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Colloquium: Theory of drag reduction by polymers in wall-bounded turbulence
Rev. Mod. Phys. 80, 225 – Published 2 January, 2008
DOI: https://doi.org/10.1103/RevModPhys.80.225
Abstract
The flow of fluids in channels, pipes, or ducts, as in any other wall-bounded flow (like water along the hulls of ships or air on airplanes) is hindered by a drag, which increases manyfold when the fluid flow turns from laminar to turbulent. A major technological problem is how to reduce this drag in order to minimize the expense of transporting fluids like oil in pipelines, or to move ships in the ocean. It was discovered that minute concentrations of polymers can reduce the drag in turbulent flows by up to 80%. While experimental knowledge had accumulated over the years, the fundamental theory of drag reduction by polymers remained elusive for a long time, with arguments raging whether this is a “skin” or a “bulk” effect. In this Colloquium the phenomenology of drag reduction by polymers is summarized, stressing both its universal and nonuniversal aspects, and a recent theory is reviewed that provides a quantitative explanation of all the known phenomenology. Both flexible and rodlike polymers are treated, explaining the existence of universal properties like the maximum drag reduction asymptote, as well as nonuniversal crossover phenomena that depend on the Reynolds number, on the nature of the polymer and on its concentration. Finally other agents for drag reduction are discussed with a stress on the important example of bubbles.
Article Text
References (65)
- Amarouchene, Y., D. Bonn, H. Kellay, T. S. Lo, V. S. L’vov, and I. Procaccia, 2007, e-print arXiv:nlin.CD/0607006.
- Bellakhel, G., J. Chahed, and L. Masbernat, 2004, J. Turbul. 5, 036.
- Benzi R., E. Ching, N. Horesh, and I. Procaccia, 2004, Phys. Rev. Lett. 92, 078302.
- Benzi, R., E. S. C. Ching, T. S. Lo, V. S. L’vov, and I. Procaccia, 2005, Phys. Rev. E 72, 016305.
- Benzi, R., E. De Angelis, V. S. L’vov, and I. Procaccia, 2005, Phys. Rev. Lett. 95, 194502.
- Benzi, R., E. De Angelis, V. S. L’vov, I. Procaccia, and V. Tiberkevich, 2006, J. Fluid Mech. 551, 185.
- Benzi, R., V. S. L’vov, I. Procaccia, and V. Tiberkevich, 2004, Europhys. Lett. 68, 825.
- Beris, A. N. and B. J. Edwards, 1994, Thermodynamics of Flowing Systems with Internal Microstructure (Oxford University Press, New York).
- Biesheuvel, A. and L. wan Wijngaarden, 1984, J. Fluid Mech. 148, 301.
- Bird, R. B., C. F. Curtiss, R. C. Armstrong, and O. Hassager, 1987, Dynamics of Polymeric Fluids (Wiley, New York).
- Bonn, D., Y. Amarouchńe, C. Wagner, S. Douady, and O. Cadot, 2005, J. Phys.: Condens. Matter 17, S1195.
- Brenner, H., 1974, Int. J. Multiphase Flow 1, 195.
- Ching, E. S. C., T. S. Lo, and I. Procaccia, 2006, Phys. Rev. E 74, 026301.
- Choi, H. J., S. T. Lim, P.-Y. Lai, and C. K. Chan, 2002, Phys. Rev. Lett. 89, 088302.
- De Angelis, E., C. M. Casciola, R. Benzi, and R. Piva, 2005, J. Fluid Mech. 531, 1.
- De Angelis, E., C. M. Casciola, V. S. L’vov, R. Piva, and I. Procaccia, 2003, Phys. Rev. E 67, 056312.
- De Angelis, E., C. Casciola, V. S. L’vov, A. Pomyalov, I. Procaccia, and V. Tiberkevich, 2004, Phys. Rev. E 70, 055301.
- de Gennes, P.-G., 1979, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, NY).
- de Gennes, P.-G., 1990, Introduction to Polymer Dynamcis (Cambridge University Press, Cambridge, England).
- den Toonder, J. M. J., F. T. M. Nieuwstadt, and G. D. C. KuiKen, 1995, Appl. Sci. Res. 54, 95.
- Dimitropousols, C. D., Y. Dubief, E. S. G. Shawfeh, P. Moin, and S. K. Lele, 2005, Phys. Fluids 17, 011705.
- Dimitropousols, C. D., S. Sureshkumar, and A. N. Beris, 1998, J. Non-Newtonian Fluid Mech. 79, 433.
- Doi, M. and S. F. Edwards, 1988, The Theory of Polymer Dynamics (Oxford University Press, New York).
- Escudier, M. P., P. Presti, and S. Smith, 1999, J. Non-Newtonian Fluid Mech. 81, 197.
- Ferrante, A. and S. Elghobashi, 2004, J. Fluid Mech. 503, 345.
- Flory, P. J., 1953 Principles of Polymer Chemistry (Cornell University Press, Ithaca, NY).
- Gyr, A. and H. W. Bewersdorff, 1995, Drag Reduction of Turbulent Flows by Additives (Kluwer Academic, Dordrecht, The Netherlands).
- Hinch, E. and L. Leal, 1975, J. Fluid Mech. 71, 481.
- Hinch, E. and L. Leal, 1976, J. Fluid Mech. 76, 187.
- Hoyt, J. W., 1972, J. Basic Eng. 94, 258.
- Kawamura, T. and Y. Kodama, 2002, Int. J. Heat Fluid Flow 23, 627.
- Kitagawa, A., K. Hishida, and Y. Kodama, 2005, Exp. Fluids 38, 466.
- Lamb, H., 1879, Hydrodynamics (Dover, New York) (reprinted 1945).
- Lance, M., J. L. Marie, and J. Bataille, 1991, ASME J. Fluids Eng. 113, 295.
- Landhal, M. T., 1973, in Proceedings of the 13th International Congress on Theoretical and Applied Mechanics (ICTAM), Moscow (USSR), edited by E. Becker and G. K. Mikhailov (Springer-Verlag, Berlin), p. 179.
- Legner, H. H., 1984, Phys. Fluids 27, 2788.
- Lo, T. S., V. S. L’vov, A. Pomyalov, and I. Procaccia, 2005, Europhys. Lett. 72, 943.
- Lo, T. S., Victor S. L’vov, and I. Procaccia, 2006, Phys. Rev. E 73, 036308.
- Lu, J., A. Fernandez, and G. Tryggvason, 2005, Phys. Fluids 17, 095102.
- Lumley, J. L., 1969, Annu. Rev. Fluid Mech. 1, 367.
- L’vov, V. S., A. Pomyalov, I. Procaccia, and V. Tiberkevich, 2004, Phys. Rev. Lett. 92, 244503.
- L’vov, S. V., A. Pomyalov, I. Procaccia, and V. Tiberkevich, 2005a, Phys. Rev. E 71, 016305.
- L’vov, V. S., A. Pomyalov, I. Procaccia, and V. Tiberkevich, 2005b, Phys. Rev. Lett. 94, 174502.
- L’vov, V. S., A. Pomyalov, and V. Tiberkevich, 2005, Environ. Fluid Mech. 5, 373.
- Manhart, M., 2003, J. Non-Newtonian Fluid Mech. 112, 269.
- McComb, W., 1990, The Fluid of Physics Turbulence (Oxford University Press, New York) (reprinted Clarendon, Oxford, 1992).
- Monin, A. S. and A. M. Yaglom, 1979, Statistical Fluid Mechanics (MIT, Cambridge, MA), Vol. 1, Chap. 3.
- Pope, S. B., 2000, Turbulent Flows (Cambridge University Press, Cambridge, England).
- Ptasinski, P. K., F. T. M. Niewstadt, B. H. A. A. van den Brule, and M. A. Hulsen, 2001, Flow, Turbul. Combust. 66, 159.
- Rollin, A. and F. A. Seyer, 1972, Can. J. Chem. Eng. 50, 714.
- Rudd, M. J., 1969, Nature (London) 224, 587.
- Ryskin, G., 1987, Phys. Rev. Lett. 59, 2059.
- Sangani, A. S. and A. K. Didwania, 1993, J. Fluid Mech. 248, 27.
- Sibila, S. and A. Baron, 2002, Phys. Fluids 14, 1123.
- Sreenivasan, K. R. and C. M. White, 2000, J. Fluid Mech. 409, 149.
- Toms, B. A., 1949, in Proceedings of the International Congress on Rheology (North-Holland, Amsterdam), p. 135.
- van den Berg, T. H., S. Luther, D. P. Lathrop, and D. Lohse, 2005, Phys. Rev. Lett. 94, 044501.
- Virk, P. S., 1975, AIChE J. 21, 625.
- Virk, P. S., D. C. Sherma, and D. L. Wagger, 1997, AIChE J. 43, 3257.
- Virk, P. S., D. L. Wagger, and E. Koury, 1996, Proceedings of ASME FED-237, 261.
- Wagner, C., Y. Amarouchène, P. Doyle, and D. Bonn, 2003, Europhys. Lett. 64, 823.
- Warholic, M. D., H. Massah, and T. J. Hanratty, 1999, Exp. Fluids 27, 461.
- Yu, B., Y. Kawaguchi, S. Takagi, and Y. Matsumoto, 2001, 7th Symposium on Smart Control of Turbulence, University of Tokyo.
- Zagarola, M. V. and A. J. Smits, 1997, Phys. Rev. Lett. 78, 239.
- Zhang, D. Z. and A. Prosperetti, 1994, Phys. Fluids 6, 2956.