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Linear stability of double-diffusive two-fluid channel flow

Published online by Cambridge University Press:  14 October 2011

Kirti Chandra Sahu  and
Rama Govindarajan
Kirti Chandra Sahu*
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology Hyderabad, Yeddumailaram 502 205, India
Rama Govindarajan
Affiliation:
Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560 064, India
*
†Email address for correspondence: [email protected]
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Abstract

Double-diffusive density stratified systems are well studied and have been shown to display a rich variety of instability behaviour. However double-diffusive systems where the inhomogeneities in solute concentration are manifested in terms of stratified viscosity rather than density have been studied far less and, to the best of the authors’ knowledge, not in high-Reynolds-number shear flows. In a simple geometry, namely the two-fluid channel flow of such a system, we find a new double-diffusive mode of instability. The instability becomes stronger as the ratio of diffusivities of the two scalars increases, even in a situation where the net Schmidt number decreases. The double-diffusive mode is destabilized when the layer of viscosity stratification overlaps with the critical layer of the perturbation.

JFM classification

Convection: Double diffusive convection Multiphase and Particle-laden Flows: Multiphase flow Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 687 , 25 November 2011 , pp. 529 - 539
Copyright
Copyright © Cambridge University Press 2011

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References

1. Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, T. A. 1987 Spectral Methods in Fluid Dynamics, 1st edn. Springer.Google Scholar
2. Drazin, P. G. & Reid, W. H. 1985 Hydrodynamic Stability. Cambridge University Press.Google Scholar
3. Ern, P., Charru, F. & Luchini, P. 2003 Stability analysis of a shear flow with strongly stratified viscosity. J. Fluid Mech. 496, 295.CrossRefGoogle Scholar
4. Govindarajan, R 2004 Effect of miscibility on the linear instability of two-fluid channel flow. Intl J. Multiphase Flow 30, 1177–1192.CrossRefGoogle Scholar
5. Govindarajan, R., L’vov, S. V. & Procaccia, I. 2001 Retardation of the onset of turbulence by minor viscosity contrasts. Phys. Rev. Lett. 87, 174501.CrossRefGoogle ScholarPubMed
6. Grosfils, P, Dubois, F., Yourassowsky, C. & De Wit, A. 2009 Hot spots revealed by simultaneous experimental measurement of the two-dimensional concentration and temperature fields of an exothermic chemical front during finger-pattern formation. Phys. Rev. E 79, 017301.CrossRefGoogle ScholarPubMed
7. Hejazi, S. H., Trevelyan, P. M. J., Azaiez, J. & De Wit, A. 2010 Viscous fingering of a miscible reactive a + b→c interface: a linear stability analysis. J. Fluid Mech. 652, 501–528.CrossRefGoogle Scholar
8. Hinch, E. J. 1984 A note on the mechanism of the instability at the interface between two shearing fluids. J. Fluid Mech. 144, 463–465.CrossRefGoogle Scholar
9. Huppert, H. E. 1971 On the stability of a series of double-diffusive layers. Deep-Sea Res. Oceanogr. Abstr. 18 (10), 1005–1021.CrossRefGoogle Scholar
10. Joseph, D. D., Bai, R., Chen, K. P. & Renardy, Y. Y. 1997 Core-annular flows. Ann. Rev. Fluid Mech. 29, 65.CrossRefGoogle Scholar
11. Lin, C. C. 1945 On the stability of two dimensional parallel flows Part III – stablilty in a viscous fluid. Q. Appl. Maths III, 277–301.Google Scholar
12. Malik, S. V. & Hooper, A. P. 2005 Linear stability and energy growth of viscosity stratified flows. Phys. Fluids 17, 024101.CrossRefGoogle Scholar
13. May, B. D. & Kelley, D. E. 1997 Effect of baroclinicity on double-diffusive interleaving. J. Phys. Oceanogr. 27, 1997–2008.2.0.CO;2>CrossRefGoogle Scholar
14. Mishra, M, Trevelyan, P. M. J., Almarcha, C & De Wit, A. 2010 Influence of double diffusive effects on miscible viscous fingering. Phys. Rev. Lett. 105, 204501.CrossRefGoogle ScholarPubMed
15. Nagatsu, Y., Matsuda, K., Kato, Y. & Tada, Y. 2007 Experimental study on miscible viscous fingering involving viscosity changes induced by variations in chemical species concentrations due to chemical reactions. J. Fluid Mech. 571, 475–493.CrossRefGoogle Scholar
16. Podgorski, T, Sostarecz, M. C., Zorman, S & Belmonte, A 2007 Fingering instabilities of a reactive micellar interface. Phys. Rev. E 76, 016202.CrossRefGoogle ScholarPubMed
17. Pritchard, D. 2004 The instability of thermal and fluid fronts during radial injection in a porous medium. J. Fluid Mech. 508, 133–163.CrossRefGoogle Scholar
18. Pritchard, D. 2009 The linear stability of double-diffusive miscible rectilinear displacements in a Hele-Shaw cell. Eur. J. Mech. (B/Fluids) 28 (4), 564–577.CrossRefGoogle Scholar
19. Ranganathan, B. T. & Govindarajan, R. 2001 Stabilisation and destabilisation of channel flow by location of viscosity-stratified fluid layer. Phys. Fluids 13 (1), 1–3.CrossRefGoogle Scholar
20. Rayleigh, L. 1880 On the stability of certain fluid motions. Proc. Lond. Math. Soc. 11, 57–70.Google Scholar
21. Sahu, K. C., Ding, H. & Matar, O. K. 2010 Numerical simulation of non-isothermal pressure-driven miscible channel flow with viscous heating. Chem. Engng Sci. 65, 3260–3267.CrossRefGoogle Scholar
22. Sahu, K. C., Ding, H., Valluri, P. & Matar, O. K. 2009 Linear stability analysis and numerical simulation of miscible channel flows. Phys. Fluids 21, 042104.CrossRefGoogle Scholar
23. Schmid, P. J. & Henningson, D. S. 2001 Stability and Transition in Shear Flows. Springer.CrossRefGoogle Scholar
24. Selvam, B, Merk, S, Govindarajan, R & Meiburg, E 2007 Stability of miscible core-annular flows with viscosity stratification. J. Fluid Mech. 592, 23–49.CrossRefGoogle Scholar
25. South, M. J. & Hooper, A. P. 1999 Linear growth in two-fluid plane Poiseuille flow. J. Fluid Mech. 381, 121–139.CrossRefGoogle Scholar
26. Swernath, S & Pushpavanam, S 2007 Viscous fingering in a horizontal flow through a porous medium induced by chemical reactions under isothermal and adiabatic conditions. J. Chem. Phys. 127, 204701.CrossRefGoogle Scholar
27. Turner, J. S. 1974 Double-diffusive phenomena. Annu. Rev. Fluid Mech. 6, 37–54.CrossRefGoogle Scholar