A study of velocity discontinuity for single air bubbles rising in an associative polymer

Physics of Fluids

Volumn 18, Issue 12, 2006, Pages

  Soto, E ^a   Goujon, C ^a   Zenit, R ^a   Manero, O ^a  

^a INSTITUTO DE INVESTIGACIONES EN MATERIALES   (Mexico)

Author keywords

Bubbles; Non Newtonian flow; Polymer solutions; Rheology; Shear flow; Surface tension; Two phase flow; Viscoelasticity; Viscosity

Indexed keywords

NON NEWTONIAN FLOW; POLYMERS; RHEOLOGY; SHEAR FLOW; TWO PHASE FLOW; VISCOELASTICITY; VISCOSITY; AIR; BUBBLES (IN FLUIDS); SHEAR DEFORMATION; SHEAR THINNING; SOLUTIONS; VELOCITY;

NEWTONIAN VISCOSITY; VELOCITY DISCONTINUITY; VISCOMETRIC FLOW; ASSOCIATIVE POLYMERS; DIMENSIONLESS NUMBER; FIRST NORMAL STRESS DIFFERENCE; RHEOLOGICAL PROPERTY; SHEAR-THICKENING BEHAVIOR; SURFACE TENSION FORCE; VIS-COELASTIC FLUIDS;

BUBBLES (IN FLUIDS); SHEAR FLOW;

BUBBLES (IN FLUIDS); NON NEWTONIAN FLOW; POLYMERS; RHEOLOGY; SHEAR FLOW; TWO PHASE FLOW; VISCOELASTICITY; VISCOSITY;

EID: 33846089711     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2397011     Document Type: Article

References (40)

1. R. Clift, J. R. Grace, and M. E. Weber, Bubbles, Drops and Particles (Academic, New York, 1978).
2. R. P. Chhabra, Bubbles, Drops and Particles in Non-Newtonian Fluids (CRC, Boca Raton, FL, 1993).
3. D. Funfschilling and H. Z. Li, "Flow of non-Newtonian fluids around bubbles: PIV measurements and birefringence visualisation," Chem. Eng. Sci. CESCAC0009-2509 56, 137(2001).
4. G. Astarita and G. Apuzzo, "Motion of gas bubbles in non-Newtonian liquids," AIChE J. AICEAC0001-154110.1002/aic.690110514 11, 815(1965).
5. S. M. Barnett, A. E. Humphrey, and M. Litt, "Bubble motion and mass transfer in non-Newtonian fluid," AIChE J. AICEAC0001-1541 12, 253(1966).
6. P. H. Calderbank, D. S. Johnson, and J. Loudon, "Velocity fields around spheres and bubbles investigated by laser-Doppler anemometry," Chem. Eng. Sci. CESCAC0009-2509 25, 235(1970).
7. L. G. Leal, J. Skoog, and A. Acrivos, "On the motion of gas bubbles in a viscoelastic fluid," Can. J. Chem. Eng. CJCEA70008-4034 49, 569(1971).
8. D. Rodrigue, D. De Kee, and C. F. Chan Man Fong, "Bubble velocities: Further developments on the jump discontinuity," J. Non-Newtonian Fluid Mech. JNFMDI0377-025710.1016/S0377-0257(98)00072-X 79, 45(1998).
9. D. Rodrigue, D. De Kee, and C. F. Chan Man Fong, "An experimental study of the effect of surfactants on the free rise velocity of gas bubbles," J. Non-Newtonian Fluid Mech. JNFMDI0377-025710.1016/ S0377-0257(96)01486-3 66, 213(1996).
10. J. R. Herrera-Velarde, R. Zenit, D. Chehata, and B. Mena, "The flow of non-Newtonian fluids around bubbles and its connection to the jump discontinuity," J. Non-Newtonian Fluid Mech. JNFMDI0377-0257 111, 199(2003).
11. O. Hassagar, "Negative wake behind bubbles in non-Newtonian liquids," Nature NATUAS0028-083610.1038/279402a0 279, 402(1979).
12. M. T. Arigo and G. H. McKinley, "An experimental investigation of negative wakes behind spheres settling in a shear-thinning viscoelastic fluid," Rheol. Acta RHEAAK0035-451110.1007/s003970050118 37, 307(1998).
13. E. Zana and L. G. Leal, "The dynamics and dissolution of gas bubbles in a viscoelastic fluid," Int. J. Multiphase FlowI JMFBP0301-9322 4, 237(1978).
14. Y. J. Liu, T. Y. Liao, and D. D. Joseph, "A two-dimensional cusp at the trailing edge of an air bubble rising in a viscoelastic liquid," J. Fluid Mech. JFLSA70022-112010.1017/S0022112095004447 304, 321(1995).
15. M. A. Winnik and A. Yekta, "Associative polymers in aqueous solution," Curr. Opin. Colloid Interface Sci. COCSFL1359-0294 2, 424(1997).
16. K. C. Tam, L. Guo, R. D. Jenkins, and D. R. Bassett, "Viscoelastic properties of hydrophobically modified alkali-soluble emulsion in salt solutions," Polymer POLMAG0032-386110.1016/S0032-3861(98)00857-X 40, 6369(1999).
17. O. Manero, F. Bautista, J. F. A. Soltero, and J. E. Puig, "Dynamics of worm-like micelles: The Cox-Merz rule," J. Non-Newtonian Fluid Mech. JNFMDI0377-025710.1016/S0377-0257(02)00082-4 106, 1(2002).
18. F. Bautista, J. M. de Santos, J. E. Puig, and O. Manero, "Understanding thixotropic and antithixotropic behaviour of viscoelastic micellar solutions and liquid crystalline dispersions. I. The model," J. Non-Newtonian Fluid Mech. JNFMDI0377-025710.1016/ S0377-0257(98)00081-0 80, 93(1999).
19. A. Belmonte, "Self oscillations of a cusped bubble rising through a micellar solution," Rheol. Acta RHEAAK0035-451110.1007/ s003970000098 39, 554(2000).
20. S. Chen and J. P. Rothstein, "Flow of a wormlike micelle solution past a falling sphere," J. Non-Newtonian Fluid Mech. JNFMDI0377-025710.1016/j.jnnfm.2003.08.005 116, 205(2004).
21. A. Jayaraman and A. Belmonte, "Oscillations of a solid sphere falling through a wormlike micellar fluid," Phys. Rev. E PLEEE81063-651X10.1103/PhysRevE.67.065301 67, 065301(R) (2003).
22. A. M. Mollinger, E. C. Cornelissen, and B. H. A. A. van den Brule, "An unexpected phenomenon observed in particle settling: oscillating falling spheres," J. Non-Newtonian Fluid Mech. JNFMDI0377-025710.1016/S0377-0257(98)00187-6 86, 389(1999).
23. P. H. T. Uhlherr, T. N. Le, and C. Tiu, "Characterisation of inelastic power-law fluids using falling sphere data," Can. J. Chem. Eng. CJCEA70008-4034 54, 497(1976).
24. D. Rodrigue (private communication).
25. Y. Caram, F. Bautista, J. E. Puig, and O. Manero, "On the rheological modeling of associative polymer," Rheol. Acta RHEAAK0035-4511 (to be published).
26. D. Hammerton and F. H. Garner, "Gas absorption from single bubbles," Trans. Inst. Chem. Eng. TICEAH0371-7496 32, S18 (1954).
27. V. G. Levich, Physico-Chemical Hydrodynamics (Prentice-Hall, Englewood Cliffs, NJ, 1962).
28. G. G. Stokes, Mathematical and Physical Papers (Cambridge University Press, England, 1880).
29. H. Schlichting, Boundary Layer Theory (McGraw-Hill, New York, 1964).
30. J. Hadamard, "Mouvement permanent lent d'une sphere liquide et visqueuse dans un liquide visqueux," C. R. Acad. Sci. Paris 152, 1735(1911).
31. W. Rybczynski, "Uber die Fortschreitende Bwegung einer-ussigen Kugel in einem zahen Medium," Bull. Acad. Sci. Cracovie Ser. A 1, 40(1911).
32. C. Bisgaard and O. Hassager, "An experimental investigation of velocity fields around spheres and bubbles moving in non-Newtonian liquids," Rheol. Acta RHEAAK0035-4511 21, 537(1982).
33. H. Z. Li, X. Frank, D. Funfschilling, and Y. Mouline, "Towards the understanding of bubble interactions and coalescence in non-Newtonian fluids: A cognitive approach," Chem. Eng. Sci. CESCAC0009-250910.1016/S0009-2509(01)00269-X 56, 6419(2001).
34. A. Mendoza Fuentes, "Diseño, construccion y aplicacion de un equipo de asentamiento de particulas en un polimero asociativo," Master thesis, Universidad Nacional Autonoma de Mexico, 2006.
35. J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics (Prentice-Hall, Englewood Cliffs, NJ, 1973).
36. G. H. McKinley, Transport Processes in Bubbles, Drops and Particles, edited by R. Chhabra and D. DeKee (Taylor and Francis, New York, 2002), Chap. 14.
37. R. P. Chhabra, C. Tiu, and P. H. T. Uhlherr, "A study of wall effects on the motion of a sphere in viscoelastic fluids," Can. J. Chem. Eng. CJCEA70008-4034 59, 771(1981).
38. R. P. Chhabra and P. H. T. Uhlherr, "The influence of fluid elasticity on wall effects for creeping sphere motion in cylindrical tubes," Can. J. Chem. Eng. CJCEA70008-4034 66, 154(1988).
39. E. S. Boek, J. T. Padding, V. J. Anderson, P. M. J. Tardy, J. P. Crawshaw, and J. R. A. Pearson, "Constitutive equations for extensional flow of wormlike micelles: Stability analysis of the Bautista-Manero model," J. Non-Newtonian Fluid Mech. JNFMDI0377-025710.1016/j.jnnfm.2005.01.001 126, 39(2005).
40. T. D. Taylor and A. Acrivos, "On the deformation and drag of a falling viscous drop at low Reynolds number," J. Fluid Mech. JFLSA70022-112010.1017/S0022112064000349 18, 466(1964).