Steady bubble rise and deformation in Newtonian and viscoplastic fluids and conditions for bubble entrapment

Journal of Fluid Mechanics

Volumn 601, Issue , 2008, Pages 123-164

  Tsamopoulos, J ^a   Dimakopoulos, Y ^a   Chatzidai, N ^a   Karapetsas, G ^a   Pavlidis, M ^a  

^a UNIVERSITY OF PATRAS   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

BUOYANCY; DIFFERENTIAL EQUATIONS; FINITE ELEMENT METHOD; FLOW VELOCITY; GALERKIN METHODS; NEWTONIAN FLOW; NON NEWTONIAN FLOW; STEADY FLOW; SURFACE TENSION; VISCOPLASTICITY; VISCOSITY;

BINGHAM FLUID; BUBBLE DEFORMATION; BUBBLE RISE; STOKES FLOW;

BUBBLES (IN FLUIDS);

BUBBLES (IN FLUIDS); BUOYANCY; DIFFERENTIAL EQUATIONS; FINITE ELEMENT METHOD; FLOW VELOCITY; GALERKIN METHODS; NEWTONIAN FLOW; NON NEWTONIAN FLOW; STEADY FLOW; SURFACE TENSION; VISCOPLASTICITY; VISCOSITY;

BUBBLE; BUOYANCY; DEFORMATION; FINITE ELEMENT METHOD; FLOW VELOCITY; GALERKIN METHOD; NAVIER-STOKES EQUATIONS; NEWTONIAN FLUID; STEADY FLOW; VISCOPLASTICITY;

EID: 42449160607     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112008000517     Document Type: Article

References (51)

1. ASTARISTA, G. & APUZZO, G. 1965 Motion of gas bubbles in non-Newtonian liquids. AIChE J. 11, 815-820.
2. BERCOVIER, M. & ENGELMAN, M. 1980 A finite element method for the incompressible non-Newtonian flows. J. Comput. Phys. 36, 313-326.
3. BERIS, A. N., TSAMOPOULOS, J. A., ARMSTRONG, R. C. & BROWN, R. A. 1985 Creeping motion of a sphere through a Bingham plastic. J. Fluid Mech. 158, 219-244.
4. BHAGA, D. & WEBER, M. E. 1981 Bubbles in viscous liquids: Shapes, wakes and velocities. J. Fluid Mech. 105, 61-85.
5. BINGHAM, E. C. 1922 Fluidity and Plasticity. McGraw-Hill.
6. BLACKERY, J. & MITSOULIS E. 1997 Creeping motion of a sphere in tubes filled with a Bingham plastic material. J. Non-Newtonian Fluid Mech. 70, 59-77.
7. BLANCO, A. & MAGNAUDET, J. 1995 The structure of the axisymmetric high-Reynolds number flow around an ellipsoidal bubble of fixed shape. Phys. Fluids 7, 1265-1274.
8. BONOMETTI, T. & MAGNAUDET, J. 2006 Transition from spherical cap to toroidal bubbles. Phys. Fluids 18, 052102 1-12.
9. BONOMETTI, T. & MAGNAUDET J. 2007 An interface capturing method for incompressible two phase flows validation and application to bubble dynamics. Intl. J. Multiphase Flow 33, 109-133.
10. BERGOS, G. R., ALEXANDROU, A. N. & ENTOV, N. M. 1999 On the determination of yield surfaces in Herschel-Bulkley fluids. J. Rheol. 43, 463-483.
11. CHRISTOV, C. I. & VOLKOV, P. K. 1985 Numerical investigation of the steady viscous flow past a stationary deformable bubble. J. Fluid Mech. 158, 341-364.
12. CLIFT, R., GRACE, J. R. & WEBER, M. E. 1978 Bubbles, Drops and Particles. Academic.
13. DIMAKOPOULOS, Y. & TSAMOPOULOS, J. 2003a Transient displacement of a viscoplastic material by air in straight and suddenly constricted tubes. J. Non-Newtonian Fluid Mech. 112, 43-75.
14. DIMAKOPOULOS, Y. & TSAMOPOULOS, J. 2003b A quasi-elliptic transformation for moving boundary problems with large anisotropic deformations. J. Comput. Phys. 192, 494-522.
15. DIMAKOPOULOS, Y. & TSAMOPOULOS, J. 2003c Transient displacement of a Newtonian fluid by air in straight or suddenly constricted tubes. Phys. Fluids 15, 1973-1991.
16. DIMAKOPOULOS, Y. & TSAMOPOULOS, J. 2004 On the gas-penetration in straight tubes completely filled with a viscoelastic fluid. J. Non-Newtonian Fluid Mech. 117, 117-139.
17. DIMAKOPOULOS, Y. & TSAMOPOULOS, J. 2006 Transient displacement of Newtonian and viscoplastic liquid by air in complex tubes. J. Non-Newtonian Fluid Mech. doi:10.10 1 6/j.jnnfm.2006.08.002.
18. DUBASH, N. & FRIGAARD, I. 2004 Conditions for static bubbles in viscoplastic fluids. Phys. Fluids 16, 4319-4330.
19. DUBASH, N. & FRIGAARD, I. 2007 Propagation and stopping of air bubbles in Carbopol solutions. J. Non-Newtonian Fluid Mech. 142 123-134.
20. DUINEVELD, P. 1995 The rise velocity and shape of bubbles in pure water at high Reynolds number. J. Fluid Mech. 292, 325-332.
21. FOTEINOPOULOU, K., MAVRANTZAS, V., DIMAKOPOULOS, Y. & TSAMOPOULOS, J. 2006 Numerical simulation of multiple bubbles growing in a Newtonian liquid filament undergoing stretching. Phys. Fluids 18, 042106.
22. FRIGAARD, I. & NOUAR, C. 2005 On the usage of viscosity regularization methods for visco-plastic fluid flow computation. J. Non-Newtonian Fluid Mech. 127, 1-26.
23. GLOWINSKI, R., LIONS, J. & TRÉMOLIÈRES, R. 1981 Numerical Analysis of Variational Inequalities, North-Holland.
24. GUESLIN, B., TALINI, L., HERZHAFT, B., PEYSSON, Y. & ALLAIN, C. 2006 Flow induced by a sphere settling in an aging yield-stress fluid. Phys. Fluids 18, 103101.
25. HABERMAN, W. L. & MORTON, R. K. 1953 An experimental investigation of the drag and shape of air bubbles rising in various liquids. Report 802, Navy Dept., David W. Taylor Model Basin. 68 Washington, DC.
26. HADAMARD, J. S. 1911 Mouvement permanent lent d'une sphère liquide et visqueuse dans un liquide visqueux. C. R. l'Acad. Sci. Paris 152, 1735-1738.
27. HARPER, J. F. 1972 The motion of bubbles and drops through liquids. Adv. Appl. Mech. 12, 59-129.
28. HNAT, J. G. & BECKMASTER, J. D. 1976 Spherical cap bubbles and skirt formation. Phys. Fluids 19, 182-194.
29. HUA, J. & LOU J. 2007 Numerical simulation of bubble rising in viscous liquid. J. Comput. Phys. 222, 769-795.
30. JOHNSON, A. & WHITE, D. B. 1991 Gas-rise velocities during kicks. SPE Drilling Engineering, 6, 257-263, and Society of Petroleum Engineers Paper 20431.
31. KARAPETSAS, G. & TSAMOPOULOS, J. 2006 Transient squeeze flow of viscoplastic materials. J. Non-Newtonian Fluid Mech. 133, 35-56.
32. KOH, C. & LEAL, L. G. 1989 The stability of drop shapes for transition at zero Reynolds number through a quiescent fluid. Phys. Fluids A 1, 1309-1313.
33. LEVICH, V. G. 1949 The motion of bubbles at high Reynolds numbers. Zh. Eksper. Teor. Fiz. 19, 18-24.
34. LIU, B. T., MULLER, S. & DENN, M. M. 2002 Convergence of a regularization method for creeping flow of a Bingham material about a rigid sphere, J. Non-Newtonian Fluid Mech. 102, 179-191.
35. MAGNAUDET, J. & EAMES, I. 2000 The motion of high-Reynolds-number bubbles in inhomogeneous flows. Annu. Rev. Fluid Mech. 32, 659-708.
36. MALAGA, C. & RALLISON, J. M. 2007 A rising bubble in a polymer solution. J. Non-Newtonian Fluid Mech. 141, 59-78.
37. MAXWORTHY, T., GNANN, C., KURTEN, M. & DURST, F. 1996 Experiments on the rise of air bubbles in clean viscous liquids. J. Fluid Mech. 321, 421-441.
38. MIKSIS, M. J., VANDEN-BROECK, J. M. & KELLER, J. B. 1982 Rising bubbles. J. Fluid Mech. 123, 31-41.
39. MOORE, D. W. 1963 The boundary layer on a spherical gas bubble. J. Fluid Mech. 16, 161-176.
40. MOORE, D. W. 1965 The velocity of rise of distorted gas bubbles in a liquid of small viscosity. J. Fluid Mech. 23, 749-766.
41. PAPANASTASIOU, T. C. 1987 Flows of materials with yield. J. Rheol. 31, 385-404.
42. PILZ, C. & BENN, G. 2007 On the critical bubble volume at the rise velocity jump discontinuity in viscoelastic liquids. J. Non-Newtonian Fluid Mech. 145, 124-138.
43. RYBCZYŃSKI, W. 1911 On the translatory motion of fluid sphere in a viscous medium. Bull. Intl l' Acad. Polonaise Scie. Lett. Classe des Sciences Mathématiques et Naturelles A, 40-46.
44. RYSKIN, G. & LEAL, L. G. 1984 Numerical solution of free-boundary problems in fluid mechanics. Part 2. Buoyancy-driven motion of a gas bubble through a quiescent liquid. J. Fluid Mech. 148, 19-35.
45. SCHENK, O. & GÄRTNER, K. 2004 Solving unsymmetric sparse systems of linear equations with PARDISO. J. Future Generations Computer Systems 20, 475-487.
46. SCHENK, O. & GÄRTNER, K. 2006 On fast factorization pivoting methods for symmetric indefinite systems. Elec. Trans. Numer. Anal. 23, 158-179.
47. SMYRNAIOS, D. & TSAMOPOULOS, J. 2001 Squeeze flow of Bingham plastics. J. Non-Newtonian Fluid Mech. 100, 165-190.
48. STEIN, S. & BUGGISCH, H. 2000 Rise of pulsating bubble in fluids with a yield stress. Z. Angew. Math. Mech. 11-12, 827-834.
49. TAYLOR, T. & ACRIVOS, A. 1964 On the deformation and drag of a falling drop at low Reynolds number. J. Fluid Mech. 18, 466-476.
50. TERASAKA, K. & TSUGE, H. 2001 Bubble formation at a nozzle submerged in viscous liquids having yield stress. Chem. Engng Sci. 56, 3237-3245.
51. UNVERDI, S. O. & TRYGGVASON, G. 1992 A front tracking method for viscous, incompressible, multi-fluid flows. J. Comput. Phys. 100, 25-37.