Flow and mass transfer of fully resolved bubbles in non-Newtonian fluids

AIChE Journal

Volumn 53, Issue 7, 2007, Pages 1861-1878

  Radl, Stefan ^a   Tryggvason, Gretar ^b   Khinast, Johannes G ^c,d  

^a GRAZ UNIVERSITY OF TECHNOLOGY   (Austria)

^b Worcester Polytechnic Institute   (United States)

^c The State University of New Jersey   (United States)

^d Institute RNS   (Austria)

Author keywords

Bubbles; Mass transfer; Non Newtonian liquids; Numerical simulation

Indexed keywords

ABNORMAL MIXING; CONCENTRATION FIELDS; SHEAR THINNING EFFECTS; VISCOELASTIC MODEL FLUIDS;

ALGORITHMS; BUBBLES (IN FLUIDS); COMPUTER SIMULATION; DIFFUSION; NUMERICAL METHODS; SHEAR DEFORMATION; VISCOUS FLOW;

NON NEWTONIAN LIQUIDS;

ALGORITHMS; BUBBLES (IN FLUIDS); COMPUTER SIMULATION; DIFFUSION; NON NEWTONIAN LIQUIDS; NUMERICAL METHODS; SHEAR DEFORMATION; VISCOUS FLOW;

EID: 34547141702     PISSN: 00011541     EISSN: 15475905     Source Type: Journal    
DOI: 10.1002/aic.11211     Document Type: Article

References (87)

1. Leduy A, Marsan AA, Coupal B. A study of the rheological properties of a non-Newtonian Fermentation broth. Biotechnol Bioeng. 1974;16:61-76.
2. Curtis W, Emery A. Plant cell suspension culture rheology. Biotechnol Bioeng. 1993;42:520-526.
3. Kieran PM, McLoughlin P, Malone D. Plant Cell suspension cultures: some engineering considerations. J Biotechnol. 1997;59:39-52.
4. Doran P. Design of mixing systems for plant cell suspensions in stirred reactors. Biotechnol Prog. 1999;16:319-335.
5. Rodriguez-Monroy M, Galindo E. Broth rheology, growth and metabolite production of Beta vutgaris suspension culture: a comparative study between cultures grown in shake flasks and in a stirred tank. Enzyme Microb Technol. 1999;24:687-693.
6. Rodriguez-Monroy M, Galindo E. Production of arabinogalactan proteins in Beta vulgaris cell suspension cultures: a response to hydrodynamic stress. In: Notthnagel E, Basic A, Clarke A, editors. Cell and Developmental Biology of Arabinogalactan-Proteins. New York: Kluwer Academic, 2000:290-292.
7. La) in batch cultivations involving non-Newtonian broths. Biochem Eng J. 2001;8:111-119.
8. Sánchez MJ, Jiménez-Aparicio A, López GG, Tapia GT, Rodríguez-Monroy M. Broth rheology of Beta vulgaris cultures growing in an air lift bioreactor. Biochem Eng J. 2002;12:37-41.
9. Kawase Y, Hashimoto N. Gas hold-up and oxygen transfer in three-phase external-loop airlift bioreactors: non-Newtonian fermentation broths. J Chem Tech Biotechnol. 1996;65:325-334.
10. Li GQ, Qui HW, Zheng ZM, Cai ZL, Yang SZ. Effect of fluid rheological properties on mass transfer in a bioreactor. J. Chem Tech Biotechnol. 2004;65:385-391.
11. Jin B, Lant P, Ge X. Hydrodynamics and mass transfer coefficient in activated sludge aerated stirred column reactor: experimental analysis and modeling. Biotechnol Bioeng. 2005;91:406-417.
12. Al-Masry WA. Effect of scale-up on average shear rates for aerated non-Newtonian liquids in external loop airlift reactors. Biotechnol Bioeng. 1999;62:494-498 (Communication to the editor).
13. Choi JH, Keum KC, Lee SY. Production of recombinant proteins by high cell density culture of Escherichia coli. Chem Eng Sci. 2006;61:876-885.
14. Duddridge JE, Kent CA, Laws JF. Effect of surface shear stress on the attachment of Pseudomonas fluorescens to stainless steel under defined flow conditions. Biotechnol Bioeng. 1982;24:153-164.
15. Kieran PM. An Investigation of the Hydrodynamic Shear Susceptibility of Suspension Cultures of Morinda citrifolia. PhD Thesis. Dublin, Ireland: University College, 1993.
16. Lau YL, Liu D. Effect of flow rate on biofilm accumulation in open channels. Water Res. 1993;27:355-360.
17. Gjaltema A, Tijhuis L, van Loosdrecht MCM, Heijnen JJ. Detachment of biomass from suspended nongrowing spherical biofilms in airlift reactors. Biotechnol Bioeng. 1995;46:258-269.
18. Gjaltema A, van der Marel N, Loosdrecht MCM, Heijnen JJ. Adhesion and biofilm development on suspended carriers in airlift reactors: hydrodynamic conditions versus surface characteristics. Biotechnol Bioeng. 1997;55:880-889.
19. Leenen EJTM, Martins dos Santos VAP, Grolle KCF, Tramper J, Wijffels RH. Characteristics of and selection criteria for cell immobilisation in wastewater treatment. Water Res. 1996;30:2895-2996.
20. Martins dos Santos VAP, Leenen EJTM, Rippoll MM, van der Sluis C, Vliet T, Tramper J, Wijffels RH. Relevance of rheological properties of gel beads for their mechanical stability in bioreactors. Biotechnol Bioeng. 1997;56:517-529.
21. Ma N, Koelling KW, Chalmers JJ. Fabrication and use of a transient contractional flow device to quantify the sensitivity of mammalian and insect cells to hydrodynamic forces. Biotechnol Bioeng. 2002;80:428-437.
22. Mollet M, Ma N, Zhao Y, Brodkey R, Taticek R, Chalmers JJ. Bio-process equipment: characterization of energy dissipation rate and its potential to damage cells. Biotechnol Prog. 2004;20:1437-1448.
23. Nienow AW. Reactor engineering in large scale animal cell culture. Cytotechnology. 2006;50:9-33.
24. Meier ST, Hatton TA, Wang DIC. Cell death from bursting bubbles: role of cell attachment to rising bubbles in sparged reactors. Biotechnol Bioeng. 1999;62:468-478.
25. Ma N, Chalmers JJ, Aunins JG, Zhou W, Xie L. Quantitative studies of cell-bubble interactions and cell damage at different pluronic F-68 and cell concentrations. Biotechnol Prog. 2004;20:1183-1191.
26. Koynov A, Khinast J. Micromixing in reactive, deformable bubble, and droplet swarms. Chem Eng Technol. 2006;29:13-23.
27. Koynov A, Tryggvason, Khinast J. Characterization of the localized hydrodynamic shear forces and dissolved oxygen distribution in sparged bioreactors. Biotechnol Bioeng. 2007;97:317-331.
28. Richard A, Margaritis A. Rheology, oxygen transfer, and molecular weight characteristics of poly(glutamic acid) fermentation by Bacillus subtilis. Biotechnol Bioeng. 2003;82:299-305.
29. Tryggvason G, Bunner B, Esmaeeli A, Juric D, Al-Rawahi N, Tauber W, Han J, Nas S, Jan Y-J. A front-tracking method for the computations of multiphase flow. J Comput Phys. 2001;169:708-759.
30. Koynov A, Khinast J, Tryggvason G. Mass transfer and chemical reactions in bubble swarms with dynamic interfaces. AIChE J. 2005;51:2786-2800.
31. Bandyopadhyay B, Humphrey AE, Taguchi H. Dynamic measurement of the volumetric oxygen transfer coefficient in fermentation systems. Biotechnol Bioeng. 1967;9:533-544.
32. Benyahia F, Jones L. Scale effects on hydrodynamic and mass transfer characteristics of external loop airlift reactors. Chem Tech Biotechnol. 1997;69:301-308.
33. Kawase Y, Halard B, Moo-Young M. Liquid-phase mass transfer coefficients in bioreactors. Biotechnol Bioeng. 1992;39:1133-1140.
34. Deen NG, Solberg T, Hjertager BH. Flow generated by an aerated rushton impeller: two-phase PIV experiments and numerical simulations. Can J Chem Eng. 2002;80:1-15.
35. Matos EM, Nunhez JR. The effect of different feed flow patterns on the conversion of bubble column reactors. Chem Eng J. 2006;116:163-172.
36. Melheim JA, Chiesa M. Simulation of turbulent electrocoalescence. Chem Eng Sci. 2006;61:4540-4549.
37. Vennerk BCH, Derksen JJ, Van der Akker HEA. Population balance modeling of aerated stirred vessels based on CFD. AIChE J. 2002;48:673-685.
38. Derksen JJ. Numerical simulation of solids suspension in a stirred tank. AIChE J. 2003;49:2700-2714.
39. Darmana D, Deen NG, Kuipers JAM. Detailed modeling of hydro-dynamics, mass transfer and chemical reactions in a bubble column using a discrete bubble model. Chem Eng Sci. 2005;60:3383-3404.
40. Darmana D. On the Multiscale Modeling of Hydrodynamics, Mass Transfer and Chemical Reactions in Bubble Columns. PhD Thesis. Twente, Netherlands: University of Twente, 2006.
41. Pera C, Réveillon J, Vervisch L, Domingo P. Modeling subgrid scale mixture fraction variance in LES of evaporating spray. Combust Flame. 2006;146:635-648.
42. Pitsch H. Large-eddy simulation of turbulent combustion. Annu Rev Fluid Mech. 2006;38:453-482.
43. Joshi JB. Computational flow modeling and design of bubble column reactors. Chem Eng Sci. 2001;56:5893-5933.
44. Deen NG, van Sint Annaland M, Kuipers JAM. Multi-scale modeling of dispersed gas-liquid two-phase flow. Chem Eng Sci. 2004;59:1853-1861.
45. Akbar MK, Ghiaasiaan SM. Simulation of Taylor flow in capillaries based on the volume-of-fluid technique. Ind Eng Chem Res. 2006;45:5396-5403.
46. Bothe D, Schmidtke M, Warnecke H-J. VOF-simulation of the lift force for single bubbles in a simple shear flow. Chem Eng Technol. 2006;29:1048-1053.
47. Shopov PJ, Minev PD. The unsteady motion of a bubble or drop towards a liquid liquid interface. J Fluid Mech. 1992;235:123-141.
48. Hu HH, Patankar NA, Zhu MY. Direct numerical simulations of fluid-solid systems using the arbitrary Lagrangian-Eulerian technique. J Comput Phys. 2001;169:427-462.
49. Ryskin GR, Leal LO. Numerical solution of free-boundary problems in fluid-mechanics, Part 1. The finite difference technique. J Fluid Mech. 1984;148:1-17.
50. Ryskin GR, Leal LG. 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. 1984;148:19-35.
51. Unverdi SO, Tryggvason G. A front-tracking method for viscous, incompressible multi-fluid flows. J Comput Phys. 1992;100:25-37.
52. Radi S, Khinast J. Prediction of mass transfer coefficients in non-Newtonian fermentation broths using first-principles methods. Biotechnol Bioeng, In press.
53. Townsend P. On the numerical simulation of two-dimensional time-dependent flows of Oldroy fluids, Part 1: basic method and preliminary result. J Non-Newtonian Fluid Mech. 1984;14:265-278.
54. Keunings R. On the high Weissenberg number problem. J Non-Newtonian Fluid Mech. 1986;20:209-226.
55. Crochet MJ, Davies AR, Walters K. Numerical Simulation of Non-Newtonian Flow. Amsterdam, Netherlands: Elsevier, 1984.
56. Marchal JM, Crochet MJ. A new mixed finite element for calculating viscoelastic flow. J Non-Newtonian Fluid Mech. 1987;26:77-114.
57. Gerritsma M. Time Dependent Numerical Simulation of a Visco-elastic Fluid on a Staggered Grid. PhD Thesis. Groningen, Netherlands: University of Groningen, 1996.
58. Sun J, Phan-Thien N, Tanner RI. An adaptive viscoelastic stress splitting scheme and its applications: AVSS/SI and AVSS/SUPG. J Non-Newtonian Fluid Mech. 1996;65:75-91.
59. Baaijens FPT. Mixed finite element methods for viscoelastic flow analysis: a review. J Non-Newtonian Fluid Mech. 1998;79:361-385.
60. Ellero M. Smoothed Particle Dynamics Methods the Simulation of Viscoelastic Fluids. PhD Thesis. Berlin, Germany: TU Berlin, 2004.
61. Fattal R, Kupferman R. Time-dependent simulation of viscoelastic flows at high Weissenberg number using the log-conformation representation. J Non-Newtonian Fluid Mech. 2005;126:23-37.
62. Hulsen MA, Fattal R, Kupferman R. Flow of viscoelastic fluids past a cylinder at thigh Weissenberg number: stabilized simulations using matrix logarithms. J Non-Newtonian Fluid Mech. 2005;127:27-39.
63. McKinley OH. Steady and transient motion of spherical particles in viscoelastic liquids. In: Chhabra R, De Kee D, editors. Transport Processes in Bubbles, Drops and Particles, 2nd ed. New York, NY: Taylor & Francis, 2002.
64. Frank X, Li HZ. Complex flow around a bubble rising in a non-Newtonian fluid. Phys Rev E. 2005;71:036309.
65. Kemiha M, Frank X, Poncin S, Li HZ. Origin of the negative wake behind a bubble rising in non-Newtonian fluids. Chem Eng Sci. 2006;61:4041-4047.
66. Astarita G, Aapuzzo G. Motion of gas bubbles in non-Newtonian liquids. AIChE J. 1965;11:815-820.
67. Hassager O. Negative wake behind bubbles in non-Newtonian liquids. Nature. 1979;279:402-403.
68. Rodrigue D, De Kee D, Chan Man Fong CF. Bubble velocities: further developments on the jump discontinuity. J Non-Newtonian Fluid Mech. 1998;79:45-55.
69. Rodrigue D, De Kee D. Bubble velocity jump discontinuity in polyacrylamide solutions: a photographic study. Rheol Acta. 1999;38:177-182.
70. Herrera-Velarde JR, Zenit R, Chehata D, Mena B. The flow of non-Newtonian fluids around bubbles and its connection to the jump discontinuity. J Non-Newtonian Fluid Mech. 2003;111:199-209.
71. Böhme G. Strömungsmechanik Nichtnewtonscher Fluide, 2nd ed. Stuttgart, Germany: B.G. Teubner, 2000.
72. Sarkar K, Schowalter WR. Deformation of a two-dimensional visco-elastic drop at non-zero Reynolds number in time-periodic extensional flows. J Non-Newtonian Fluid Mech. 2000;95:315-342.
73. Gaskell PH, Lau AKC. Curvature-compensated convective transport: SMART, a new boundedness-preserving transport algorithm. Int J Numer Methods Fluids. 1988;8:617-641.
74. Sureshkumar R, Beris AN. Effect of artificial stress diffusivity on the stability of numerical calculations and the flow dynamics of time-dependent viscoelastic flows. J Non-Newtonian Fluid Mech. 1995;60:53-80.
75. Atalik K, Keunings R. Non-linear temporal stability analysis of viscoelastic plan channel flows using a fully-spectral method. J Non-Newtonian Fluid Mech. 2002;102:299-319.
76. Staniforth A, Côté J. Semi-Lagrangian integration schemes for atmospheric models - a review. Mon Weather Rev. 1991;119:2006-2223.
77. Spiegelman M, Katz RF. A semi-Lagrangian Crank-Nicholson algorithm for the numerical solution of advection-diffusion problems. Available at http://www.ldeo.columbia.edu/~mspieg/SLCN_paper.pdf (accessed May 02, 2006).
78. Khinast J. Impact of 2-D bubble dynamics on the selectivity of fast gas-liquid reactions. AIChE J. 2001;47:2304-2319.
79. Bhavaraju SM, Mashelkar RA, Blanch HW. Bubble motion and mass transfer in non-Newtonian fluids, part 1: single bubble in power law and Bingham fluids. AIChE J. 1978;24:1063-1070.
80. Hirose T, Moo-Young M. Bubble drag and mass transfer in non-Newtonian fluids: creeping flow with power-law fluids. Can J Chem Eng. 1969;47:265-267.
81. Moo-Young M, Hirose T, Ali S. Rheological effects on liquid phase mass transfer in two phase dispersions: results for creeping flow. In: Proceedings of Fifth International Congress on Rheology, Kyoto, 1970:233.
82. Ohta M, Iwasaki E, Obata E, Yoshida Y. Dynamic processes in a deformed drop rising through shear-thinning fluids. J Non-Newtonian Fluid Mech. 2005;132:100-107.
83. Bhaga D, Weber ME. In-line interaction of a pair of bubbles in a viscous liquid. Chem Eng Sci. 1980;35:2467-2474.
84. Tse K, Martin T, McFarlane CM, Nienow AW. Visualization of bubble coalescence in a coalescence cell, a stirred tank and a bubble column. Chem Eng Sci. 1998;53:4031-4036.
85. Balay S, Buschelman K, Eijkhout V, Gropp WD, Kaushik D, Knepley MG, McInnes LC, Smith BF, Zhang H. PETSc User Manual ANL-95/11, Revision 2.1.5. Illinois: Argonne National Laboratory, 2004.
86. Margaritis A, te Bokkel DW, Karamev DG. Bubble rise velocities and drag coefficients in non-Newtonian polysaccharide solutions. Biotechnol Bioeng. 1999;64:257-266.
87. Rodrigue D. A simple correlation for gas bubbles rising in power-law fluids. Can J Chem Eng. 2002;80:289-292.