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SHAPE AND RISING VELOCITY OF BUBBLES

36th Conference of Slovak Society of Chemical Engineering M ay 25 - 29, 2009 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

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SHAPE AND RISING VELOCITY OF BUBBLES

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  1. 36th Conference of Slovak Society of Chemical Engineering May 25 - 29, 2009 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: 420 596 994 328, Fax: 420 596 918 647, e-mail: kamil.wichterle@vsb.cz

  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 purelow-viscosity liquids • Medium bubbles in contaminedlow-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 purelow-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 ELLIPSOIDsemiaxes 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 ELLIPSOIDsemiaxes a, b • Improved procedure: • Determination of the object width, heightand 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 bubblesTheoretical prediction for static bubbles

  21. RISING VELOCITY

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

  23. RISING VELOCITYfor 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 VELOCITYdimensional analysis • Rising velocity • Bubble equivalent diameter • Gravity acceleration • Liquid density • Density difference • Liquid viscosity • Surface tension

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

  28. RISING VELOCITYclassical variables Drag coefficient Not very successful !!

  29. RISING VELOCITYeffect 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 isS = pa2New 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.

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