, V. 2015 Extensional relaxation times of dilute, aqueous polymer solutions. ACS Macro Lett. 4, 804808.
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, 267312.
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
Dubief, Y., Terrapon, V. E. & Soria, J. 2013 On the mechanism of elasto-inertial turbulence. Phys. Fluids 25 (11), 110817.
Eckhardt, B., Schneider, T. M., Hof, B. & Westerweel, J. 2007 Turbulence transition in pipe flow. Annu. Rev. Fluid Mech. 39 (1), 447468.
Escudier, M. P., Nickson, A. K. & Poole, R. J. 2009 Turbulent flow of viscoelastic shear-thinning liquids through a rectangular duct: quantification of turbulence anisotropy. J. Non-Newtonian Fluid Mech. 160 (1), 210.
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), 143155.
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), 213217.
Garg, P., Chaudhary, I., Khalid, M., Shankar, V. & Subramanian, G. 2018 Viscoelastic pipe flow is linearly unstable. Phys. Rev. Lett. 121, 024502.
Gasljevic, K., Aguilar, G. & Matthys, E. F. 1999 An improved diameter scaling correlation for turbulent flow of drag-reducing polymer solutions. J. Non-Newtonian Fluid Mech. 84 (2), 131148.
Gasljevic, K., Aguilar, G. & Matthys, E. F. 2001 On two distinct types of drag-reducing fluids, diameter scaling, and turbulent profiles. J. Non-Newtonian Fluid Mech. 96, 405425.
Graham, M. D. 2004 Drag reduction in turbulent flow of polymer solutions. Rheol. Rev. 2, 143170.
Graham, M. D. 2014 Drag reduction and the dynamics of turbulence in simple and complex fluids. Phys. Fluids 26, 101301.
Hansen, R. J., Little, R. C. & Forame, P. G. 1973 Experimental and theoretical studies of early turbulence. J. Chem. Engng Japan 6 (4), 310314.
Hinch, E. J. 1977 Mechanical models of dilute polymer solutions in strong flows. Phys. Fluids 20 (10), S22S30.
Housiadas, K. D. & Beris, A. N. 2013 On the skin friction coefficient in viscoelastic wall-bounded flows. Intl J. Heat Fluid Flow 42, 4967.
Jackson, D. & Launder, B. 2007 Osborne Reynolds and the publication of his papers on turbulent flow. Annu. Rev. Fluid Mech. 39, 1935.
Lee, D. H. & Akhavan, R. 2009 Scaling of polymer drag reduction with polymer and flow parameters in turbulent channel flow. In Advances in Turbulence XII (ed. Eckhardt, B.), pp. 359362. Springer.
Neelamegam, R. & Shankar, V. 2015 Experimental study of the instability of laminar flow in a tube with deformable walls. Phys. Fluids 27, 043305.
Oliver, D. R. & Bakhtiyarov, S. I. 1983 Drag reduction in exceptionally dilute polymer solutions. J. Non-Newtonian Fluid Mech. 12 (1), 113118.
Owolabi, B. E., Dennis, D. J. C. & Poole, R. J. 2017 Turbulent drag reduction by polymer additives in parallel-shear flows. J. Fluid Mech. 827, R4.
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.
Park, J. T., Mannheimer, R. J., Grimley, T. A. & Morrow, T. B. 1989 Pipe flow measurements of a transparent non-Newtonian slurry. J. Fluids Engng 111 (3), 331336.
Poole, R. J. 2016 Elastic instabilities in parallel shear flows of a viscoelastic shear-thinning liquid. Phys. Rev. Fluids 1, 041301.
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, 8499.
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, 1055710562.
Sharp, K. V. & Adrian, R. J. 2004 Transition from laminar to turbulent flow in liquid filled microtubes. Exp. Fluids 36, 741747.
Shekar, A., McMullen, R. M., Wang, S. N., McKeon, B. J. & Graham, M. D. 2019 Critical-layer structures and mechanisms in elastoinertial turbulence. Phys. Rev. Lett. 122, 124503.
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).
Sreenivasan, K. R. & White, C. M. 2000 The onset of drag reduction by dilute polymer additives, and the maximum drag reduction asymptote. J. Fluid Mech. 409, 149164.
Srinivas, S. S. & Kumaran, V. 2017 Effect of viscoelasticity on the soft-wall transition and turbulence in a microchannel. J. Fluid Mech. 812, 10761118.
Toms, B. 1948 Observation on the flow of linear polymer solutions through straight tubes at large Reynolds numbers. In Proceedings of the 1st International Congress on Rheology, vol. 2, pp. 135141. North-Holland.
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, 322347.
Virk, P. S. 1975 Drag reduction fundamentals. AIChE J. 21, 625656.
Virk, P. S., Merrill, E. W., Mickley, H. S., Smith, K. A. & Mollo-Christensen, E. L. 1967 The Toms phenomenon: turbulent pipe flow of dilute polymer solutions. J. Fluid Mech. 30 (2), 305328.
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.
White, C. M., Somandepalli, V. S. R. & Mungal, M. G. 2004 The turbulence structure of drag-reduced boundary layer flow. Exp. Fluids 36, 6269.
White, M. C. & Mungal, M. G. 2008 Mechanics and prediction of turbulent drag reduction with polymer additives. Annu. Rev. Fluid Mech. 40, 235256.
Xi, L. & Graham, M. D. 2010 Turbulent drag reduction and multistage transitions in viscoelastic minimal flow units. J. Fluid Mech. 647, 421452.
Zakin, J. L., Ni, C. C., Hansen, R. J. & Reischman, M. M. 1977 Laser Doppler velocimetry studies of early turbulence. Phys. Fluids 20 (10), S85S88.
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Early transition, relaminarization and drag reduction in the flow of polymer solutions through microtubes

  • Bidhan Chandra (a1), V. Shankar (a1) and Debopam Das (a2)


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