1. SHAPE AND RISING VELOCITY OF BUBBLES
36th Conference of Slovak Society of Chemical Engineering
May , Tatranské Matliare
SHAPE AND RISING VELOCITY OF BUBBLES
Kamil Wichterle, Kateřina Smutná, Marek Večeř
VSB-Technical University of Ostrava
Faculty of Metallurgy and Material Engineering
Department of Chemistry,
70833 Ostrava Poruba, CR
Phone: , Fax: ,

2. Everyting is known about bubbles
Clift, R., Grace, J.R. and Weber, M.E., 1978: Bubbles, Drops, and Particles. Academic Press, New York. ?

3. Classes of bubbles Small bubbles in high-viscosity liquids
Small bubbles in low-viscosity liquids
Medium bubbles in high-viscosity liquids
Medium bubbles in pure low-viscosity liquids
Medium bubbles in contamined low-viscosity liquids
Large bubbles

4. SIZE OF RISING BUBBLES
increasing volume

5. LIQUID VISCOSITY
Low– and medium-viscosity …. Re > 50

6. PURE OR CONTAMINED LIQUID
Pure liquid (surface-active components carefully removed)
Mobil surface
Lower drag resistance
Higher rising velocity
Contamined liquid
Immobile surface
Drag like for solid bodies
Lower rising velocity
NO QUANTITATIVE PARAMETER !!!

7. Focus of our interest Small bubbles
Medium bubbles in pure low-viscosity liquids
Medium bubbles in contamined low-viscosity liquids
Large bubbles
EASY EXPERIMENTS, SIMPLE THEORY Stokes (or Hadamard-Rybczinski) -law
COMPLICATED EXPERIMENTS
ELLIPSOIDAL BUBBLES, THE MOST COMMON IN BUBBLE COLUMNS
PULSATING BUBBLE SHAPE AND VELOCITY, FREQUENT BREAKUP

8. LOWER DRAG (hypothetical)
Why not ??

9. BUBBLE SHAPE
Surface tension
Hydrostatics

10. SYMMETRIC OBLATE BUBBLE

11. Our laboratories

12. DETERMINATION OF THE SHAPE OF BUBBLES
Bubble levitating
in dowstream flow

13. IDEAL OBLATE ELLIPSOID semiaxes a, b
Image analysis
Standard procedure how to approximate the bubble:
Determination of the projected bubble area
Determination of perimeter (usually overestimated)

14. IDEAL OBLATE ELLIPSOID semiaxes a, b
Improved procedure:
Determination of the object width, height and inclination
In front view
In side view

15. Untreated data

16. Reynolds number ?

17. Weber number ?

18. Eötvös number

19. Static bubble profile (under a wetted plate)
„Laplace length!“

20. Normalized semiaxes of rising bubbles Theoretical prediction for static bubbles

21. RISING VELOCITY

22. Time = 10 s , (corresponding path 2,3 m)

23. RISING VELOCITY for medium contaminated bubbles
Effects of
Viscosity
Surface tension
Electrolyte

24. Our data compared with that of Clift

25. Our data compared with that of Tomiyama

26. RISING VELOCITY dimensional analysis
Bubble equivalent diameter
Gravity acceleration
Liquid density
Density difference
Liquid viscosity
Surface tension

27. RISING VELOCITY effect of surface tension
Morton number
Dimensionless bubble diameter
Dimensionless bubble velocity
„Laplace velocity“
Viscosity cannot be neglected !!

28. RISING VELOCITY classical variables
Drag coefficient
Not very successful !!

29. RISING VELOCITY effect of viscosity
Drag coefficient
Dimensionless bubble diameter
Dimensionless bubble velocity
There is still an effect of surface tension!!

30. RISING BUBBLE
Oscillatory movement of a bubble Bubble front area is S = p a2 New definition of the drag coefficient

31. New dimensionless variables
OK !!!

32. RESULTING FORMULAS Correlation of the bubble shape
Correlation of the bubble velocity
This correlation fits well the data for medium size bubbles in contaminated low- and medium- viscosity liquids. In carefully prepared pure liquids, the rising velocity of can be somewhat higher.

33. Thank you for your attention
Acknowledgments
We gratefully acknowledge financial support by the grant No.104/07/1110 from the Grant Agency of the Czech Republic.