화학공학소재연구정보센터
Korea-Australia Rheology Journal, Vol.28, No.4, 315-326, November, 2016
Hydrodynamic extensional stress during the bubble bursting process for bioreactor system design
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Cell damage, one of critical issues in the bioreactor design for animal cell culture, is caused mainly from the bubble bursting at the free surface subjected to strong extensional flows. In this work, extensive computational studies are performed to investigate bubble bursting process in great details. Extensive numerical simulations are performed for a wide range of bubble diameters (from 0.5 to 6 mm) and the surface tension values (from 0.03 to 0.072 N/m), with which effects of the bubble size and surfactant (PF68) concentration on the hydrodynamic stress are investigated. For all the cases, the maximum extensional stress appears at the instance when receding films impact each other at the bottom of the bubble. A model equation based on numerical simulations is presented to predict the maximum extensional stress as a function of the bubble diameter and the surface tension. The bubble diameter has turned out to contribute significantly the maximum hydrodynamic extensional stress. In addition, the bubble collapsed time and the affected volume around a bubble subjected to the critical extensional stress are investigated. The extensional stress estimation is reported as a function of the bubble size and the surface tension. The influence of the bubble size on the maximum stress dominates and extensional stress reaches up to the order of 104 Pa for bubble size of 0.5 mm.
  1. Augenstein DC, Sinskey AJ, Wang DIC, Biotechnol. Bioeng., 13, 409 (1971)
  2. Bae YB, Jang HK, Shin TH, Phukan G, Tran TT, Lee G, Hwang WR, Kim JM, Lab Chip, 16, 96 (2016)
  3. Bhararaju SM, Russell TWF, Blanch HW, AIChE J., 24, 454 (1978)
  4. Boulton-Stone JM, Blake JR, J. Fluid Mech., 254, 437 (1993)
  5. Bourlioux A, 1995, Coupled level set volume of fluid algorithm for tracking material interfaces, Proc. of the 6th Int. Sym. on CFD, Lake Tahoe, United States, 15-22.
  6. Brackbill JU, Kothe DB, Zemach C, J. Comput. Phys., 100, 335 (1992)
  7. Butler M, Appl. Microbiol. Biotechnol., 68(3), 283 (2005)
  8. Cha S, Shin T, Lee SS, Shim W, Lee G, Lee SJ, Kim Y, Kim JM, Anal. Chem., 84, 10471 (2012)
  9. Chakraborty I, Biswas G, Ghoshdastidar PS, Int. J. Heat Mass Transf., 58(1-2), 240 (2013)
  10. Chalmers JJ, Cytotechnology, 15, 311 (1994)
  11. Cherry RS, Papoutsakis ET, Biotechnol. Bioeng., 32, 1001 (1988)
  12. Chisti Y, Trends Biotechnol., 18, 420 (2000)
  13. Croughan MS, Hamel JF, Wang DIC, Biotechnol. Bioeng., 29, 130 (1987)
  14. Deshpande KB, Smith D, Zimmerman WBJ, 2006, Modeling of multi-phase flow using the level set method, In: Zimmerman, W.B.J., eds., Multiphysics Modelling with Finite Element Methods, World Scientific, 277-299.
  15. Dey D, 1998, Cell-Bubble Interactions during Bubble Disengagement in Aerated Bioreactors, Ph.D Thesis, University of Birmingham.
  16. Duchemin L, Popinet S, Josserand C, Zaleski S, Phys. Fluids, 14, 3000 (2002)
  17. Garciabriones MA, Chalmers JJ, Biotechnol. Bioeng., 44(9), 1089 (1994)
  18. Garciabriones MA, Brodkey RS, Chalmers JJ, Chem. Eng. Sci., 49(14), 2301 (1994)
  19. Godoy-Silva R, Berdugo C, Chalmers JJ, Encyclopedia of Industrial Biotechnology, 1 (2010)
  20. Grace HP, Chem. Eng. Commun., 14, 225 (1982)
  21. Gregoriades N, Clay J, Ma N, Koelling K, Chalmers JJ, Biotechnol. Bioeng., 69(2), 171 (2000)
  22. Hirt C, Nichols B, J. Comput. Phys., 39, 201 (1981)
  23. Jacqmin D, J. Comput. Phys., 155, 96 (1999)
  24. Kirkpatrick RD, Lockett MJ, Chem. Eng. Sci., 29, 2363 (1974)
  25. Kolmogorov AN, Proc. R. Soc. Lon. A, 434, 9 (1991)
  26. Koynov A, Tryggvason G, Khinast JG, Biotechnol. Bioeng., 97(2), 317 (2007)
  27. Kresta S, Can. J. Chem. Eng., 76(3), 563 (1998)
  28. Kunas KT, Papoutsakis ET, Biotechnol. Bioeng., 36, 467 (1990)
  29. Ma NN, Koelling KW, Chalmers JJ, Biotechnol. Bioeng., 80(4), 428 (2002)
  30. MacIntyre F, J. Geophys. Res., 27, 5211 (1972)
  31. McQueen A, Meilhoc E, Bailey JE, Biotechnol. Lett., 9, 831 (1987)
  32. McQueen A, Bailey JE, Biotechnol. Lett., 11, 531 (1989)
  33. Michaels JD, Mallik AK, Papoutsakis ET, Biotechnol. Bioeng., 51(4), 399 (1996)
  34. Mollet M, Ma NN, Zhao Y, Brodkey R, Taticek R, Chalmers JJ, Biotechnol. Prog., 20(5), 1437 (2004)
  35. Mollet M, Godoy-Silva R, Berdugo C, Chalmers JJ, Biotechnol. Bioeng., 98(4), 772 (2007)
  36. Murhammer DW, Goochee CF, Biotechnol. Prog., 6, 391 (1990)
  37. Nichita BA, Zun I, Thome JR, J. Fluids. Eng., 132, 081302 (2010)
  38. Oh SKW, Nienow AW, Al-Rubeai M, Emery AN, J. Biotechnol., 12, 45 (1989)
  39. Osher S, Sethian JA, J. Comput. Phys., 79, 12 (1988)
  40. Reddy JN, 2013, An Introduction to Continuum Mechanics, 2nd ed., Cambridge University Press, Cambridge.
  41. Sussman M, Fatemi E, Smereka P, Osher S, Comput. Fluids, 27, 663 (1998)
  42. Sussman M, Puckett EG, J. Comput. Phys., 162, 301 (2000)
  43. Tong AY, Wang Z, J. Comput. Phys., 221, 506 (2007)
  44. Tramper JJ, Joustra D, Vlak JM, 1987, Bioreactor design for growth of shear sensitive insect cells, In: Webb C, Mavituna F, eds., Plant and Animal Cell Cultures: Process Possibilities, Ellis Horwood, Chichester, 125-136.
  45. Trinh K, Garciabriones M, Hink F, Chalmers JJ, Biotechnol. Bioeng., 43(1), 37 (1994)
  46. Vrij A, Disc. Faraday Soc., 42, 23 (1966)
  47. Wernersson ES, Tragardh C, Chem. Eng. Sci., 54(19), 4245 (1999)
  48. Wu JY, Goosen MF, Enzyme Microb. Technol., 17(12), 1036 (1995)
  49. Zhang H, 2004, Application of Computational Fluid Dynamics to Microtiter Plate Scale Bioreactors, Ph.D Thesis, University College of London.
  50. Zhang H, Wang W, Quan C, Fan S, Curr. Pharm. Biotechnol., 11, 103 (2010)
  51. Zhou GW, Kresta SM, AIChE J., 42(9), 2476 (1996)