Transient and steady state of a rising bubble in a viscoelastic fluid

Journal of Fluid Mechanics

Volumn 589, Issue , 2007, Pages 215-252

  Pillapakkam, Shriram B ^a   Singh, Pushpendra ^a   Blackmore, Denis ^b   Aubry, Nadine ^c  

^a NEW JERSEY INSTITUTE OF TECHNOLOGY   (United States)

^b NEW JERSEY INSTITUTE OF TECHNOLOGY   (United States)

^c CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CAPILLARY FLOW; CONSTITUTIVE EQUATIONS; DIRECT NUMERICAL SIMULATION; FINITE ELEMENT METHOD; NON NEWTONIAN LIQUIDS; SURFACE TENSION; VISCOELASTICITY; WAKES;

DEBORAH NUMBER; LEVEL-SET METHOD; OLDROYD-B; VORTEX RING;

BUBBLES (IN FLUIDS);

BUBBLES (IN FLUIDS); CAPILLARY FLOW; CONSTITUTIVE EQUATIONS; DIRECT NUMERICAL SIMULATION; FINITE ELEMENT METHOD; NON NEWTONIAN LIQUIDS; SURFACE TENSION; VISCOELASTICITY; WAKES;

BUBBLE; COMPUTATIONAL FLUID DYNAMICS; COMPUTER SIMULATION; CONSTITUTIVE EQUATION; FINITE ELEMENT METHOD; NEWTONIAN FLUID; STEADY FLOW; TRANSIENT FLOW; VISCOELASTIC FLUID; VORTEX FLOW; WAKE;

EID: 36749034942     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112007007628     Document Type: Article

References (41)

1. ARIGO, M. I & MCKINLEY, G. H. 1998 An experimental investigation of negative wakes behind spheres settling in a shear-thinning viscoelastic fluid. Rheol. Acta 37(4), 307-327.
2. ASTA RITA, G. & APUZZO, G. 1965 Motion of gas bubbles in non-Newtonian liquids, AIChE J. 11(5), 815-820.
3. BARNETT, S. M., HUMPHREY, A. E. & LITT, M. 1966 Bubble motion and mass transfer in non-Newtonian fluid AIChE J. 12(2), 253-259.
4. BELMONTE, A. 2000 Self oscillations of a cusped bubble rising through a micellar solution. Rheol. Acta 39, 554-559.
5. BISGAARD, C. 1983 Velocity fields around spheres and bubbles investigated by laser-Doppler anemometry. J. Non-Newtonian Fluid Mech. 12, 283-302.
6. BLACKMORE, D. & TING, L. 1985 Surface integral of its mean curvature vector. SIAM Rev. 27-4.
7. BRISTEAU, M. O., GLOWINSKI, R. & PERIAUX, J. 1987 Numerical methods for Navier-Stokes equations. Application to the simulation of compressible and incompressible flows. Comput. Phys. Rep. 6, 73.
8. CALDERBANK, P. H., JOHNSON, D. S. & LOUDON, J. 1970 Velocity fields around spheres and bubbles investigated by laser-doppler anemometry. Chem. Engng. Sci. 25, 235-256.
9. CHEN, S. & ROTHSTEIN, J. P. 2004 Flow of a wormlike micelle solution past a falling sphere. J. Non-Newtonian Fluid Mech. 116, 205-234.
10. CHILCOTT, M. D. & RALLISON, J. M. 1988 Creeping flow of dilute polymer solutions past cylinders and spheres. J. Non-Newtonian Fluid Mech. 29, 381.
11. FUNFSCHILLING, D. & LI, H. Z. 2001 Flow of Non-Newtonian fluids around bubbles: PIV measurements and birefringence visualization, Chem. Engng Sci. 56, 1137-1141.
12. GLOWINSKI, R., TALLEC, P., RAVACHOL, M. & TSIKKINIS, V. 1992 In Finite Elements in Fluids, (ed. T. J. Chung), vol. 8, chap. 7. Hemisphere.
13. GLOWINSKI, R. & PIRONNEAU, O. 1992 Finite element methods for Navier-Stokes equations. Annu. Rev. Fluid Mech. 24, 167.
14. GLOWINSKI, R., PAN, T. W, HESLA, T. I. & JOSEPH, D. D. 1999 A distributed Lagrange multiplier/fictitious domain method for particulate flows. Intl J. Multiphase Flows 25(5), 755.
15. HANDZY, N. Z. & BELMONTE, A. 2004 Oscillatory motion of rising bubbles in wormlike micellar fluid with different micro structures. Phys. Rev. Lett. 92, 124501.
16. HAPPEL, J. & BRENNER, H. 1981 Low Reynolds Number Hydrodynamics: With special applications to particulate media. Springer.
17. HASSAGAR, O. 1979 Negative wake behind bubbles in non-Newtonian liquids. Nature 279, 402-403.
18. HERRERA-VELARDE, J. R. ZENIT, R., CHEHATA, D. & MENA, B. 2003 The flow of non-Newtonian fluids around bubbles and its connection to the jump discontinuity. J. non-Newtonian Fluid Mech. 111, 199-209.
19. JAYARAMAN, A. & BELMONTE, A. 2003 Oscillations of a solid sphere falling through a wormlike micellar fluid. Phys. Rev. E 67, 65301.
20. JEONG, J. & MOFFATT, H. K. 1992 Free-surface cusps associated with flow at low Reynolds number. J. Fluid Mech. 241, 1-22.
21. JOSEPH, D. D., NELSON, J., RENARDY, M. & RENARDY, Y. 1991 Two-dimensional cusped interfaces. J. Fluid Mech. 223, 383-409.
22. KING, M. J. & WALTERS, N.D. 1972 The unsteady motion of a sphere in an elastico-viscous liquid. J. Phys. D: Appl. Phys. 5 141-150.
23. LEAL, L. G., SKOOG, J. & ACRIVOS, A. 1971 On the motion of gas bubbles in a viscoelastic fluid. Can. J. Chem. Engng 49, 569-575.
24. Liu, Y. J., LIAO, T.Y. & JOSEPH, D. D. 1995 A two-dimensional cusp at the trailing edge of an air bubble rising in a viscoelastic liquid. J. Fluid Mech. 304, 321-342.
25. MARCHUK, G. I. 1990 Splitting and alternate direction methods. In Handbook of Numerical Analysis (ed. P. G. Ciarlet & J. L. Lions), Vol. 1, P. 197. North-Holland.
26. MCKINLEY, G. H. 2001 Transport Processes in Bubbles, Drops and Particles. (ed. R. P. Chhabra & D. DeKee), 2nd edn, Taylor Francis.
27. NOH, D. S., KANG I. S. & LEAL, L. G. 1993 Numerical solutions for the deformation of a bubble rising in dilute polymeric fluids. Phys. Fluids 5, 1315-1332.
28. PHILIPPOFF, W. 1937 Viscosity characteristics of rubber solution. Rubber Chem. Tech. 10, 76.
29. PILLAPAKKAM, S. B. & SINGH, P. 2001 A level-set method for computing solutions to viscoelastic two-phase flow. J. Comput. Phys. 174, 552-578.
30. RAMASWAMY, S. & LEAL, L. G. 1999 The deformation of a viscoelastic drop subjected to steady uniaxial extensional flow of a Newtonian fluid. J. Non-Newtonian Fluid Mech. 85, 127.
31. RODRIGUE, D., CHHABRA, R. P. & CHAN MAN FONG, C. F. 1996 An experimental study of the effect of surfactants on the free rise velocity of gas bubbles. J. Non-Newtonian Fluid Mech. 66, 213-232.
32. RODRIGUE, D., CHHABRA, R. P. & FONG, C. F. C. M. 1998 Bubble velocities: Further developments on the jump and discontinuity. J. Non-Newtonian Fluid Mech. 79, 45-55.
33. SHIKHMURZEAV, Y. D. 1998 On cusped interfaces. J. Fluid Mech. 359, 131-328.
34. SINGH, P. & JOSEPH, D. D. 2000 Sedimentation of a sphere near a vertical wall in an Oldroyd-B fluid. J. Non-Newtonian Fluid Mech. 94, 179-203.
35. SINGH, P., JOSEPH, D. D., HESLA, T. I., GLOWINSKI, R. & PAN, T.W. 2000 A distributed Lagrange multiplier/fictitious domain method for viscoelastic particulate flows. J. Non-Newtonian Fluid Mech. 91 165.
36. SINGH, P. & LEAL, L.G. 1993 Finite element simulation of the start-up problem for a viscoelastic problem in an eccentric cylinder geometry using third-order upwind scheme Theor. Comput. Fluid Dyn. 5, 107-137.
37. SINGH, P. & LEAL, L. G. 1994 Computational studies of dumbbell model fluids in a co-rotating two-roll mill. J. Rheol. 38, 485-517.
38. SINGH, P. & LEAL, L. G. 1995 Viscoelastic flows with corner singularities. J. Non-Newtonian Fluid Mech. 58, 279-313.
39. SUSSMAN, M., SMEREKA, P. & OSHER, S. 1994 A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114, 146.
40. WAGNER, A. J., GIRAUD, L. & SCOTT, C. E. 2000 Simulations of a cusped bubble rising in a viscoelastic fluid with a new numerical method. Comput. Phys. Comm. 129, 227-231.
41. ZHENG, R. & PAN-THIEN, N. 1992 A boundary element simulation of the unsteady motion of a sphere in a cylindrical tube containing a viscoelastic fluid. Rheol. Acta 31, 323-332.