Stability of miscible core-annular flows with viscosity stratification

Journal of Fluid Mechanics

Volumn 592, Issue , 2007, Pages 23-49

  Selvam, B ^a   Merk, S ^a   Govindarajan, Rama ^b   Meiburg, E ^a  

^a University of California   (United States)

^b JAWAHARLAL NEHRU CENTRE FOR ADVANCED SCIENTIFIC RESEARCH   (India)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CHANNEL FLOW; PIPE FLOW; REYNOLDS NUMBER; VISCOSITY;

CORE-ANNULAR FLOWS; MISCIBLE FLOWS; SCHMIDT NUMBERS; VISCOSITY STRATIFICATION; VISCOUS FLUID;

VISCOUS FLOW;

APPROXIMATION THEORY; CHANNEL FLOW; PIPE FLOW; REYNOLDS NUMBER; VISCOSITY; VISCOUS FLOW;

CHANNEL FLOW; FLOW STABILITY; PIPE FLOW; REYNOLDS NUMBER; STRATIFICATION; VISCOSITY;

EID: 36348962351     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112007008269     Document Type: Article

References (48)

1. BAI, R., CHEN, K. P. & JOSEPH, D. D. 1992 Lubricated pipelining: Stability of core-annular flow. Part 5. Experiments and comparison with theory. J. Fluid Mech. 240, 97.
2. BALASUBRAMANIAM, R., RASHIDNIA, N., MAXWORTHY, T. & KUANG, J. 2005 Instability of miscible interfaces in a cylindrical tube. Phys. Fluids 17, 052103.
3. BOOMKAMP, P. A. M. & MIESEN, R. H. M. 1996 Classification of instabilities in parallel two-phase flow. Intl J. Multiphase Flow 22, 67.
4. CHARRU, F. & HINCH, E. J. 2000 'Phase diagram' of interracial instabilities in a two-layer Couette flow and mechanism for the long-wave instability. J. Fluid Mech. 414, 195.
5. CHEN, C.-Y. & MEIBURG, E. 1996 Miscible displacement in capillary tubes. Part 2. Numerical simulations. J. Fluid Mech. 326, 57.
6. CHEN, K. P. 1993 Wave formation in a gravity-driven low Reynolds number flow of two liquid films down an inclined plane. Phys. Fluids A 5, 3038.
7. Cox, B. G. 1962 On driving a viscous fluid out of a tube. J. Fluid. Mech. 14, 81.
8. DRAZIN, P. G. & REID, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
9. ERN, P., CHARRU, F. & LUCHINI, P. 2003 Stability analysis of a shear flow with strongly stratified viscosity. J. Fluid Mech. 496, 295.
10. GOVINDARAJAN, R. 2004 Effect of miscibility on the linear instability of two-fluid channel flow. Intl J. Multiphase Flow 30, 1177.
11. GOVINDARAJAN, R., L'vov, V. S. & PROCACCIA, I. 2001 Retardation of the onset of turbulence by minor viscosity contrasts. Phys. Rev. Lett. 87, 174501.
12. GOYAL, N. & MEIBURG, E. 2006 Miscible displacements in Hele-Shaw cells: Two-dimensional base states and their linear stability. J. Fluid Mech. 558, 329.
13. HICKOX, C. E. 1971 Instability due to viscosity and density stratification in axisymmetric pipe flow. Phys. Fluids 14, 251.
14. HINCH, E. J. 1984 A note on the mechanism of the instability at the interface between two shearing fluids. J. Fluid Mech. 144 463.
15. HOOPER, A. P. & BOYD, W. G. C. 1983 Shear-flow instability at the interface between two fluids. J. Fluid Mech. 128, 507.
16. HU, H. H. & JOSEPH, D. D. 1989 Lubricated pipelining: Stability of core-annular flow. Part 2. J. Fluid Mech. 205, 359.
17. HU, H. H. & PATANKAR, N. 1995 Non-axisymmetric instability of core-annular flow. J. Fluid Mech. 290, 213.
18. HU, H. H., LUNDGREN, T. S. & JOSEPH, D. D. 1990 Stability of core-annular flow with a small viscosity ratio. Phys. Fluids A 2(11), 1945.
19. JIANG, W. Y., HELENBROOK, B. & LIN, S. P. 2004 Inertialess instability of a two-layer liquid film flow. Phys. Fluids 16 3), 652.
20. JOSEPH, D. D. & RENARDY, Y. Y. 1992 Fundamentals of Two-Fluid Dynamics. Part II: Lubricated Transport, Drops and Miscible Liquids. Springer.
21. JOSEPH, D. D., RENARDY, Y. & RENARDY, M. 1984 Instability of the flow of immiscible liquids with different viscosities in a pipe. J. Fluid Mech. 141, 319.
22. JOSEPH, D. D., BAI, R., CHEN, K. P. & RENARDY, Y. Y. 1997 Core - annular flows. Annu. Rev. Fluid Mech. 29, 65.
23. KHORRAMI, M. R. 1991 A Chebyshev spectral collocation method using a staggered grid for the stability of cylindrical flows. Intl J. Numer. Meth. Fluids 12, 825.
24. KHORRAMI, M. R., MALIK, M. R. & ASH, R. L. 1989 Application of spectral collocation techniques to the stability of swirling flows. J. Comput. Phys. 81, 206.
25. KOURIS, C. & TSAMOPOULOS, J. 2001a Core - annular flow in a periodically constricted circular tube. Part 1. Steady-state linear stability and energy analysis. J. Fluid Mech. 432, 31.
26. KOURIS, C. & TSAMOPOUIDS, J. 2001b Dynamics of axisymmetric core-annular flow in a straight tube. i. The more viscous fluid in the core, bamboo waves. Phys. Fluids 13(4), 841.
27. KOURIS, C. & TSAMOPOULOS, J. 2002a Core - annular flow in a periodically constricted circular tube. Part 2. Nonlinear dynamics. J. Fluid Mech. 470, 181.
28. KOURIS, C. & TSAMOPOULOS, J. 2002b Dynamics of axisymmetric core-annular flow in a straight tube. ii. The less viscous fluid in the core, saw tooth waves. Phys. Fluids 14(3), 1011.
29. KUANG, J., MAXWORTHY, T. & PETITJEANS, P. 2003 Miscible displacements between silicone oils in capillary tubes. Eur. J. Mech. 22, 271.
30. LI, J. & RENARDY, Y. Y. 1999 Direct simulation of unsteady axisymmetric core-annular flow with high viscosity ratio. J. Fluid Mech. 391, 123.
31. LOEWENHERZ, D. S. & LAWRENCE, C. J. 1989 The effect of viscosity stratification on the instability of a free surface flow at low Reynolds number. Phys. Fluids A 1, 1686.
32. MACK, I. M. 1976 A numerical study of the temporal eigenvalue spectrum of Blasius boundary layer flow. J. Fluid Mech. 73, 497.
33. MALIK, S. V. & HOOPER, A. P. 2005 Linear stability and energy growth of viscosity stratified flows. Phys. Fluids 17, 024101.
34. PANTON, R. L. 1984 Incompressible Flow. John Wiley.
35. PETITJEANS, P. & MAXWORTHY, T. 1996 Miscible displacements in capillary tubes. Part 1. Experiments. J. Fluid Mech. 326, 37.
36. PREZIOSI, L., CHEN, K. & JOSEPH, D. D. 1989 Lubricated pipelining: Stability of core-annular flow. J. Fluid Mech. 201, 323.
37. RANGANATHAN, B. T. & GOVINDARAJAN, R. 2001 Stabilization and destabilization of channel flow by the location of viscosity-stratified fluid layer. Phys. Fluids 13(1), 1-3.
38. RIAZ, A., PANKIEWITZ, C. & MEIBURG, E. 2004 Linear stability of radial displacements in porous media: Influence of velocity-induced dispersion and concentration-dependent diffusion. Phys. Fluids 16(10), 3592.
39. SAHU, K. C. & GOVINDARAJAN, R. 2005 Stability of flow through a slowly diverging pipe. J. Fluid Mech. 531, 325.
40. SCHMID, P. J. & HENNINGSON, D. S. 2001 Stability and Transition in Shear Flows. Springer.
41. SCOFFONI, J., LAJEUNESSE, E. & HOMSY, G. M. 2001 Interface instabilities during displacements of two miscible fluids in a vertical pipe. Phys. Fluids 13(3), 553.
42. SMITH, M. K. 1990 The mechanism for the long-wave instability in thin liquid films. J. Fluid Mech. 217, 469.
43. TAN, C. T. & HOMSY, G. M. 1986 Stability of miscible displacements: Rectilinear flow. Phys. Fluids 29, 73549.
44. TAYLOR, G. I. 1960 Deposition of a viscous fluid on the wall of a tube. J. Fluid Mech. 10, 161.
45. VANAPARTHY, S. H., BARTHE, C. & MEIBURG, E. 2006 Density-driven instabilities in capillary tubes: Influence of a variable diffusion coefficient. Phys. Fluids 18, 048101.
46. WEI, H. H. & RUMSCHITZKI, D. S. 2002a The linear stability of a core-annular flow in an asymptotically corrugated tube. J. Fluid Mech. 466, 113.
47. WEI, H. H. & RUMSCHITZKI, D. S. 2002b The weakly nonlinear interfacial stability of a core-annular flow in a corrugated tube. J. Fluid Mech. 466, 149.
48. YIH, C.-S. 1967 Instability due to viscous stratification. J. Fluid Mech. 27, 337.