Instabilities of the upstream meniscus in directional viscous fingering

Journal of Fluid Mechanics

Volumn 312, Issue , 1996, Pages 125-148

  Michalland, Sylvain ^a,b   Rabaud, Marc ^a,c   Couder, Yves ^a  

^a ECOLE NORMALE SUPÉRIEURE   (France)

^b MFPM   (France)

^c Centre National de la Recherche Scientifique   (France)

Author keywords

[No Author keywords available]

Indexed keywords

INSTABILITY; MENISCUS; VISCOUS FLOW;

FLOW OF FLUIDS; FLUIDS; STABILITY; WAVE PROPAGATION;

DIRECTIONAL VISCOUS FINGERING; MENISCUS; ONE DIMENSIONAL; SUPERCRITICAL TRANSITION;

VISCOSITY;

EID: 0030111534     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112096001942     Document Type: Article

References (32)

1. BRATTKUS, K. 1989 Capillary instabilities in deep cells during directional solidification. J. Phys. Paris 50, 2999-3006.
2. BRETHERTON, F. P. 1961 The motion of long bubbles in tubes. J. Fluid Mech. 10, 166-188.
3. COULLET, P. & Iooss, G. 1990 Instabilities of one-dimensional cellular patterns. Phys. Rev. Lett. 64, 866-869.
4. CROSS, M. C. & HOHENBERG, P. C. 1993 Pattern formation outside equilibrium. Rev. Mod. Phys. 65, 851-1112.
5. CUMMINS, H. Z., FOURTUNE, L. & RABAUD, M. 1993 Successive bifurcations in directional viscous fingering. Phys. Rev. E 47, 1727-1738.
6. DAVIAUD, F., BONNETTI, M. & DUBOIS, M. 1990 Transition to turbulence via spatiotemporal intermittency in one-dimensional Rayleigh-Bénard convection. Phvs. Rev. A 42. 3388-3399.
7. DECRÉ, M. 1994 Etude expérimentale des comportements de l'interface dans l'enduisage par rouleaux. Thèse de l'Université Paris VI.
8. DOUADY, S., FAUVE, S. & THUAL, O. 1989 Oscillatory phase modulation of parametrically forced surface waves. Europhys. Lett. 10, 309-315.
9. FAIVRE, G., DE CHEVEIGNÉ, S., GUTHMANN, C. & KUROWSKI, P. 1989 Solitary tilt waves in thin lamellar eutectics. Europhys. Lett. 9, 779-784.
10. FLESSELLES, J.-M., SIMON, A. J. & LIBCHABER, A. J. 1991 Dynamics of one-dimensional interfaces: an experimentalist's view. Adv. Phys. 40, 1-51.
11. GASKELL, P. H., SAVAGE, M. D., SUMMERS, J. L. & THOMPSON, H. M. 1995 Modelling and analysis of meniscus coating. J. Fluid Mech. 298, 113-137.
12. GOEDDE, E. F. & YUEN, M. C. 1970 Experiments on liquid jet instability. J. Fluid Mech. 40, 495-511.
13. HAKIM, V., RABAUD, M., THOMÉ, H. & COUDER, Y. 1990 Directional growth in viscous fingering. In New trends in Nonlinear Dynamics and Pattern Forming Phenomena (ed. P. Coullet & P. Huerre). pp. 327-337. Plenum.
14. JACKSON, K. A. & HUNT, J. D. 1965 Transparent compounds that freeze like metals. Acta Metall. 13, 1212-1215.
15. KUROWSKI, P., DE CHEVEIGNÉ, S., FAIVRE, G. & GUTHMANN, C. 1989 Cusp instability in cellular growth. J. Phys. Paris 50, 3007-3019.
16. KUROWSKI, P., DE CHEVEIGMÉ, S. & GUTHMANN, C. 1990 Shapes, wavelength-selection, and the cellular-dendritic "transition" in directional solidification. Phys. Rev. A 42, 7368-7376.
17. LIMAT, L., JENFFER, P., DAGENS, B., TOURON, E., FERMIGIER, M. & WESFREID, J. E. 1992 Gravitational instabilities of thin liquid layers: dynamics of pattern selection. Physica D 61, 166-182.
18. MELO, F. & DOUADY, S. 1993 From solitary waves to static patterns via spatiotemporal intermittency. Phys. Rev. Lett. 71, 3283-3286.
19. MICHALLAND, S. 1992 Etude des différents régimes dynamiques de l'instabilité de l'imprimeur. Thèse de l'Université Paris VI.
20. MICHALLAND, S., RABAUD, M. & COUDER, Y. 1993 Transition to chaos by spatio-temporal intermittency in directional viscous fingering. Europhys. Lett. 22, 17-22.
21. MOFFATT, H. K. 1977 Behaviour of a viscous film on the outer surface of a rotating cylinder. J. Méc. 16, 651-673.
22. OSWALD, P., BECHHOEFFER, J. & LIBCHABER, A. 1987 Instabilities of a moving nematic-isotropic interface. Phys. Rev. Lett. 58, 2318-2321.
23. PAN, L. & DE BRUYN, J. R. 1993 Spatially uniform travelling cellular patterns at a driven interface. Phvs. Rev. E 49, 483-493.
24. RABAUD, M., COUDER, Y. & MICHALLAND, S. 1991 Wavelength selection and transients in the one-dimensional array of cells of the printer's instability. Euro. J. Mech. B/Fluids 10, 253-260.
25. RABAUD, M., MICHALLAND, S. & COUDER, Y. 1990 Dynamical regimes of directional viscous fingering: spatiotemporal chaos and wave propagation. Phys. Rev. Lett. 64, 184-187.
26. RAYLEIGH, LORD 1945 Hydrodynamics (6th edn). Dover.
27. REINELT, D. A. 1995 The primary and the inverse instabilities of directional viscous fingering. J. Fluid Mech. 285, 303-327.
28. SAFFMAN, P. G. & TAYLOR, G. I. 1958 The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid. Proc. R. Soc. Lond. A 245, 312-329.
29. SAVAGE, M. D. 1977 Cavitation in lubrication. Part 1. On boundary conditions and cavity-fluid interfaces. J. Fluid Mech. 80, 743-755.
30. SIMON, A. J. & LIBCHABER, A. 1990 Moving interface: the stability tongue and phenomena within Phys. Rev. A 41, 7090-7093.
31. TAYLOR, G. I. 1963 Cavitation of a viscous fluid in narrow passages. J. Fluid Mech. 16, 595-619.
32. VALETTE, D. P., EDWARDS, W. S. & GOLLUB, J. P. 1994 Transition to spatiotemporal chaos via spatially subharmonic oscillations of a periodic front. Phys. Rev. E 49, R4783-R4786.