SLGP Header

Rise Time Calculations of a Single Air Bubble under the Influence of Gravity in a Pool of Water

jasem Front Page
Gas-liquid transfer operations are of considerable interest to the process industries. If the gas is brought into contact with the liquid in the form of bubbles, a better mass transfer is ensured. Usually, their size varies widely, from a few micrometers to a few millimetres. In this work, the influence of the initial bubble diameter, the liquid head and surface tension on the rise time calculations was exemplified for an air bubble in water, using the bubble expansion factor. Further, it was shown that smaller air bubbles are highly influenced by the surface tension. In contrast, for air bubbles in liquid head, if the initial size is larger than 0.1 mm the information needed for the rise time calculation is the liquid head only.

Keywords:initial bubble diameter, liquid head, rise time, single bubble, surface tension.


  1. A.A. Kulkarni and J.B. Joshi, Bubble formation and bubble rise velocity in gas-liquid system: a review, Ind. Eng. Chem. Res., 44(16), 2005, 5873-5931.
  2. M. Maldonado, J.J. Quinn, C.O. Gomez, C.O. and J.A. Finch, An experimental study examining the relationship between bubble shape and rise velocity, Chem. Eng. Sci., 98, 2013,7-11.
  3. W.L. Haberman and R.K. Morton, An experimental investigation of the drag and shape of air bubbles rising in various liquids. David Taylor Model Basin, NR 715-102 (Sep., 1953)
  4. D.W. Moore, The rise of a gas bubble in a viscous liquid, J. Fluid Mech., 6, 1956, 113-130.
  5. M. Wu and M. Gharib, Experimental studies on the shape and path of small air bubble rising in clean water, Phys. Fluids A, 14(7), 2002, 49-52.
  6. P.M. Lovalenti and J.F. Brady, The forces on bubble, drop, or particle in arbitrary time-dependent motion at small Reynolds number, Phys. Fluids A, 5(9), 1993, 2104-2116.
  7. H.D. Mendelson, The prediction of bubble terminal velocities from wave theory, AIChE Journal, 13(2), 1976, 250-253.
  8. C.C. Maneri and H.D. Mendelson, The rise velocity of bubbles in tubes and rectangular channels as predicted by wave theory, AIChE Journal, 14(2), 1968, 295-300.
  9. K.R. Weller, Expansion of a single gas bubble rising in a column of liquid , Can. J. Chem. Eng, 49(1), 1971, 154-156.
  10. D.A. Rodrigue, Generalized correlation for bubble motion, AIChE Journal, 79, 2001b, 119-126.
  11. D.A. Rodrigue, Simple correlation for gas bubbles rising in power law fluids, Can. J.Chem. Eng., 80(2), 2002, 289-292.
  12. Lehrer, I.H., A rational terminal velocity equation for bubbles and drops at intermediate and high Reynolds numbers, J. Chem. Eng. Japan, 9(3), 1976, 237-240.
  13. Aybers, N.M. and Tapucu, A., The motion of gas bubbles rising through stagnant liquid.Wärme-und Stoffübertragung Bd., 2, 1969, 118-128.
  14. I.H. Lehrer, A theoretical criterion of transition in the free motion of single bubbles and drops. AIChE Journal, 26(1), 1980, 170-172.
  15. I.H. Lehrer, Single bubbles and drops, simple derivation of slug velocity and formulation of a general velocity equation, Proc. 9th Australasian Fluid Mechanics Conf., Auckland, New Zealand, 1986, 8-12.
  16. R.E. Treybal, Mass transfer operations (New York: McGraw Hill, 1980).
  17. J.O. Wilkes and S.G. Bike, Three Problems in Fluid Mechanics, Chem. Eng. Educ., 26(3), 1992, 130-132.
  18. S. Middleman, An introduction to fluid dynamics, (New York: John Wiley & Sons, Inc., 1997).
  19. B. A. Finlayson, J.F. Davis, A.W. Westerberg and Y. Yamashita, Mathematics, in Perry, R.H. and Green, D.W., (Eds.)Perry’s Chemical Engineer’s Hand book 6 (New York: McGraw-Hill, 1984) 3-14.