A spherical-cap bubble moving at terminal velocity in a viscous liquid

Journal of Fluid Mechanics

Volumn 579, Issue , 2007, Pages 347-371

  Feng, James Q ^a  

^a BOSTON SCIENTIFIC CORPORATION   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FINITE ELEMENT METHOD; FLOW VELOCITY; GALERKIN METHODS; LAMINAR FLOW; NAVIER STOKES EQUATIONS; REYNOLDS NUMBER; VISCOSITY; VISCOUS FLOW;

SPHERICAL-CAP BUBBLE; TERMINAL VELOCITY; VISCOUS LIQUID;

BUBBLES (IN FLUIDS);

BUBBLES (IN FLUIDS); FINITE ELEMENT METHOD; FLOW VELOCITY; GALERKIN METHODS; LAMINAR FLOW; NAVIER STOKES EQUATIONS; REYNOLDS NUMBER; VISCOSITY; VISCOUS FLOW;

BUBBLE; FINITE ELEMENT METHOD; GALERKIN METHOD; LAMINAR FLOW; NAVIER-STOKES EQUATIONS; REYNOLDS NUMBER; STEADY FLOW; VISCOUS FLOW;

EID: 34548176076     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112007005319     Document Type: Article

References (55)

1. BATCHELOR, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
2. BHAGA, D. & WEBER, M. E. 1981 Bubbles in viscous liquids: Shapes, wakes and velocities. J. Fluid Mech. 105, 61-85.
3. BONOMETTI, T. & MAGNAUDET, J. 2006 Transition from spherical cap to toroidal bubbles. Phys. Fluids 18, 052102.
4. BOUDOUVIS, A. G. 1987 Mechanisms of surface instabilities and pattern formation in ferromagnetic liquids. PhD thesis, University of Minnesota. Available from University Microfilms International, Ann Arbor, MI 48106.
5. BOZZI, L. A., FENG, J. Q., SCOTT, T. C. & PEARLSTEIN, A. J. 1997 Steady axisymmetric motion of deformable drops falling or rising through a homoviscous fluid in a tube at intermediate Reynolds number. J. Fluid Mech. 336, 1-32.
6. BRIGNELL, A. S. 1973 The deformation of a liquid drop at small Reynolds number. Q. J. Mech. Appl. Maths 26, 99-107.
7. CARVALHO, M. S. 1996 Roll coating flows in rigid and deformable gaps. PhD thesis, University of Minnesota.
8. CHAN, T. F. 1984 Newton-like pseudo-arclength methods for computing simple turning points. SIAM J. Sci. Statist. Comput. 5, 135-148.
9. CHEN, L., GARIMELLA, S. V., REIZES, J. A. & LEONARDI, E. 1999 The development of a bubble rising in a viscous liquid. J. Fluid Mech. 387, 61-96.
10. CHEN, K. S., SCHUNK, P. R. & SACKINGER, P. A. 1995 Finite-element analyses of blade and slot coating flows using a Newton-Raphson pseudo-solid domain mapping technique and unstructured grid. In Proc. TAPPI Coating Fundamentals Symposium, pp. 131-152.
11. CHRISTODOULOU, K. N. 1989 Computational physics of slide coating flow. PhD thesis, University of Minnesota.
12. CHRISTODOULOU, K. N. & SCRIVEN, L. E. 1992 Discretization of free surface flows and other moving boundary problems. J. Comput. Phys. 99, 39-55.
13. 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.
14. CLIFT, R. C., GRACE, J. R. & WEBER, M. E. 1978 Bubbles, Drops and Particles. Academic.
15. COLLINS, R. 1966 A second approximation for velocity of a large gas bubble rising in an infinite liquid. J. Fluid Mech. 25, 469-480.
16. DAVIES, R. M. & TAYLOR, G. I. 1950 The mechanics of large bubbles rising through extended liquids and through liquids in tubes. Proc. R. Soc. Lond. A 200, 375-390.
17. FENG, J. Q. 1998 Computational analysis of slot coating on a tensioned web. AIChE J. 44, 2137-2143.
18. FENG, J. Q. 2000 Contact behavior of spherical elastic particles: A computational study of particle adhesion and deformation. Colloids Surf. A 172, 175-198.
19. FENG, J. Q. & BASARAN, O. A. 1994 Shear flow over a translationally symmetric cylindrical bubble pinned on a slot in a plane wall. J. Fluid Mech. 275, 351-378.
20. FENG, J. Q. & SCRIVEN, L. E. 1992 Electrostatic effects in continuous liquid coating. Paper 38d in Intl. Symposium on Coating Science and Technology. AIChE National Meeting. New Orleans, Louisiana.
21. GRACE, J. R., WAIREGI, T. & BROPHY, J. 1978 Break-up of drops and bubbles in stagnant media. Can. J. Chem. Engng 56, 3-8.
22. HABERMAN, W. L. & MORTON, R. K. 1953 An experimental investigation of the drag and shape of air bubbles in various liquids. David Taylor Model Basin Rep. 802.
23. HABERMAN, W. L. & SAYRE, R. M. 1958 Motion of rigid and fluid spheres in stationary and moving liquids inside cylindrical tubes. David Taylor Model Basin Rep. 1143.
24. HARPER, J. F. 1972 The motion of bubbles and drops through liquids. Adv. Appl. Mech. 12, 59-129.
25. HNAT, J. G. & BUCKMASTER, J. D. 1976 Spherical cap bubbles and skirt formation. Phys. Fluids 19, 182-194.
26. HOOD, P. 1976 Frontal solution program for unsymmetric matrices. Intl J. Numer. Meth. Engng 10, 379-399. (corrigendum 11 1055 (1977)).
27. HUYAKORN, P. S., TAYLOR, C., LEE, R. L. & GRESHO, P. M. 1978 A comparison of various mixed interpolation finite elements in the velocity-pressure formulation of the Navier-Stokes equations. Comput. Fluids 6, 25-35.
28. IOOSS, G. & JOSEPH, D. D. 1990 Elementary Stability and Bifurcation Theory, 2nd edn. Springer.
29. JOSEPH, D. D. 2003 Rise velocity of a spherical-cap bubble. J. Fluid Mech. 488, 213-223.
30. KELLER, H. B. 1977 Numerical solution of bifurcation and nonlinear eigenvalue problems. In Applications of Bifurcation Theory (ed. P. H. Rabinovich), pp. 359-384. Academic.
31. KOH, C. J. & LEAL, L. G. 1990 An experimental investigation on the stability of viscous drops translating through a quiescent fluid. Phys. Fluids A 2, 2103-2109.
32. LEVICH, V. G. 1962 Physicochemical Hydrodynamics. Prentice-Hall.
33. LEVICH, V. G. & KRYLOV, V. S. 1969 Surface-tension-driven phenomena. Annu. Rev. Fluid Mech. 1, 293-316.
34. MIKSIS, M. J., VANDEN-BROECK, J.-M. & KELLER, J. B. 1981 Axisymmetric bubble or drop in a uniform flow. J. Fluid Mech. 108, 89-100.
35. MIKSIS, M. J., VANDEN-BROECK, J.-M. & KELLER, J. B. 1982 Rising bubbles. J. Fluid Mech. 123, 31-41.
36. MOORE, D. W. 1959 The rise of a gas bubble in a viscous liquid. J. Fluid Mech. 6, 113-130.
37. MOORE, D. W. 1965 The velocity of rise of distorted gas bubbles in a liquid of small viscosity. J. Fluid Mech. 23, 749-766.
38. MUSSON, L. C. 2001 Two-layer slot coating. PhD thesis, University of Minnesota.
39. OHTA, M., IMURA, T., YOSHIDA, Y. & SUSSMAN, M. 2005 A computational study of the effect of initial bubble condition on the motion of a gas bubble rising in viscous liquids. Intl J. Multiphase Flow 31, 223-237.
40. ORTEGA, J. M. & RHEINBOLDT, W. C. 1970 Iterative Solution of Nonlinear Equations in Several Variables. Academic.
41. PARLANGE, J. Y. 1969 Spherical-cap bubbles with laminar wakes. J. Fluid Mech. 37, 257-263.
42. POZRIKIDIS, C. 1990 The instability of a moving viscous drop. J. Fluid Mech. 210, 1-21.
43. RIKS, R. 1972 The application of Newton's method to the problem of elastic stability. J. Appl. Mech. 39, 1060-1065.
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. SACKINGER, P. A., SCHUNK, P. R. & RAO, R. R. 1996 A Newton-Raphson pseudo-solid domain mapping technique for free and moving boundary problems: A finite element implementation. J. Comput. Phys. 125 83-103.
46. DE SANTOS, J. M. 1991 Two-phase cocurrent downflow through constricted passages. PhD thesis, University of Minnesota.
47. SLAUGHTER, I. & WRAITH, A. E. 1968 The wake of a large gas bubble. Chem. Eng. Sci. 23, 932.
48. STEWART, G. W. 1981 On the implicit deflation of nearly singular systems of linear equations. SIAM J. Sci. Statist. Comput. 2 136-140.
49. STRANG, G. & FIX, G. J. 1973 An Analysis of the Finite Element Method. Prentice-Hall.
50. SUGIYAMA, K., TAKAGI, S. & MATSUMOTO, Y. 2001 Multi-scale analysis of bubbly flows. Comput. Methods Appl. Mech. Engng 191, 689-704.
51. TAYLOR, T. D. & ACRIVOS, A. 1964 On the deformation and drag of a falling viscous drop at low Reynolds number. J. Fluid Mech. 18 166-176.
52. THOMPSON, J. F., WARSI, Z. U. A. & MASTIN, C. W. 1985 Numerical Grid Generation. Elsevier.
53. TRYGGVASON, G., BUNNER, B. ESMAEELI, A., JURIC, D. AL-RAWAHI, N., TAUBER, W., HAN, J., NAS, S. & JAN, Y.-J. 2001 A front-tracking method for the computations of multiphase flow. J. Comput. Phys. 169, 708-759.
54. VAN DYKE, M. 1975 Perturbation Methods in Fluid Mechanics. The Parabolic Press.
55. WEGENER, P. P. & PARLANGE, J.-Y. 1973 Spherical-cap bubbles. Annu. Rev. Fluid Mech. 5, 79-100.