Hostname: page-component-7dd5485656-wjfd9 Total loading time: 0 Render date: 2025-10-31T04:44:42.508Z Has data issue: false hasContentIssue false
  • English
  • Français

Rayleigh–Taylor instability in a viscoelastic binary fluid

Published online by Cambridge University Press:  15 January 2010

GUIDO BOFFETTA ,
ANDREA MAZZINO ,
STEFANO MUSACCHIO  and
LARA VOZELLA
GUIDO BOFFETTA*
Affiliation:
Department of General Physics, INFN and CNISM, University of Torino, via P. Giuria 1, 10125 Torino, Italy ISAC-CNR, Sezione di Torino, corso Fiume 4, 10132 Torino, Italy
ANDREA MAZZINO
Affiliation:
Department of Physics – University of Genova, and CNISM & INFN – Unit of Genova, via Dodecaneso 33, 16146 Genova, Italy
STEFANO MUSACCHIO
Affiliation:
Department of General Physics, INFN and CNISM, University of Torino, via P. Giuria 1, 10125 Torino, Italy
LARA VOZELLA
Affiliation:
Department of Physics – University of Genova, and CNISM & INFN – Unit of Genova, via Dodecaneso 33, 16146 Genova, Italy
*
†Email address for correspondence: boffetta@to.infn.it
Get access Rights & Permissions [Opens in a new window]

Abstract

The effects of polymer additives on Rayleigh–Taylor (RT) instability of immiscible fluids is investigated using the Oldroyd-B viscoelastic model. Analytic results obtained exploiting the phase-field approach show that in polymer solution the growth rate of the instability speeds up with elasticity (but remains slower than in the pure solvent case). Numerical simulations of the viscoelastic binary fluid model confirm this picture.

Information

Type
Papers
Information
Journal of Fluid Mechanics , Volume 643 , 25 January 2010 , pp. 127 - 136
Copyright
Copyright © Cambridge University Press 2010

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.)

Article purchase

Temporarily unavailable

References

REFERENCES

Badalassi, V. E., Ceniceros, H. D. & Banerjee, S. 2003 Computation of multiphase systems with phase field models. J. Comput. Phys. 190, 371–397.Google Scholar
Berti, S., Boffetta, G., Cencini, M. & Vulpiani, A. 2005 Turbulence and coarsening in active and passive binary mixtures. Phys. Rev. Lett. 95, 224501-1–224501-4.Google Scholar
Bird, R. B., Hassager, O., Armstrong, R. C. & Curtiss, C. F. 1987 Dynamics of Polymeric Liquids. Wiley-Interscience.Google Scholar
Boffetta, G., Celani, A., Mazzino, A., Puliafito, A. & Vergassola, M. 2005 The viscoelastic Kolmogorov flow: eddy viscosity and linear stability. J. Fluid Mech. 523, 161–170.CrossRefGoogle Scholar
Boffetta, G., Mazzino, A., Musacchio, S. & Vozella, L. 2009 Kolmogorov scaling and intermittency in Rayleigh–Taylor turbulence. Phys. Rev. E 79, 065301-1–065301-4.Google Scholar
Bray, A. J. 2002 Theory of phase-ordering kinetics. Adv. Phys. 51, 481–587.CrossRefGoogle Scholar
Cabot, W. H. & Cook, A. W. 2006 Reynolds number effects on Rayleigh–Taylor instability with possible implications for type Ia supernovae. Nature Phys. 2, 562–568.CrossRefGoogle Scholar
Cahn, J. W. & Hilliard, J. E. 1958 Free energy of a non uniform system. J. Chem. Phys. 28, 258–267.Google Scholar
Celani, A., Mazzino, A., Muratore–Ginanneschi, P. & Vozella, L. 2009 Phase-field model for the Rayleigh–Taylor instability of immiscible fluids. J. Fluid Mech. 622, 115–134.Google Scholar
Celani, A., Mazzino, A. & Vozella, L. 2006 Rayleigh–Taylor turbulence in two-dimensions. Phys. Rev. Lett. 96, 134504-1–134504-4.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Dover.Google Scholar
Cook, A. W. & Zhou, Y. 2002 Energy transfer in Rayleigh–Taylor instability. Phys. Rev. E 66, 026312-1–026312-12.CrossRefGoogle Scholar
Coussot, P. 1999 Saffman–Taylor instability in yield-stress fluids. J. Fluid Mech. 380, 363–376.CrossRefGoogle Scholar
Dimotakis, P. E. 2005 Turbulent mixing. Annu. Rev. Fluid. Mech. 37, 329–356.CrossRefGoogle Scholar
Ding, H., Spelt, P. D. M. & Shu, C. 2007 Diffuse interface model for incompressible two-phase flows with large density ratios. J. Comput. Phys. 226, 2078–2095.CrossRefGoogle Scholar
Doi, M. & Edwards, S. F. 1986 The Theory of Polymer Dynamics. Oxford University Press.Google Scholar
Drazin, P. G. & Reid, W. D. 1981 Hydrodynamic Stability. Cambridge University Press.Google Scholar
Frisch, U. 1995 Turbulence. The legacy of A. N. Kolmogorov. Cambridge University Press.CrossRefGoogle Scholar
Groisman, A. & Steinberg, V. 1996 Couette–Taylor flow in dilute polymer solutions. Phys. Rev. Lett. 77, 1480–1483.Google Scholar
Hinch, E. J. 1977 Mechanical models of dilute polymer solutions in strong flows. Phys. Fluids 20, S22–S30.Google Scholar
Joseph, D. D., Beavers, G. S. & Funada, T. 2002 Rayleigh–Taylor instability of viscoelastic drops at high Weber numbers. J. Fluid Mech. 453, 109–132.Google Scholar
Kundu, P. K. & Cohen, I. M. 2001 Fluids Mechanics, 2nd edn. Academic Press.Google Scholar
Landau, L. D. & Lifshitz, E. M. 2000 Fluid Mechanics Volume 6 of Course of Theoretical Physics, 2nd edn Revised. Butterworth Heinemann.Google Scholar
Larson, R. G., Shaqfeh, E. S. & Muller, S. J. 1990 A purely elastic instability in Taylor–Couette flow. J. Fluid Mech. 218, 537–600.Google Scholar
Liu, C. & Shen, J. 2003 A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method. Physica D 179, 211–228.Google Scholar
Menikoff, R., Mjolsness, R. C., Sharp, D. H. & Zemach, C. 1977 Unstable normal mode for Rayleigh–Taylor instability in viscous fluids. Phys. Fluids 20 (12), 2000–2004.CrossRefGoogle Scholar
Mikaelian, K. O. 1993 Effect of viscosity on Rayleigh–Taylor and Richtmyer–Meshkov instabilities. Phys. Rev. E 47, 375–383.Google Scholar
Morro, A. 2007 Phase-field models for fluid mixtures. Math. Comput. Model. 45, 1042–1052.Google Scholar
Muller, H. W. & Zimmermann, W. 1999 Faraday instability in a linear viscoelastic fluid. Europhys. Lett. 45, 169–174.Google Scholar
Oldroyd, J. G. 1950 On the formulation of rheological equations of state. Proc. R. Soc. Lond. Ser. A 200, 523–541.Google Scholar
Rayleigh, Lord 1883 Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density. Proc. Lond. Math. Soc. 14, 170–177.Google Scholar
Sharma, R. C. & Rajput, A. 1992 Rayleigh–Taylor instability of viscoelastic fluids with suspended particles in porous medium in hydromagnetics. Czech. J. Phys. 42, 919–926.Google Scholar
Siggia, E. D. 1994 High Rayleigh number convection. Annu. Rev. Fluid. Mech. 26, 137–168.CrossRefGoogle Scholar
Sokolov, M. & Tanner, R. I. 1972 Convective stability of a general viscoelastic fluid heated from below. Phys. Fluids 15, 534–539.Google Scholar
Taylor, G. I. 1950 The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. Proc. R. Soc. A 201, 192–197.Google Scholar
Toms, B. A. 1949 Observation on the flow of linear polymer solutions through straight tubes at large Reynolds numbers. Proc. First Intl Congr. Rheol. 2, 135–141.Google Scholar
Vest, C. M. & Arpaci, V. S. 1969 Overstability of a viscoelastic fluid layer heated from below. J. Fluid Mech. 36, 613–623.CrossRefGoogle Scholar
Virk, P. S. 1975 Drag reduction fundamentals. AIChE J. 21, 625–656.Google Scholar
Vladimirova, N. & Chertkov, M 2009 Self-similarity and universality in Rayleigh–Taylor, Boussinesq turbulence. Phys. Fluids 21, 015102-1–015102-9.Google Scholar
Wagner, C., Muller, H. W. & Knorr, K. 1999 Faraday waves on a viscoelastic liquid. Phys. Rev. Lett. 83, 308–311.Google Scholar
Warnatz, J., Maas, U. & Dibble, R. W. 2001 Combustion: Physical and Chemical Fundamentals, Modeling and Simulation, Experiments, Pollutant Formation. Springer.Google Scholar
Wilson, S. D. R. 1990 The Taylor–Saffman problem for a non-Newtonian liquid. J. Fluid Mech. 220, 413–425.CrossRefGoogle Scholar
Yue, P., Feng, J. J., Liu, C. & Shen, J. 2004 A diffuse-interface method for simulating two-phase flows of complex fluids. J. Fluid Mech. 515, 293–317.CrossRefGoogle Scholar