The steady propagation of an air finger into a rectangular tube

Journal of Fluid Mechanics

Volumn 614, Issue , 2008, Pages 173-195

  De Lózar, Alberto ^a   Juel, Anne ^a   Hazel, Andrew L ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

AIR; CAPILLARITY; DROPS; PRESSURE DROP; SURFACE TENSION;

EXPERIMENTAL ERRORS; GOVERNING PARAMETERS; GRAVITATIONAL FIELDS; QUANTITATIVE AGREEMENT; RE-CIRCULATION FLOW; RECTANGULAR CROSS-SECTIONS; SURFACE TENSION FORCE; TWO DIMENSIONAL MODEL;

ASPECT RATIO;

AIRFLOW; EMPIRICAL ANALYSIS; EXPERIMENTAL STUDY; GRAVITY FIELD; PRESSURE DROP; STEADY FLOW; SURFACE TENSION; THREE-DIMENSIONAL MODELING; VISCOUS FLOW;

EID: 54849414522     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112008003455     Document Type: Article

References (30)

1. AJAEV, V. S. & HOMSY, G. M. 2006 Modeling shapes and dynamics of confined bubbles. Annu. Rev. Fluid Mech. 38, 277.
2. BAROUD, C. N. & WILLAIME, H. 2004 Multiphase flows in microfluidics. Compt. Rendus Phys. 7, 547.
3. BRETHERTON, F. P. 1961 The motion of long bubbles in tubes. J. Fluid Mech. 10, 166.
4. CLANET, C., HÉRAUD, P. & SEARBY, G. 2004 On the motion of bubble, in vertical tubes of arbitrary cross-sections: Some complements to the Dumitrescu-Taylor problem. J. Fluid Mech. 519, 359.
5. DUFF, I. S. & SCOTT, J. A. 1996 The design of a new frontal code for solving sparse, unsymmetric linear system. ACM Trans. Math. Software 22, 30-45.
6. GIAVEDONI, M. D. & SAITA, F. A. 1997 The axisymmetric and plane cases of a gas phase steadily displacing a Newtonian liquid-A simultaneous solution of the governing equntions. Phys. Fluids 9, 2420.
7. GRESHO, P. M. & SANI, R. L. 2000 Incompressible Flow and the Finite Element Method. Volume Two: Isothermal Laminar Flow. John Wiley & Sons Ltd.
8. HAZEL, A. L. & HEIL, M. 2002 The steady propagation of a semi-infinite bubble into a tube of elliptical or rectangular cross-section. J. Fluld Mech. 470, 91.
9. HEIL, M. & HAZEL, A. L. 2006 oomph-lib-An Object-Oriented Multi-Physics Finite-Element Library. In Fluid-Structure Interaction (ed. M. Schafer & H.-J. Bungartz), p. 19. Springer.
10. HOMSY, G. M. 987 Viscous fingering in porous media. Annu. Rev. Fluid Mech. 19, 271.
11. JENSEN, M. H., LIBCHABER, A., PELCÉ, P. & ZOCCHI, G. 1987 Effect of gravity on Saffman-Taylor meniscus: Theory and experiment. Phys. Rev. A 35, 2221.
12. KISTLER, S. F. & SCRIVEN, L. E. 1983 Coating flows. In Computational Analysis of Polymer Processing (ed. J. R. A. Pearson & S. M. Richnrdson), p. 243 Applied Science Publishers.
13. KOLB, W. B. & CERRO, R. L. 1991 Coating the inside of a capillary of square cross section. Chem. Engng Sci. 46, 2181.
14. LANDAU, L. D. & LEVICH, V. G. 1942 Dragging of a liquid by a moving plate. Acta Physiocochimica URSS 17, 42.
15. LISTER, J. R., MORRISON, N. F. & RALLISON, J. M. 2006 Sedimentation of a two-dimensional drop towards a rigid horizontal plane. J. Fluid Mech. 552, 345.
16. DE LÓZAR, A., HAZEL, A. L. & JUEL, A. 2007 Scaling properties of coating flows in rectangular channels. Phys. Rev. Lett. 99 234501.
17. MCLEAN, J. W. & SAFFMAN, P. G. 1981 The effect of surface tension on the shape of fingers in a Hele-Shaw cell. J. Fluid Mech. 102 455.
18. MOORE, M. G., JUEL, A., BURGESS, J. M., MCCORMICK, W. D. & SWINNEY, H. L. 2002 Fluctuations in viscous fingering. Phys. Rev. E 65, 030601(R).
19. PARK, C. W. & HOMSY, G. M. 1984 Two-phase displacement in Hele-Shaw cells: Theory. J. Fluid Mech. 139, 291.
20. RATULOWSKI, J. & CHANG, H.-C. 1989 Transport of gas bubbles in capillaries. Phys. Fluids A 1, 1642-1655.
21. REINELT, D. A. 1987 Interface conditions for two-phase displacement in Hele-Shaw cells. J. Fluid Mech. 483, 219.
22. REINELT, D. A. & SAFFMANN, P. G. 1985 The penetration of a finger into a viscous fluid in a channel and tube. SIAM J. Sci. Stat. Comput. 6, 542.
23. RUSCHAK, K. J. 1980 A method for incorporating free boundaries with surface tension in finite element fluid-flow simulators. Intl. J. Num. Meth. Engng 15, 639.
24. 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.
25. TABELING, P. & LIBCHABER, A. 1986 Film draining and the Saffman-Taylor problem. Phys. Rev. A 33, 794.
26. TABELING, P., ZOOCHI, G. & LIBCHABER, A. 1987 An experimental study of the Saffman-Taylor instability. J. Fluid Mech. 177, 67.
27. TAYLOR, G. I. 1961 Deposition of viscous fluid on the wall of a tube. J. Fluid Mech. 10, 161.
28. WHITESIDES. G. M. & STROOCK, A. D. 2001 Flexible methods for microfluidics. Physics Today 54 (6), 42.
29. WONG, H., RADKE, C. J. & MORRIS, S. 1995a The motion of long bubbles in polygonal capillaries. part 1. thin films. J. Fluid Mech. 292, 71.
30. WONG, H., RADKE, C. J. & MORRIS, S. 1995b The motion of long bubbles in polygonal capillaries. Part 2. Drag, fluid pressure and fluid flow. J. Fluid Mech. 292, 95.