A numerical study of the motion of a spherical drop rising in shear-thinning fluid systems

Journal of Non-Newtonian Fluid Mechanics

Volumn 116, Issue 1, 2003, Pages 95-111

  Ohta, Mitsuhiro ^a   Iwasaki, Eiji ^a   Obata, Eiji ^a   Yoshida, Yutaka ^a  

^a MURORAN INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

Drop free motion; Numerical analysis; Shear thinning fluid; VOF method

Indexed keywords

BUBBLES (IN FLUIDS); MATHEMATICAL MODELS; NON NEWTONIAN FLOW; REYNOLDS NUMBER; VISCOSITY;

DROP MOTION; SHEAR-THINNING FLUIDS;

FLUID MECHANICS;

DROPLET; MATHEMATICAL ANALYSIS; NON-NEWTONIAN FLUID; REYNOLDS NUMBER; SHEAR THINNING; VISCOSITY;

EID: 0344925133     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jnnfm.2003.08.004     Document Type: Article

References (61)

1. EAstarita G.Apuzzo G.Motion of gas bubbles in non-Newtonian liquids AIChE J. 11 1965 815-820
2. Leal L.G.Skoog S.Acrivos A.On the motion of gas bubbles in a viscoelastic liquid Can. J. Chem. Eng. 49 1971 569-575
3. Carreau P.J.Devic M.Kapellas M.Dynamique des bulles en milieu viscoélastique Rheol. Acta 13 1974 477-489
4. Zana E.Leal L.G.The dynamics and dissolution of gas in a viscoelastic fluid Int. J. Multiphase Flow 4 1978 237-262
5. Kawase Y.Ulbrecht J.On the abrupt change of velocity of bubbles rising in non-Newtonian liquids J. Non-Newtonian Fluid Mech. 8 1981 203-212
6. De Kée D.Carreau P.J.Mordarski J.Bubble velocity and coalescence in viscoelastic liquids Chem. Eng. Sci. 41 1986 2273-2283
7. Gummalam S.Narayan K.A.Chhabra R.P.Rise velocity of a swarm of spherical through a non-Newtonian fluid: effect of zero shear viscosity Int. J. Multiphase Flow 14 1988 361-373
8. De Kée D.Chhabra R.P.Dajan A.Motion and coalescence of gas bubbles in non-Newtonian polymer solutions J. Non-Newtonian Fluid Mech. 37 1990 1-18
9. Mmanjunath S.Chhabra R.P.Free rise velocity of a swarm of spherical gas bubbles through a quiescent power law liquid Int. J. Eng. Sci. 30 1992 871-878
10. Miyahara T.Yamanaka S.Mechanics of motion and deformation of a single bubble rising through quiescent highly viscous Newtonian and non-Newtonian media J. Chem. Eng. Jpn. 26 1993 297-302
11. Liu Y.J.Liao T.Y.Joseph D.D.A two-dimensional cusp at the trailing edge of an air bubble rising in a viscoelastic liquid J. Fluid Mech. 304 1995 321-342
12. Rodrigue D.De Kée D.Chan Man Fong C.F.An experimental study of the effect of surfactants on the free rise velocity of gas bubbles J. Non-Newtonian Fluid Mech. 66 1996 213-232
13. Li H.Z.Mouline Y.Choplin L.Midoux N.Chaotic bubble coalescence in non-Newtonian fluids Int. J. Multiphase Flow. 23 1997 713-723
14. Chhabra R.P.Rising velocity of a swarm of spherical bubbles in power law fluids at high Reynolds numbers Can. J. Chem. Eng. 76 1998 137-139
15. Gauri V.Koelling K.W.The motion of long bubbles through viscoelastic fluids in capillary tubes Rheol. Acta 38 1999 458-470
16. Warshay M.Bogusz E.Johnson M.Kintner R.C.Ultimate velocity of drops in stationary liquid media Can. J. Chem. Eng. 37 1959 29-36
17. Fararoui A.Kintner R.C.Flow and shape of drops in velocity of drops in non-Newtonian fluids Trans. Soc. Rheol. 5 1961 369-380
18. Marrucci G.Apuzzo G.Astarita G.Motion of liquid drops in non-Newtonian systems AIChE J. 16 1970 538-541
19. Mohan V.Nagarajan R.Venkateswarlu D.Fall of drops in non-Newtonian media Can. J. Chem. Eng. 50 1972 37-43
20. Kawase Y.Hirose Y.Motion of drops in non-Newtonian fluid systems at low Reynolds number J. Chem. Eng. Jpn. 10 1977 68-70
21. Acharya A.Mashelkar R.A.Ulbrecht J.Motion of liquid drops in rheologically complex fluids Can. J. Chem. Eng. 56 1978 19-25
22. Gillaspy P.H.Hoffer T.R.Experimental measurements of the effect of viscosity on drag for liquid drops AIChE J. 29 1983 229-236
23. Quintana G.C.Cheh H.Y.Maldarelli C.M.The translation of a Newtonian droplet in a 4-constant Oldroyd fluid J. Non-Newtonian Fluid Mech. 22 1987 253-270
24. Gürkan T.Motion of a circulating power-law drop translating through Newtonian fluids at intermediate Reynolds numbers Chem. Eng. Commun. 80 1989 53-67
25. Delaby I.Ernst B.Muller R.Drop deformation during elongational in blends of viscoelastic fluids-small deformation theory and comparison with experimental results Rheol. Acta 34 1995 525-533
26. Gonzalez-Nunez R.Chan Man Fong C.F.Favis B.D.De Kée D.Deformation of drops in extensional viscoelastic flow J. Appl. Polym. Sci. 62 1996 1627-1634
27. Mighri F.Ajji A.Carreau P.J.Influence of elastic properties on drop deformation in elongational flow J. Rheol. 41 1997 1183-1201
28. R.P. Chhabra, Bubbles, Drops and Particles in Non-Newtonian Fluids, CRC Press, Tokyo, 1992.
29. Satrape J.V.Crochet M.J.Numerical simulation of the motion of a sphere in a Boger fluid J. Non-Newtonian Fluid Mech. 55 1994 91-111
30. Bush M.B.On the stagnation flow behind a sphere in a shear-thinning viscoelastic liquid J. Non-Newtonian Fluid Mech. 55 1994 229-247
31. Bodart C.Crochet M.J.The time-dependent flow of a viscoelastic fluid around a sphere J. Non-Newtonian Fluid Mech. 54 1994 303-329
32. Becker L.E.Mckinley G.H.Rasmussen H.K.Hassager O.The unsteady motion of a sphere in a viscoelastic fluid J. Rheol. 38 1994 377-403
33. Yurun F.Crochet M.J.High-order finite element methods for steady viscoelastic flows J. Non-Newtonian Fluid Mech. 57 1995 283-311
34. Joseph D.D.Feng J.The negative wake in a second-order fluid J. Non-Newtonian Fluid Mech. 57 1995 313-320
35. Harlen O.G.Rallison J.M.Szabo P.A split Lagrangian-Eulerian method for simulating transient viscoelastic flows J. Non-Newtonian Fluid Mech. 60 1995 81-104
36. Luo X.L.Operator splitting algorithm for viscoelastic flow and numerical analysis for the flow around a sphere in a tube J. Non-Newtonian Fluid Mech. 63 1996 121-140
37. Baaijens F.P.T.Selen S.H.A.Baaijens H.P.W.Peters G.W.M.Meijer H.E.H.Viscoelastic flow past a confined cylinder of a low density polyethylene melt J. Non-Newtonian Fluid Mech. 68 1997 173-203
38. Luo X.L.An incremental difference formulation for viscoelastic flows and high resolution FEM solutions at high Weissenberg numbers J. Non-Newtonian Fluid Mech. 79 1998 57-75
39. Tsukada T.Mikami H.Hozawa M.Imaishi N.Theoretical and experimental studies of the deformation of bubbles moving in quiescent Newtonian and non-Newtonian liquids J. Chem. Eng. Jpn. 23 1990 192-198
40. Noh D.S.Kang I.S.Leal L.G.Numerical solutions for the deformation of a bubble rising in dilute polymeric fluids Phys. Fluids A 5 1993 1315-1332
41. Pillapakkam S.B.Dynamics of drops and bubbles in Newtonian and viscoelastic flows Proc. ASME FED 250 1999 169-174
42. Pillapakkam S.B.Singh P.A level set method for computing solutions to viscoelastic two-phase flow J. Comput. Phys. 174 2001 552-578
43. Sussman M.Smereka P.Osher S.A level set approach for computing solutions to incompressible two-phase flow J. Comput. Phys. 114 1994 146-159
44. Sussman M.Fatemi E.Smereka P.Osher S.An improved level set method for incompressible two-phase flows Comput. Fluids 27 1998 663-680
45. Tang Y.N.Chen Y.S.Chen W.F.Numerical simulation of bubble evolution in non-Newtonian fluids Sci. Chin. A 37 1994 42-51
46. Toose E.M.Geurts B.J.Kuerten J.G.M.A 2d boundary element method for simulating the deformation of axisymmetric compound non-Newtonian drops Int. J. Numer. Methods Fluids 30 1999 653-674
47. Ramaswamy S.Leal L.G.The deformation of a Newtonian drop in the uniaxial extensional flow of a viscoelastic liquid J. Non-Newtonian Fluid Mech. 88 1999 149-172
48. Yasuda K.Armstrong R.C.Cohen R.E.Shear flow properties of concentrated solution of linear and star branched polystyrenes Rheol. Acta 20 1981 163-178
49. Hieber C.A.Chiang H.H.Shear-rate-dependence modeling of polymer melt viscosity Polym. Eng. Sci. 32 1992 931-938
50. Grace J.R.Wairegi T.Nguyen T.H.Shapes and velocities of single drops and bubbles moving freely through immiscible liquids Trans. Inst. Chem. Engrs. 54 1976 167-173
51. B.D. Nichols, C.W. Hirt, R.S. Hotchkiss, SOLA-VOF: A Solution Algorithm for Transient Fluid Flow with Multiple Free Boundaries, Los Alamos Scientific Laboratory Report, LA-8355, 1980.
52. D.B. Kothe, R.C. Mjolsness, M.D. Torrey, RIPPLE: A Computer Program for Incompressible Flows With Free Surfaces, Los Alamos National Laboratory Report, LA-12007-MS, 1991.
53. Brackbill J.U.Kothe D.B.Zemach C.A continuum method for modeling surface tension J. Comput. Phys. 100 1992 335-354
54. Kothe D.B.Mjolsness R.C.RIPPLE: a new model for incompressible flows with free surfaces AIAA J. 30 1992 2694-2700
55. Tomiyama A.Son A.Minagawa H.Sakaguchi T.Numerical analysis of a single bubble with VOF method Trans. JSME B 57 1991 2167-2173 (in Japanese)
56. Ohta M.Suzuki M.Numerical analysis of dispersed drop behavior in the pulsed sieve-plate extraction column Int. Comm. Heat Mass Transfer 25 1998 521-530
57. Chhabra R.P.Uhlherr P.H.T.Creeping motion of spheres through shear-thinning elastic fluids described by the Carreau viscosity equation Rheol. Acta 19 1980 187-195
58. Bush M.B.Phan-Thien N.Drag force on a sphere in creeping motion through a Carreau model fluid J. Non-Newtonian Fluid Mech. 16 1984 303-313
59. Sutterby J.L.Laminar converging flow of dilute polymer solutions in conical sections. Part 1. Viscosity data, new viscosity model, tube flow solution AIChE J. 12 1966 63-68
60. N. Mitsuishi, A. Yamanaka, Y. Sueyasu, Drag force on a moving bubble and droplet in viscoelastic fluids, in: Proceedings of the PACHEC, 1972, pp. 316-317.
61. Bhaga D.Weber M.E.Bubbles in viscous liquids: shapes, wakes and velocities J. Fluid Mech. 105 1981 61-85