Three-dimensional convective and absolute instabilities in pressure-driven two-layer channel flow

International Journal of Multiphase Flow

Volumn 37, Issue 8, 2011, Pages 987-993

  Sahu, K C ^a   Matar, O K ^a,b  

^a INDIAN INSTITUTE OF TECHNOLOGY HYDERABAD   (India)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Immiscible fluids; Interfacial instability; Linear stability analysis; Multiphase flow; Three dimensional disturbances

Indexed keywords

EID: 79960924754     PISSN: 03019322     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijmultiphaseflow.2011.05.005     Document Type: Article

References (33)

1. Bers A. Space-time evolution of plasma instabilities - absolute and convective. Handbook of Plasma Physics 1983, vol. 1:451-517. North-Holland Publishing Company, Amsterdam, Amsterdam: North Holland.
2. Boomkamp P.A.M., Miesen R.H.M. Classification of instabilities in parallel two-phase flow. Int. J. Multiphase Flow 1996, 22:67.
3. Briggs R.J. Research Monograph No. 29 1964, MIT Press, Cambridge.
4. Canuto C., Hussaini M.Y., Quarteroni A., Zang T. Spectral Methods in Fluid Dynamics 1987, Springer-Verlag, Amsterdam. 1st ed.
5. Cao Q., Ventresca L., Sreenivas K.R., Prasad A.K. Instability due to viscosity stratification downstream of a centreline injector. Can. J. Chem. Eng. 2003, 81:913.
6. Chomaz J.-M. Global instabilities in spatially developing flows: non-normality and nonlinearity. Ann. Rev. Fluid Mech. 2005, 37:357-392.
7. Criminale W.O., Jackson T.L., Roslin R.D. Theory and Computation of Hydrodynamic Stability 2003, Cambridge University Press, Cambridge, UK.
8. Drazin P.G., Reid W.H. Hydrodynamic Stability 1985, Cambridge University Press, Cambridge.
9. Frigaard I.A. Super-stable parallel flows of multiple visco-plastic fluids. J. Non-Newt. Fluid Mech. 2001, 100:49-76.
10. Govindarajan R., L'vov S.V., Procaccia I. Retardation of the onset of turbulence by minor viscosity contrasts. Phys. Rev. Lett. 2001, 87:174501.
11. Hinch E.J. A note on the mechanism of the instability at the interface between shearing fluids. J. Fluid Mech. 1984, 144:463-465.
12. Hooper A.P., Boyd W.G.C. Shear flow instability at the interface between two fluids. J. Fluid Mech. 1983, 128:507.
13. Huerre P., Monkewitz P.A. Local and global instability in spatially developing flows. Ann. Rev. Fluid Mech. 1990, 22:473-537.
14. Joseph D.D., Bai R., Chen K.P., Renardy Y.Y. Core-annular flows. Ann. Rev. Fluid Mech. 1997, 29:65.
15. Kaiktsis L., Monkewitz P.A. Global destabilization of flow over a backward-facing step. Phys. Fluids 2003, 15(12):3647-3658.
16. Kao T.W., Park C. Experimental investigations of the stability of channel flows. Part 2. Two-layered co-current flow in a rectangular channel. J. Fluid Mech. 1972, 52:401-423.
17. Khomami B. Interfacial stability and deformation of two stratified power-law fluids in plane poiseuille flow. Part I. Stability analysis. J. Non-Newt. Fluid Mech. 1990, 36:289-303.
18. Khomami B. Interfacial stability and deformation of two stratified power-law fluids in plane poiseuille flow. Part II. Interface deformation. J. Non-Newt. Fluid Mech. 1990, 37:19-36.
19. Regner M., Henningsson M., Wiklund J., Östergren K., Trägårdh C. Predicting the displacement of yoghurt by water in a pipe using CFD. Chem. Eng. Technol. 2007, 30:844-853.
20. Malik S.V., Hooper A.P. Three-dimensional disturbances in channel flows. Phys. Fluids 2007, 19:052102.
21. Nouar C., Kabouya N., Dusek J., Mamou M. Modal and non-modal linear stability of the plane Bingham-Poiseuille flow. J. Fluid Mech. 2007, 577:211-239.
22. Sahu K.C., Ding H., Valluri P., Matar O.K. Linear stability analysis and numerical simulation of miscible channel flows. Phys. Fluids 2009, 21:042104.
23. Sahu K.C., Matar O.K. Three-dimensional linear instability in pressure-driven two-layer channel flow of a newtonian and a Herschel-Bulkley fluid. Phys. Fluids 2010, 22:112103.
24. Sahu K.C., Valluri P., Spelt P.D.M., Matar O.K. Linear instability of pressure-driven channel flow of a newtonian and Herschel-Bulkley fluid. Phys. Fluids 2007, 19:122101.
25. Schmid P.J., Henningson D.S. Stability and Transition in Shear Flows 2001, Springer, New York.
26. Selvam B., Merk S., Govindarajan R., Meiburg E. Stability of miscible core-annular flows with viscosity stratification. J. Fluid Mech. 2007, 592:23-49.
27. South M.J., Hooper A.P. Linear growth in two-fluid plane Poiseuille flow. J. Fluid Mech. 1999, 381:121-139.
28. Squire H.B. On the stability for three-dimensional disturbances of viscous fluid flow between parallel walls. Proc. Roy. Soc. Lond. Ser. A 1933, 142:621-628.
29. Valluri P., Naraigh L.O., Ding H., Spelt P.D.M. Linear and nonlinear spatio-temporal instability in laminar two-layer flows. J. Fluid Mech. 2010, 656:458-480.
30. Vihinen I., Honohan A.M., Lin S.P. Image of absolute instability in a liquid jet. Phys. Fluids 1997, 9(11):3117-3119.
31. Yiantsios S.G., Higgins B.G. Linear stability of plane Poiseuille flow of two superposed fluids. Phys. Fluids 1988, 31:3225-3238.
32. Yiantsios S.G., Higgins B.G. Numerical solution of eigenvalue problems using the compound matrix-method. J. Comput. Phys. 1988, 74:25.
33. Yih C.S. Instability due to viscous stratification. J. Fluid Mech. 1967, 27:337.