Bubble formation and dynamics in gas-liquid-solid fluidization-A review

Chemical Engineering Science

Volumn 62, Issue 1-2, 2007, Pages 2-27

  Yang, G Q ^a   Du, Bing ^a   Fan, L S ^a  

^a Ohio State University   (United States)

Author keywords

Bubble breakup; Bubble dynamics; Bubble formation; Bubble particle collision; Computational fluid dynamics (CFD); Gas liquid solid fluidization; Measurement techniques; Pressure

Indexed keywords

BUBBLE COLUMNS; COMPUTATION THEORY; COMPUTATIONAL FLUID DYNAMICS; COMPUTER SIMULATION; FLUID DYNAMICS; FLUIDIZATION;

BUBBLE BREAKUP; BUBBLE DYNAMICS; BUBBLE PARTICLE COLLISION; GAS LIQUID SOLID FLUIDIZATION; MEASUREMENT TECHNIQUES;

BUBBLE FORMATION;

BUBBLE COLUMNS; BUBBLE FORMATION; COMPUTATION THEORY; COMPUTATIONAL FLUID DYNAMICS; COMPUTER SIMULATION; FLUID DYNAMICS; FLUIDIZATION;

EID: 33750993457     PISSN: 00092509     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ces.2006.08.021     Document Type: Article

References (247)

1. Agresar G., Linderman J.J., Triggvason G., and Powell K.G. An adaptive, cartesian, front-tracking method for the motion deformation adhesion of circulation calls. Journal of Computational Physics 143 (1998) 346-380
2. Akagi Y., Okada K., Kosaka K., and Takahashi K. Liquid weeping accompanied by bubble formation at submerged orifices. Industrial and Engineering Chemistry Research 26 (1987) 1546-1550
3. Al-Masry W., Ali E., and Aqeel Y. Determination of bubble characteristics in bubble columns using statistical analysis of acoustic sound measurement. Chemical Engineering Research and Design 83 (2005) 1196-1207
4. Anderson T.B., and Jackson R. A fluid mechanical description of fluidized beds. Equation of motion. Industrial and Engineering Chemistry Fundamentals 6 (1967) 525-539
5. Azbel D. Two-Phase Flows in Chemical Engineering (1981), Cambridge University Press, Cambridge, UK
6. Batchelor G.K. The stability of a large gas bubble rising through liquid. Journal of Fluid Mechanics 184 (1987) 399-422
7. Bech K. Dynamic simulation of a 2D bubble column. Chemical Engineering Science 60 (2005) 5294-5304
8. Bellman R., and Pennington R.H. Effect of surface tension and viscosity on Taylor instability. Quarterly of Applied Mathematics XII (1954) 151-162
9. Bemrose C.R., Fowles P., Hawkesworth M.R., and O'Dwyer M.A. Application of positron emission tomography to particulate flow measurement in chemical engineering processes. Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors, and Associated Equipment A 273 (1988) 874-880
10. Bessler W.F., and Littman H. Experimental studies of wakes behind circularly capped bubbles. Journal of Fluid Mechanics 185 (1987) 137-151
11. Bhaga D., and Weber M.E. Bubbles in viscous liquids: shapes, wakes and velocities. Journal of Fluid Mechanics 105 (1981) 61-85
12. Boyer C., Duquenne A.M., and Wild G. Measuring techniques in gas-liquid and gas-liquid-solid reactors. Chemical Engineering Science 57 (2002) 3185-3215
13. Boys, C.V., 1959. Soap Bubble and the Forces which Mould Them. Doubleday Anchor Book.
14. Brackbill J.U., Kothe D.B., and Zemach C. A continuum method for modeling surface tension. Journal of Computational Physics 100 (1992) 335-354
15. Braeske H., Brenn G., Domnick J., Durst F., Melling A., and Ziema M. Extended phase-Doppler anemometry for measurements in three-phase flows. Chemical Engineering Technology 21 (1998) 415-420
16. Brenn G., Braeske H., and Durst F. Investigation of the unsteady two-phase flow with small bubbles in a model bubble column using phase-Doppler anemometry. Chemical Engineering Science 57 (2002) 5143-5159
17. Briens C.L., Ibrahim Y.A.A., Margaritis A., and Bergougnou M.A. Effect of coalescence inhibitors on the performance of three-phase inverse fluidized-bed columns. Chemical Engineering Science 54 (1999) 4975-4980
18. Briens L.A., and Ellis N. Hydrodynamics of three-phase fluidized bed systems examined by statistical, fractal, chaos and wavelet analysis methods. Chemical Engineering Science 60 (2005) 6094-6106
19. Broering S., Fischer J., Korte T., Sollinger S., and Luebbert A. Flow structure of the dispersed gas phase in real multiphase chemical reactors investigated by a new ultrasound-Doppler technique. Canadian Journal of Chemical Engineering 69 (1991) 1247-1256
20. Bussmann M., Mostaghimi J., and Chandra S. On a three-dimensional volume tracking model of droplet impact. Physics of Fluids 11 (1999) 1406-1417
21. Bussmann M., Mostaghimi J., and Chandra S. Modeling the splash of a droplet impacting a solid surface. Physics of Fluids 12 (2000) 3121-3132
22. Cassanello M., Larachi F., Marie M.N., Guy C., and Chaouki J. Experimental characterization of the solid phase chaotic dynamics in three-phase fluidization. Industrial and Engineering Chemistry Research 34 (1995) 2971-2980
23. Chabot J., and de Lasa H.I. Gas holdups and bubble characteristics in a bubble column operated at high temperature. Industrial and Engineering Chemistry Research 32 (1993) 2595-2601
24. Chabot J., Lee S.L.P., Soria A., and De Lasa H.I. Interaction between bubbles and fiber optic probes in a bubble column. Canadian Journal of Chemical Engineering 70 (1992) 61-68
25. Chaouki J., Larachi F., and Dudukovic M.P. Noninvasive tomographic and velocimetric monitoring of multiphase flows. Industrial and Engineering Chemistry Research 36 (1997) 4476-4503
26. Chaudhari R.V., and Hoffmann H. Coalescence of gas bubbles in liquids. Reviews in Chemical Engineering 10 (1994) 131-190
27. Che D.F., and Chen J.J.J. Bubble formation and liquid weeping at an orifice submerged in a liquid. Chemical Engineering Technology 62 (1990) 947-949
28. Chen C., and Fan L.S. Discrete simulation of gas-liquid bubble column and gas-liquid-solid fluidized bed. A.I.Ch.E. Journal 50 (2004) 288-301
29. Chen J., Kemoun A., Al-Dahhan M.H., Dudukovic M.P., Lee D.J., and Fan L.S. Comparative hydrodynamics study in a bubble column using computer-automated radioactive particle tracking (CARPT)/computed tomography (CT) and particle image velocimetry (PIV). Chemical Engineering Science 54 (1999) 2199-2207
30. Chen J.J.J., Jamialahmadi M., and Li S.M. Effect of liquid depth on circulation in bubble columns: a visual study. Chemical Engineering Research and Design 67 (1989) 203-207
31. Chen K., and Richter H.J. Instability analysis of the transition from bubbling to jetting in a gas injected into a liquid. International Journal of Multiphase Flow 23 (1997) 699-712
32. Chen R.C., and Fan L.S. Particle image velocimetry for characterizing the flow structures in three-dimensional gas-liquid-solid fluidized beds. Chemical Engineering Science 47 (1992) 3615-3622
33. Chen R.C., Reese J., and Fan L.S. Flow structure in a three-dimensional bubble column and three-phase fluidized beds. A.I.Ch.E. Journal 40 (1994) 1093-1104
34. Chen Y.M., and Fan L.S. Bubble breakage mechanisms due to collision with a particle in a liquid medium. Chemical Engineering Science 44 (1989) 117-132
35. Chen Z., Zheng C., Feng Y., and Hoffmann H. Local bubble behavior in three-phase fluidized beds. Canadian Journal of Chemical Engineering 76 (1998) 315-318
36. Chilekar V., Warnier M., van der Schaaf J., Kuster B., Schouten J., and van Ommen J. Bubble size estimation in slurry bubble columns from pressure fluctuations. A.I.Ch.E. Journal 51 (2005) 1924-1937
37. Clift R., Grace J.R., and Weber M.E. Bubbles Drops, and Particles (1978), Academic Press, New York
38. Crowe C.T., Sharma M.P., and Stock D.E. The particle-source-in-cell method for gas and droplet flow. Journal of Fluids Engineering 99 (1977) 325-332
39. Cui Z., and Fan L.S. Turbulence energy distributions in bubbling gas-liquid and gas-liquid-solid flow systems. Chemical Engineering Science 59 (2004) 1755-1766
40. Cui Z., and Fan L.-S. Energy spectra for interactive turbulence fields in a bubble column. Industrial and Engineering Chemistry Research 44 (2005) 1150-1159
41. Dandy D.S., and Leal L.G. Buoyancy-driven motion of a deformable drop through a quiescent liquid at intermediate Reynolds numbers. Journal of Fluid Mechanics 208 (1989) 161-192
42. Darton R.C., and Harrison D. The rise of single gas bubbles in liquid fluidised beds. Transactions of the Institute of Chemical Engineers 52 (1974) 301-306
43. Darwin C. Note on hydrodynamics. Proceedings of the Cambridge Philosophical Society 49 (1953) 342-354
44. Dayan A., and Zalmanovich S. Axial dispersion and entrainment of particles in wakes of bubbles. Chemical Engineering Science 37 (1982) 1253-1257
45. Dechsiri C., Ghione A., van de Wiel F., Dehling H.G., Paans A.M.J., and Hoffmann A.C. Positron emission tomography applied to fluidization engineering. Canadian Journal of Chemical Engineering 83 (2005) 88-96
46. Delnoij E., Kuipers J.A.M., and Van Swaaij W.P.M. Computational fluid dynamics applied to gas-liquid contactors. Chemical Engineering Science 52 (1997) 3623-3638
47. Dijkhuizen W., van den Hengel E.I.V., Deen N.G., van Sint Annaland M., and Kuipers J.A.M. Numerical investigation of closures for interface forces acting on single air-bubbles in water using volume of fluid and front tracking models. Chemical Engineering Science 60 (2005) 6169-6175
48. Drahos J., Zahradnik J., Puncochar M., Fialova M., and Bradka F. Effect of operating conditions on the characteristics of pressure fluctuations in a bubble column. Chemical Engineering and Processing 29 (1991) 107-115
49. Drahos J., Bradka F., and Puncochar M. Fractal behavior of pressure fluctuations in a bubble column. Chemical Engineering Science 47 (1992) 4069-4075
50. Du, B., Warsito, W., Fan, L.-S., 2005. Transient 3-dimensional behavior of gas-solid fluidization measured using electrical capacitance volume tomography (ECVT). A.I.Ch.E. Annual Meeting, Conference Proceedings, Cincinnati, OH, USA.
51. El-Temtamy S.A., and Epstein N. Rise velocities of large single two-dimensional and three-dimensional gas bubbles in liquids and in liquid fluidized beds. Chemical Engineering Journal 19 (1980) 153-156
52. Fan L.-S. Gas-Liquid-Solid Fluidization Engineering (1989), Butterworth, Stoneham, MA
53. Fan L.-S., and Tsuchiya K. Bubble Wake Dynamics in Liquids and Liquid-Solid Suspensions (1990), Butterworth-Heinemann, Stoneham, MA
54. Fan L.-S., Tzeng J.W., and Bi H.T. Flow structure in a two-dimensional bubble column and three-phase fluidized bed. Fluidization VII (1992), Engineering Foundation, New York pp. 399-406
55. Fan L.-S., Yang G.Q., Lee D.J., Tsuchiya K., and Luo X. Some aspects of high-pressure phenomena of bubbles in liquids and liquid-solid suspensions. Chemical Engineering Science 54 (1999) 4681-4709
56. Feng J., Hu H.H., and Joseph D.D. Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid. Part 1: Sedimentation. Journal of Fluid Mechanics 261 (1994) 95-134
57. Fournier T., and Jeandey C. Optimization of an experimental setup for void fraction determination by the X-ray attenuation technique. Measuring Techniques in Gas-Liquid Two-Phase Flows (1993), Springer, New York pp. 199-228
58. Fox J.M. Fischer-Tropsch reactor selection. Catalysis Letters 7 (1990) 281-292
59. Frijlink, J., 1987. Physical aspects of gassed suspension reactors. Ph.D. Thesis, Delft University of Technology.
60. Fukai J., Shiiba Y., Yamamoto T., and Miyatake O. Wetting effects on the spreading of a liquid droplet colliding with a flat surface: experiment and modeling. Physics of Fluids 7 (1995) 236-247
61. Ge, Y., Fan, L.S., 2006. 3-D direct numerical simulation of gas-liquid and gas-liquid-solid flow systems using the level-set and immersed boundary methods. Advances in Chemical Engineering, in press.
62. George D.L., Shollenberger K.A., Torczynski J.R., O'Hern T.J., and Ceccio S.L. Three-phase material distribution measurements in a vertical flow using gamma-densitometry tomography and electrical-impedance tomography. International Journal of Multiphase Flow 27 (2001) 1903-1930
63. Gladden L.F. Nuclear magnetic resonance in chemical engineering: principles and applications. Chemical Engineering Science 49 (1994) 3339-3408
64. Gladden L.F. Recent advances in MRI studies of chemical reactors: ultrafast imaging of multiphase flows. Topics in Catalysis 24 (2003) 19-28
65. Gladden L.F., Anadon L.D., Lim M.H.M., Sederman A.J., and Stitt E.H. Insights into the mechanism of the trickle-to-pulse transition in trickle-bed reactors. Industrial and Engineering Chemistry Research 44 (2005) 6320-6331
66. Gnyloskurenko S., Byakova A., Raychenko O., and Nakamura T. Influence of wetting conditions on bubble formation at orifice in an inviscid liquid. Transformation of bubble shape and size. Colloids and Surface, A: Physicochemical and Engineering Aspects 218 (2003) 73-87
67. Gnyloskurenko S., Byakova A., Nakamura T., and Raychenko O. Influence of wettability on bubble formation in liquid. Journal of Material Science 40 (2005) 2437-2441
68. Grace J.R. Shapes and velocities of bubbles rising in infinite liquids. Transactions of the Institute of Chemical Engineers 51 (1973) 116-120
69. Grace J.R., Wairegi T., and Brophy J. Break-up of drops and bubbles in stagnant media. Canadian Journal of Chemical Engineering 56 (1978) 3-8
70. Harlow F.H., and Welch J.E. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Physics of Fluids 8 (1965) 2182-2189
71. Harvie D.J.E., and Fletcher D.F. A hydrodynamic and thermodynamic simulation of droplet impacts on hot surface. Part I: Theoretical model. International Journal of Heat and Mass Transfer 44 (2001) 2633-2642
72. Harvie D.J.E., and Fletcher D.F. A hydrodynamic and thermodynamic simulation of droplet impacts on hot surface. Part II: Validation and applications. International Journal of Heat and Mass Transfer 44 (2001) 2643-2659
73. Henriksen H.K., and Ostergaard K. Characteristics of large two-dimensional air bubbles in liquids and in three-phase fluidized beds. Chemical Engineering Journal 7 (1974) 141-146
74. Hills J.H., and Darton R.C. The rising velocity of a large bubble in a bubble swarm. Transactions of the Institution of Chemical Engineers 54 (1976) 258-264
75. Hinze J.O. Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. A.I.Ch.E. Journal 1 (1955) 289-295
76. Hirt C.W., and Nichols B.D. Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics 39 (1981) 201-225
77. Hirt C.W., Amsden A.A., and Cook J.L. An arbitrary Lagrangian Eulerian computing method for all speeds. Journal of Computational Physics 14 (1974) 227-253
78. Hoffmann A.C., Dechsiri C., Van de Wiel F., and Dehling H.G. PET investigation of a fluidized particle: spatial and temporal resolution and short term motion. Measurement Science and Technology 16 (2005) 851-858
79. Hong, T., Fan, L.-S., 1994. Bubble breakup due to bubble-particle collisions, unpublished work.
80. Hong T., Fan L.-S., and Lee D.J. Force variations on particle induced by bubble-particle collision. International Journal of Multiphase Flow 25 3 (1999) 477-500
81. Hoomans B.P.B., Kuipers J.A.M., Briels W.J., and van Swaaij W.P.M. Discrete particle simulation of a two-dimensional gas-fluidized bed: a hard sphere approach. Chemical Engineering Science 51 (1996) 99-118
82. Hubers J.L., Striegel A.C., Heindel T.J., Gray J.N., and Jensen T.C. X-ray computed tomography in large bubble columns. Chemical Engineering Science 60 (2005) 6124-6133
83. Idogawa K., Ikeda K., Fukuda T., and Morooka S. Behavior of bubbles of the air-water system in a column under high pressure. International Chemical Engineering 26 (1986) 468-474
84. Idogawa K., Ikeda K., Fukuda T., and Morooka S. Formation and flow of gas bubbles in a pressurized bubble column with a single orifice or nozzle gas distributor. Chemical Engineering Communications 59 (1987) 201-210
85. Jackson R. The Dynamics of Fluidized Particles (2000), Cambridge University Press, New York
86. Jager B., and Espinoza R. Advances in low temperature Fischer-Tropsch synthesis. Catalysis Today 23 (1995) 17-28
87. Jamet D., Lebaigue O., Coutris N., and Delhaye J.M. The second gradient method for the direct numerical simulations of liquid-vapor flows with phase-change. Journal of Computational Physics 169 (2001) 624-651
88. Jiang P., Arters D., and Fan L.-S. Pressure effects on the hydrodynamic behavior of gas-liquid-solid fluidized beds. Industrial and Engineering Chemistry Research 31 (1992) 2322-2327
89. Jiang P., Lin T.J., Luo X., and Fan L.S. Visualization of high pressure (21 MPa) bubble column: bubble characteristics. Chemical Engineering Research and Design 73 (1995) 269-274
90. Jiang P., Luo X., Lin T.J., and Fan L.-S. High temperature and high pressure three-phase fluidization-bed expansion phenomena. Powder Technology 90 (1997) 103-113
91. Jin H., Yang S., Guo Z., He G., and Tong Z. The axial distribution of holdups in an industrial-scale bubble column with evaluated pressure using γ-ray attenuation approach. Chemical Engineering Journal 115 (2005) 45-50
92. Johnsson F., Zijerveld R.C., Schouten J.C., Van den Bleek C.M., and Leckner B. Characterization of fluidization regimes by time-series analysis of pressure fluctuations. International Journal of Multiphase Flow 26 (2000) 663-715
93. Joseph D.D., and Lundgren T.S. Ensemble averaged and mixture theory equations for incompressible fluid-particle suspensions. International Journal of Multiphase Flow 16 (1990) 35-42
94. Julia J.E., Harteveld W.K., Mudde R.F., and Van den Akker H.E.A. On the accuracy of the void fraction measurements using optical probes in bubbly flows. Review of Scientific Instruments 76 (2005) 035103/1-035103/13
95. Kanai, A., Miyata, H., 1995. Numerical simulation of bubbles in a boundary layer by Maker-Density-Function. In: Proceedings of the Third International Conference on Multiphase Flow, Lion, France.
96. Karl A., Anders K., Rieber M., and Frohn A. Deformation of liquid droplets during collisions with hot walls: experimental and numerical results. Particle & Particle Systems Characterization 13 (1996) 186-191
97. Kiambi S.L., Duquenne A.M., Dupont J.B., Colin C., Risso F., and Delmas H. Measurements of bubble characteristics: comparison between double optical probe and imaging. Canadian Journal of Chemical Engineering 81 (2003) 764-776
98. Kiared K., Larachi F., Chaouki J., and Guy C. Mean and turbulent particle velocity in the fully developed region of a three-phase fluidized bed. Chemical Engineering Technology 22 (1999) 683-689
99. Kim J.O., and Kim S.D. Bubble breakage phenomena, phase holdups and mass transfer in three-phase fluidized beds with floating bubble breakers. Chemical Engineering and Processing 28 (1990) 101-111
100. Kim M.C., Kim K.Y., and Kim S. Improvement of impedance imaging for two-phase systems with boundary estimation approach in electrical impedance tomography. Canadian Journal of Chemical Engineering 83 (2005) 55-63
101. Kitscha J., and Kocamustafaogullari G. Breakup criteria for fluid particles. International Journal of Multiphase Flow 15 (1989) 573-588
102. Klug P., and Vogelpohl A. Bubble formation with superimposed liquid motion at single-hole plates and sieve plates. Ger. Chem. Engineering 6 (1983) 311-317
103. Kluytmans J.H., van Wachem B.G.M., Kuster B.F.M., Krishna R., and Schouten J.C. 2D slurry bubble column hydrodynamic phenomena clarified with a 3D gas-liquid model. Canadian Journal of Chemical Engineering 81 (2003) 456-464
104. Kluytmans J.H.J., van Wachem B.G.M., Kuster B.F.M., and Schouten J.C. Gas holdup in a slurry bubble column: influence of electrolyte and carbon particles. Industrial and Engineering Chemistry Research 40 (2001) 5326-5333
105. Kothe, D.B., Rider, W.J., 1995. Comments on modeling interfacial flows with volume-of fluid methods. Los Alamos National Laboratory Research Report, LA-UR-94-3384.
106. Krishna R., and van Baten J.M. Scaling up bubble column reactors with the aid of CFD. Chemical Engineering Research and Design 79 A3 (2001) 283-309
107. Krishna R., and van Baten J.M. A strategy for scaling up the Fischer-Tropsch bubble column slurry reactor. Topics in Catalysis 26 (2003) 21-28
108. Krishna R., de Swart J.W.A., Hennephof D.E., Ellenberger J., and Hoefsloot C.J. Influence of increased gas density on hydrodynamics of bubble column reactors. A.I.Ch.E. Journal 40 (1994) 112-119
109. Krishna R., van Baten J.M., Urseanu M.I., and Ellenberger J. A scale up strategy for bubble column slurry reactors. Catalysis Today 66 (2001) 199-207
110. Kulkarni A., Joshi J., and Ramkrishna D. Determination of bubble size distribution in bubble columns using LDA. A.I.Ch.E. Journal 50 (2004) 3068-3084
111. Kulkarni A.A., and Joshi J.B. Bubble formation and bubble rise velocity in gas-liquid systems: a review. Industrial and Engineering Chemistry Research 44 (2005) 5873-5931
112. Kumar R., and Kuloor N.R. The formation of bubbles and drops. Advances in Chemical Engineering 8 (1970) 255-368
113. Kumar S., Kusakabe K., Raghunathan K., and Fan L.S. Mechanism of heat transfer in bubbly liquid and liquid-solid systems: single bubble injection. A.I.Ch.E. Journal 38 (1992) 733-741
114. Kumar S.B., Moslemian D., and Dudukovic M.P. A γ-ray tomographic scanner for imaging voidage distribution in two-phase flow systems. Flow Measurement and Instrumentation 6 (1995) 61-73
115. Kumar, S.B., Dudukovic, M.P., Toseland, B.A., 1997. Measurement techniques for local and global fluid dynamic quantities in two and three phase systems. Non-Invasive Monitoring of Multiphase Flows 1-45.
116. Kupferberg A., and Jameson G.J. Bubble formation at a submerged orifice above a gas chamber of finite volume. Transactions of the Institute of Chemical Engineers 47 (1969) T241-T250
117. L'Homme G.A. Chemical Engineering of Gas-Liquid-Solid Catalyst Reactions (1979), CEBEDOC, Liege
118. La Nauze R.D., and Harris I.J. Gas bubble formation at elevated system pressures. Transactions of the Institute of Chemical Engineers 52 (1974) 337-348
119. Lapin A., and Lübbert A. Numerical simulation of the dynamics of two-phase gas-liquid flows in bubble columns. Chemical Engineering Science 49 (1994) 3661-3674
120. Larachi F., Cassanello M., Chaouki J., and Guy C. Flow structure of the solids in a 3-D gas-liquid-solid fluidized bed. A.I.Ch.E. Journal 42 (1996) 2439-2452
121. Larachi F., Chaouki J., Kennedy G., and Dudukovic M.P. Radioactive particle tracking in multiphase reactors: principles and applications. Non-Invasive Monitoring of Multiphase Flows (1997), Elsevier, Amsterdam 335-406
122. Lau R., Cui Z., and Fan L.-S. Liquid entrainment in high-pressure bubble columns. Industrial and Engineering Chemistry Research 44 (2005) 3776-3782
123. Lazarek G.M., and Littman H. Pressure field due to a large circular capped air bubble rising in water. Journal of Fluid Mechanics 66 (1974) 673-687
124. Leblond J., Javelot S., Lebrun D., and Lebon L. Two-phase flow characterization by nuclear magnetic resonance. Nuclear Engineering and Design 184 (1998) 229-237
125. Lee D.J., Luo X., and Fan L.-S. Gas disengagement technique in a slurry bubble column operated in the coalesced bubble regime. Chemical Engineering Science 54 (1999) 2227-2236
126. Lee S.L.P., and De Lasa H.I. Phase holdups in three-phase fluidized beds. A.I.Ch.E. Journal 33 (1987) 1359-1370
127. Lee S.L.P., De Lasa H.I., and Bergougnou M.A. A U-shaped fiber optic probe to study three-phase fluidized beds. Particulate Science and Technology 4 (1986) 61-71
128. Le Gall F., Pascal-Ribot S., and Leblond J. Nuclear magnetic resonance measurements of fluctuations in air-water two-phase flow: pipe flow with and without "disturbing" section. Physics of Fluids 13 (2001) 1118-1129
129. Leibson I., Holcomb E.G., Cacoso A.G., and Jacmic J.J. Rate of flow and mechanics of bubble formation from single submerged orifices. A.I.Ch.E. Journal 2 (1956) 296-306
130. Levich V.G. Physiochemical Hydrodynamics (1962), Prentice-Hall, Englewood Cliffs, NJ
131. Li Y., Zhang J., and Fan L.-S. Numerical simulation of gas-liquid-solid fluidization systems using a combined CFD-VOF-DPM method: bubble wake behavior. Chemical Engineering Science 54 (1999) 5101-5107
132. Li Y., Yang G.Q., Zhang J.P., and Fan L.-S. Numerical studies of bubble formation dynamics in gas-liquid-solid fluidization at high pressures. Powder Technology 116 (2001) 246-260
133. Lim M.H.M., Sederman A.J., Gladden L.F., and Stitt E.H. New insights to trickle and pulse flow hydrodynamics in trickle-bed reactors using MRI. Chemical Engineering Science 59 (2004) 5403-5410
134. Lin J.N., Banerji S.K., and Yasuda H. Role of interfacial tension in the formation and the detachment of air bubbles: a single hole on a horizontal plane immersed in water. Langmuir 10 (1994) 936-942
135. Lin T.J., and Fan L.-S. Characteristics of high-pressure liquid-solid fluidization. A.I.Ch.E. Journal 43 (1997) 45-57
136. Lin T.J., Tsuchiya K., and Fan L.-S. Bubble flow characteristics in bubble columns at elevated pressure and temperature. A.I.Ch.E. Journal 44 (1998) 545-560
137. Liu T.J. Bubble size and entrance length effects on void development in a vertical channel. International Journal of Multiphase Flow 19 (1993) 99-113
138. Luo X., Zhang J., Tsuchiya K., and Fan L.-S. On the rise velocity of bubbles in liquid-solid suspensions at elevated pressure and temperature. Chemical Engineering Science 52 (1997) 3693-3699
139. Luo X., Yang G.Q., Lee D.J., and Fan L.-S. Single bubble formation in high pressure liquid-solid suspensions. Powder Technology 100 (1998) 103-112
140. Luo X., Tsuchiya K., and Fan L.-S. Gas jetting and bubble formation in high pressure liquid-solid suspensions. In: Fan L.S., and Knowlton T.M. (Eds). Fluidization IX (1998), Engineering Foundation, New York 637-644
141. Luo X., Lee D.J., Lau R., Yang G.Q., and Fan L.S. Maximum stable bubble size and gas holdup in high-pressure slurry bubble columns. A.I.Ch.E. Journal 45 (1999) 665-680
142. Maneri C.C. New look at wave analogy for prediction of bubble terminal velocities. A.I.Ch.E. Journal 41 (1995) 481-487
143. Massimilla L., Solimando A., and Squillace E. Gas dispersion in solid-liquid fluidized beds. British Chemical Engineering 6 (1961) 232-239
144. Matonis D., Gidaspow D., and Bahary M. CFD simulation of flow and turbulence in a slurry bubble column. A.I.Ch.E. Journal 48 (2002) 1413-1429
145. Matsuura A., and Fan L.-S. Distribution of bubble properties in a gas-liquid-solid fluidized bed. A.I.Ch.E. Journal 30 (1984) 894-903
146. McCann D.J., and Prince R.G.H. Bubble formation and weeping at a submerged orifice. Chemical Engineering Science 24 (1969) 801-814
147. McNallan M.J., and King T.B. Fluid dynamics of vertical submerged gas jets in liquid metal processing systems. Metallurgical Transactions B: Process Metallurgy 13B (1982) 165-173
148. Mehdi-Nejad V., Mostaghimi J., and Chandra S. Air bubble entrapment under an impacting droplet. Physics of Fluids 15 (2003) 173-183
149. Mendelson H.D. The prediction of bubble terminal velocities from wave theory. A.I.Ch.E. Journal 13 (1967) 250-253
150. Mersmann A. Flooding point of liquid/liquid countercurrent columns. Chemical Engineering Technology 52 (1980) 933-942
151. Mills P.L., Turner J.R., Ramachandran P.A., and Dudukovic M.P. The Fischer-Tropsch synthesis in slurry bubble column reactors: analysis of reactor performance using the axial dispersion model. Topics in Chemical Engineering 8 (1996) 339-386 679-739
152. Mittal R., and Iaccarino G. Immersed boundary methods. Annual Review of Fluid Mechanics 37 (2005) 239-261
153. Miyahara T., and Takahashi T. Bubble volume in single bubbling regime with weeping at a submerged orifice. Journal of Chemical Engineering of Japan 17 (1984) 597-602
154. Miyahara T., Haga N., and Takahashi T. Bubble formation from an orifice at high gas flow rates. International Chemical Engineering 23 (1983) 524-531
155. Miyahara T., Iwata M., and Takahashi T. Bubble formation pattern with weeping at a submerged orifice. Journal of Chemical Engineering of Japan 17 (1984) 592-597
156. Miyahara T., Tsuchiya K., and Fan L.-S. Mechanism of particle entrainment in a gas-liquid-solid fluidized bed. A.I.Ch.E. Journal 35 (1989) 1195-1198
157. Monaghan J. Simulating free surface flows with SPH. Journal of Computational Physics 110 (1994) 399-406
158. Mudde R.F., and Simonin O. Two- and three-dimensional simulations of bubble plume using a two-fluid model. Chemical Engineering Science 54 (1999) 5061-5069
159. Nacef S., Poncin S., and Wild G. Onset of fluidization and flow regimes in gas-liquid-solid fluidization-influence of the coalescence behavior of the liquid. In: Large J.F., and Laguerie C. (Eds). Fluidization VIII (1995), Engineering Foundation, New York 631-638
160. Nedeltchev S., Kumar S.B., and Dudukovic M.P. Flow regime identification in a bubble column based on both Kolmogorov entropy and quality of mixedness derived from CARPT data. Canadian Journal of Chemical Engineering 81 (2003) 367-374
161. Oestergaard K. Flow phenomena of three-phase (gas-liquid-solid) fluidized beds. A.I.Ch.E. Symposium Series 69 (1973) 28-29
162. Osher S., and Sethian J.A. Fronts propagation with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulation. Journal of Computational Physics 79 (1988) 12-49
163. Ozawa Y., and Mori K. Characteristics of jetting observed in gas injection into liquid. Transactions ISIJ 23 (1983) 764-768
164. Ozawa Y., and Mori K. Effect of physical properties of gas and liquid on bubbling-jetting phenomena in gas injection into liquid. Transactions ISIJ 26 (1986) 291-297
165. Page R.E., and Harrison D. Particle entrainment from a three-phase fluidized bed. In: Angelino H., Couderc J.P., Gibert H., and Laguerie C. (Eds). Fluidization and its Applications (1974), Cepadues-Editions, Toulouse 393-401
166. Peng W.L., Yang G.Q., and Fan L.-S. Experimental studies of liquid weeping and bubbling phenomena at submerged orifices. Industrial and Engineering Chemistry Research 41 (2002) 1666-1677
167. Peng X.D., Toseland B.A., and Tijm P.J.A. Kinetic understanding of chemical synergy under LPDME conditions-once-through applications. Chemical Engineering Science 54 (1999) 2787-2792
168. Peskin C.S. Numerical analysis of blood flow in the heart. Journal of Computational Physics 25 (1977) 220-252
169. Peters M.H., Fan L.-S., and Sweeney T.L. Study of particle ejections in the freeboard region of a fluidized bed with an image carrying probe. Chemical Engineering Science 38 (1983) 481-485
170. Rabiger N., and Vogelpohl A. Bubble formation in stagnant and flowing Newtonian liquids. German Chemical Engineering 5 (1982) 314-323
171. Raghunathan K., Kumar S., and Fan L.S. Pressure distribution and vortical structure in the wake behind gas bubble in liquid and liquid-solid systems. International Journal of Multiphase Flow 18 (1992) 41-50
172. Ramachandran, P.A., Chaudhari, R.V., 1983. Three-Phase Catalytic Reactors. Gordon and Breach Science, New York.
173. Ramakrishnan S., Kumar R., and Kuloor N.R. Studies in bubble formation-I: bubble formation under constant flow conditions. Chemical Engineering Science 24 (1969) 731-747
174. Reese J., Chen R.C., and Fan L.S. Three-dimensional particle image velocimetry for use in three-phase fluidization systems. Experiments in Fluids 19 (1995) 367-378
175. Reese J., Jiang P., and Fan L.S. Bubble characteristics in three-phase systems used for pulp and paper processing. Chemical Engineering Science 51 (1996) 2501-2510
176. Rowe P.N., and Masson H. Interaction of bubbles with probes in gas fluidized beds. Transactions of the Institute of Chemical Engineers 59 (1981) 177-185
177. Ruzicka M.C., Drahos J., Zahradnik J., and Thomas N.H. Intermittent transition from bubbling to jetting regime in gas-liquid two phase flows. International Journal of Multiphase Flow 23 (1997) 671-682
178. Safoniuk M., Grace J.R., Hackman L., and McKnight C.A. Use of dimensional similitude for scale-up of hydrodynamics in three-phase fluidized beds. Chemical Engineering Science 54 (1999) 4961-4966
179. Sagert N.H., and Quinn M.J. Influence of high-pressure gases on the stability of thin aqueous films. Journal of Colloid and Interface Science 61 (1977) 279-286
180. Sagert N.H., and Quinn M.J. Surface viscosities at high pressure gas-liquid interfaces. Journal of Colloid and Interface Science 65 (1978) 415-422
181. Sato T., and Richardson S.M. Numerical simulation method for viscoelastic flows with free surface-fringe element generation method. International Journal for Numerical Methods in Fluids 19 (1994) 555-574
182. Saxena S.C. Bubble column reactors and Fischer-Tropsch synthesis. Catalysis Reviews: Science and Engineering 37 (1995) 227-309
183. Scardovelli R., and Zeleski S. Direct numerical simulation of free-surface and interfacial flow. Annual Review of Fluid Mechanics 31 (1999) 567-603
184. Sederman A.J., and Gladden L.F. Transition to pulsing flow in trickle-bed reactors studied using MRI. A.I.Ch.E. Journal 51 (2005) 615-621
185. Seeger A., Kertzscher U., Affeld K., and Wellnhofer E. Measurement of the local velocity of the solid phase and the local solid hold-up in a three-phase flow by X-ray based particle tracking velocimetry (XPTV). Chemical Engineering Science 58 (2003) 1721-1729
186. Sethian J.A., and Smereka P. Level set methods for fluid interfaces. Annual Review of Fluid Mechanics 35 (2003) 341-372
187. Seville, J.P.K., Morgan, J.E.P., Clift, R., 1986. Tomographic determination of the voidage structure of gas fluidized beds in the jet region. Fluidization V. Engineering Foundation, New York, p. 87.
188. Shah Y.T. Gas-Liquid-Solid Reactor Design (1979), McGraw-Hill, New York
189. Shoukri M., Hassan I., and Gerges I. Two-phase bubbly flow structure in large-diameter vertical pipes. Canadian Journal of Chemical Engineering 81 (2003) 205-211
190. Sokolichin A., and Eigenberger G. Gas-liquid flow in bubble columns and loop reactors: part 1. Detailed modeling and numerical simulation. Chemical Engineering Science 49 (1994) 5735-5746
191. Sokolichin A., and Eigenberger G. Applicability of the standard k-ε{lunate} turbulence model to the dynamic simulation of bubble column: part 1. Detailed numerical simulation. Chemical Engineering Science 54 (1999) 2273-2284
192. Song, G.H., 1989. Hydrodynamics and interfacial gas-liquid mass transfer of gas-liquid-solid fluidized beds. Ph.D. Dissertation, The Ohio State University, Columbus, OH.
193. Sookai S., Langenhoven P.L., and Shingles T. Scale-up and commercial reactor fluidization related experience with Synthol, gas to liquid fuel, dense phase fluidized bed reactors. In: Kwauk M., Li J., and Yang W.-C. (Eds). Fluidization X (2001) 621-628
194. Soong Y., Harke F.W., Gamwo I.K., Schehl R.R., and Zarochak M.F. Hydrodynamic study in a slurry-bubble-column reactor. Catalysis Today 35 (1997) 427-434
195. Stein M., Ding Y.L., Seville J.P.K., and Parker D.J. Solids motion in bubbling gas fluidized beds. Chemical Engineering Science 55 (2000) 5291-5300
196. Stewart P.S.B., and Davidson J.F. Three-phase fluidization: water, particles, and air. Chemical Engineering Science 19 (1964) 319-321
197. Stolojanu V., and Prakash A. Hydrodynamic measurements in a slurry bubble column using ultrasonic techniques. Chemical Engineering Science 52 (1997) 4225-4230
198. Sundar R., and Tan R.B.H. A model for bubble-to-jet transition at a submerged orifice. Chemical Engineering Science 54 (1999) 4053-4060
199. Sussman M., Smereka P., and Osher S. A level set approach for computing solutions to incompressible two-phase flow. Journal of Computational Physics 114 (1994) 146-159
200. Tang W.T., and Fan L.S. Hydrodynamics of a three-phase fluidized bed containing low-density particles. A.I.Ch.E. Journal 35 (1989) 355-364
201. Tomiyama A., Kataoka I., and Sakaguchi T. Drag coefficients of bubbles. 1. Drag coefficients of a single bubble in a stagnant liquid. Nippon Kikai Gakkai Ronbunshu B-hen 61 (1995) 2357-2364
202. Tryggvason T., Bunner B., Esmaeeli A., Juric D., Al-Rawahi N., Tauber W., Han J., Nas S., and Jan Y.J. A front-tracking method for the computations of multiphase flow. Journal of Computational Physics 169 (2001) 708-759
203. Tsuchiya K., and Fan L.S. Near-wake structure of a single gas bubble in a two-dimensional liquid-solid fluidized bed: vortex shedding and wake size variation. Chemical Engineering Science 43 (1988) 1167-1181
204. Tsuchiya K., Song G.H., and Fan L.S. Effects of particle properties on bubble rise and wake in a two-dimensional liquid-solid fluidized bed. Chemical Engineering Science 45 (1990) 1429-1434
205. Tsuchiya K., Song G.H., Tang W.T., and Fan L.S. Particle drift induced by a bubble in a liquid-solid fluidized bed with low-density particles. A.I.Ch.E. Journal 38 (1992) 1847-1851
206. Tsuchiya K., Furumoto A., Fan L.S., and Zhang J. Suspension viscosity and bubble velocity in liquid-solid fluidized beds. Chemical Engineering Science 52 (1997) 3053-3066
207. Tsuge H., and Hibino S. Bubble formation from an orifice submerged in liquids. Chemical Engineering Communications 22 (1983) 63-79
208. Tsuge H., Nakajima Y., and Terasaka K. Behavior of bubbles formed from a submerged orifice under high system pressure. Chemical Engineering Science 47 (1992) 3273-3280
209. Tsuji Y., Kawaguchi T., and Tanaka T. Discrete particle simulation of two-dimensional fluidized bed. Powder Technology 77 (1993) 79-81
210. Tsutsumi A., Nieh J.Y., and Fan L.S. Particle wettability effects on bubble wake dynamics in gas-liquid-solid fluidization. Chemical Engineering Science 46 (1991) 2381-2384
211. Tsutsumi A., Dastidar A.G., and Fan L.S. Characteristics of gas-liquid-solid fluidization with nonwettable particles. A.I.Ch.E. Journal 37 (1991) 951-952
212. Tzeng J.W., Chen R.C., and Fan L.S. Visualization of flow characteristics in a 2-D bubble column and three-phase fluidized bed. A.I.Ch.E. Journal 39 (1993) 733-744
213. Unverdi S.O., and Tryggvason G. A front-tracking method for viscous, incompressible, multi-fluid flows. Journal of Computational Physics 100 (1992) 25-37
214. 2 particles in slurry bubble column using ultrasonic computed tomography. Chemical Engineering Science 56 (2001) 6073-6079
215. Vakhrushev I.A., and Efremov G.I. Chemistry and Technology of Fuels and Oils 5/6 (1970) 376-380
216. van Baten J.M., and Krishna R. Scale effects on the hydrodynamics of bubble columns operating in the heterogeneous flow regime. Chemical Engineering Research and Design 82 A8 (2004) 1043-1053
217. van Sint Annaland M., Deen N.G., and Kuipers J.A.M. Numerical simulation of gas bubbles behavior using a three-dimensional volume of fluid method. Chemical Engineering Science 60 (2005) 2999-3011
218. Vandu C.O., Koop K., and Krishna R. Large bubble sizes and rise velocities in a bubble column slurry reactor. Chemical Engineering and Technology 27 (2005) 1195-1199
219. Veera U.P., and Joshi J.B. Measurement of gas hold-up profiles in bubble column by gamma ray tomography. Chemical Engineering Research and Design 78 (2000) 425-434
220. Vial C., Laine R., Poncin S., Midoux N., and Wild G. Influence of gas distribution and regime transitions on liquid velocity and turbulence in a 3-D bubble column. Chemical Engineering Science 56 (2001) 1085-1093
221. Vrij A. Possible mechanism for the spontaneous rupture of thin, free liquid films. Discussions of the Faraday Society 42 (1966) 23-33
222. Walter J.F., and Blanch H.W. Bubble break-up in gas-liquid bioreactors: break-up in turbulent flows. Chemical Engineering Journal 32 (1986) B7-B17
223. Wang G., and Ching C.Y. Measurement of multiple gas-bubble velocities in gas-liquid flows using hot-film anemometry. Experiments in Fluids 31 (2001) 428-439
224. Warsito W., and Fan L.S. Measurement of real-time flow structures in gas-liquid and gas-liquid-solid flow systems using electrical capacitance tomography (ECT). Chemical Engineering Science 56 (2001) 6455-6462
225. Warsito W., and Fan L.S. ECT imaging of three-phase fluidized bed based on three-phase capacitance model. Chemical Engineering Science 58 (2003) 823-832
226. Warsito W., and Fan L.S. Dynamics of spiral bubble plume motion in the entrance region of bubble columns and three-phase fluidized beds using 3D ECT. Chemical Engineering Science 60 (2005) 6073-6084
227. Warsito W., Ohkawa M., Kawata N., and Uchida S. Cross-sectional distributions of gas and solid holdups in slurry bubble column investigated by ultrasonic computed tomography. Chemical Engineering Science 54 (1999) 4711-4728
228. West R.M., Tapp H.S., Spink D.M., Bennett M.A., Williams, and Richard A. Application-specific optimization of regularization for electrical impedance tomography. Measurement Science and Technology 12 (2001) 1050-1054
229. Wilkinson P.M., and van Dierendonck L.L. Pressure and gas density effects on bubble break-up and gas hold-up in bubble columns. Chemical Engineering Science 45 (1990) 2309-2315
230. Wilkinson P.M., and van Dierendonck L.L. A theoretical model for the influence of gas properties and pressure on single-bubble formation at an orifice. Chemical Engineering Science 49 (1994) 1429-1438
231. Wolf J. Investigation of bubbly flow by ultrasonic tomography. Particle & Particle Systems Characterization 5 (1988) 170-173
232. Xiao Z., and Tan R.B.H. A model for bubble-bubble and bubble-wall interaction in bubble formation. A.I.Ch.E. Journal 52 (2006) 86-98
233. Xu L., Han Y., Xu L.A., and Yang J. Application of ultrasonic tomography to monitoring gas/liquid flow. Chemical Engineering Science 52 (1997) 2171-2183
234. Xue J., Al-Dahhan M., Dudukovic M.P., and Mudde R.F. Bubble dynamics measurements using four-point optical probe. Canadian Journal of Chemical Engineering 81 (2003) 375-381
235. Yabe, T., 1997. Interface capturing and universal solution of solid, liquid and gas by CIP method. In: Proceedings of the High-Performance Computing of Multi-Phase Flow, Tokyo, July 18-19.
236. Yang G.Q., Luo X., Lau R., and Fan L.S. Bubble formation in high-pressure liquid-solid suspensions with plenum pressure fluctuation. A.I.Ch.E. Journal 46 (2000) 2162-2174
237. Yoo D.H., Tsuge H., Terasaka K., and Mizutani K. Behavior of bubble formation in suspended solution for an elevated pressure system. Chemical Engineering Science 52 (1997) 3701-3707
238. Yu Y.H., and Kim S.D. Bubble characteristics in the radial direction of three-phase fluidized beds. A.I.Ch.E. Journal 34 (1988) 2069-2072
239. Zaruba A., Krepper E., Prasser H.M., and Vanga B.N.R. Experimental study on bubble motion in a rectangular bubble column using high-speed video observations. Flow Measurement and Instrumentation 16 (2005) 277-287
240. Zenit R., Koch D.L., and Sangani A.S. Measurements of the average properties of a suspension of bubbles rising in a vertical channel. Journal of Fluid Mechanics 429 (2001) 307-342
241. Zenit R., Koch D.L., and Sangani A.S. Impedance probe to measure local gas volume fraction and bubble velocity in a bubbly liquid. Review of Scientific Instruments 74 (2003) 2817-2827
242. Zhang D.Z., and Prosperetti A. Averaged equations for inviscid disperse two phase flow. Journal of Fluid Mechanics 267 (1994) 185-219
243. Zhang D.Z., and Prosperetti A. A method for particle simulation. Journal of Applied Mechanics 70 (2003) 64-74
244. Zhang J., Fan L.S., Zhu C., Pfeffer R., and Qi D. Dynamic behavior of collision of elastic spheres in viscous fluids. Powder Technology 106 (1999) 98-109
245. Zhang J., Li Y., and Fan L.S. Numerical studies of bubble and particle dynamics in a three-phase fluidized bed at elevated pressures. Powder Technology 112 (2000) 46-56
246. Zhang K., and Zhao Y. A scale-up strategy for low-temperature methanol synthesis in a circulating slurry bubble reactor. Chemical Engineering Science 61 (2006) 1459-1469
247. Zhang Y., Xiao Z., and Tan R.B.H. Interfacial element modeling of bubble formation with liquid viscosity. Journal of Chemical Engineering of Japan 38 (2005) 478-485