Density-driven instabilities of miscible fluids in a capillary tube: Linear stability analysis

Journal of Fluid Mechanics

Volumn 497, Issue , 2003, Pages 99-121

  Vanaparthy, Surya Harith ^a   Meiburg, E ^a   Wilhelm, D ^a  

^a University of California   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CAPILLARY TUBES; DIFFUSION; PERTURBATION TECHNIQUES;

RAYLEIGH NUMBER;

FLUID MECHANICS;

CAPILLARY TUBE; DENSITY; EXPERIMENTAL STUDY; FLUID MECHANICS; INSTABILITY; MATHEMATICAL METHOD; MISCIBLE DISPLACEMENT;

EID: 0842284585     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112003006499     Document Type: Article

References (25)

1. BATCHELOR, G. K. & NITSCHE, J. M. 1991 Instability of stationary unbounded stratified fluid. J. Fluid Mech 227, 357.
2. BATCHELOR, G. K. & NITSCHE, J. M. 1993 Instability of stratified fluid in a vertical cylinder. J. Fluid Mech 252, 419.
3. CHEN, C.-Y. & MEIBURG, E. 1996 Miscible displacements in capillary tubes. Part 2. Numerical simulations. J. Fluid Mech. 326, 57.
4. CHEN, C.-Y. & MEIBURG, E. 2002 Miscible displacements in capillary tubes. Influence of Korteweg stresses and divergence effects. Phys. Fluids 14, 2052.
5. COX, B. G. 1962 On driving a viscous fluid out of a tube. J. Fluid Mech. 14, 81.
6. DEBACQ, M., FANGUET, V., HULIN, J. P. & SALIN, D. 2001 Self-similar concentration profiles in buoyant mixing of miscible fluids in a vertical tube. Phys. Fluids 13, 3097.
7. FERNANDEZ, J., KUROWSKI, P., PETITJEANS, P. & MEIBURG, E. 2002 Density-driven, unstable flows of miscible fluids in a Hele-Shaw cell. J. Fluid Mech. 451, 239.
8. FLETCHER, C. A. J. 1991 Computational Techniques for Fluid Dynamics. Springer.
9. GRAF, F., MEIBURG, E. & HÄRTEL, C. 2002 Density-driven instabilities of miscible fluids in a Hele-Shaw cell: Linear stability analysis of the three-dimensional Stokes equations. J. Fluid Mech. 451, 261.
10. HALES, A. L. 1937 Convection currents in geysers. Mon. Not. R. Astron. Soc., Geophys. Suppl. 4, 122.
11. JOSEPH, D. & RENARDY, Y. 1992 Fundamentals of Two-Fluid Dynamics. Springer.
12. KORTEWEG, D. 1901 Sur la forme que prennent les équations du mouvement des fluides si l'on tient compte des forces capillaires causées par des variations de densité. Arch. Neel. Sci. Ex. Nat. 11, 6.
13. KUANG, J., MAXWORTHY, T. & PETITJEANS, P. 2002 Miscible displacements in cylindrical tubes: velocity fields and streamline patterns. Eur. J. Mech. B 22, 271.
14. MASCHHOFF, M. J. & SORENSEN, D. C. 1996 P-ARPACK: An efficient portable large scale eigenvalue package for distributed memory parallel architectures. In Applied Parallel Computing in Industrial Problems and Optimization. Lecture Notes in Computer Science, vol. 1184. Springer.
15. PETITJEANS, P. & MAXWORTHY, T. 1996 Miscible displacements in capillary tubes. Part 1. Experiments. J. Fluid Mech. 326, 37.
16. REINELT, D. A. & SAFFMAN, P. G. 1985 The penetration of a finger into a viscous fluid in a channel and tube. SIAM J. Sci. Statist. Comput. 6, 542.
17. SCOFFONI, J., LAJEUNESSE, E. & HOMSY, G. M. 2000 Interface instabilities during displacements of two miscible fluids in a vertical pipe. Phys. Fluids 13. 553.
18. SOARES, E. J., CARVALHO, M. S. & SOUZA MENDES, P. R. 2002 Immiscible liquid-liquid displacement in capillary tubes. Preprint.
19. SORENSEN, D. C. 1992 Implicit application of polynomial filters in a k-step Arnoldi method. SIAM J. Matrix Anal. Appl. 13, 357.
20. TAYLOR, G. I. 1953 Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. Lond. A 219, 186.
21. TAYLOR, G. I. 1954 Diffusion and mass transport in tubes. Proc. Phys. Soc. B 67, 857.
22. TAYLOR, G. I. 1960 Deposition of a viscous fluid on the wall of a tube. J. Fluid Mech. 10, 161.
23. VERZICCO, R. & ORLANDI, P. A. 1996 A finite-difference scheme for three-dimensional incompressible flows in cylinder coordinates. J. Comput. Phys 123, 402.
24. WILHELM, D. & MEIBURG, E. 2003 Three-dimensional spectral element simulations of variable density and viscosity, miscible displacements in a capillary tube. Computers and Fluids (to appear).
25. WOODING, R. A. 1959 The stability of a viscous liquid in a vertical tube containing porous material. Proc. R. Soc. Lond. A 252, 120.