Shape and rising velocity of bubbles
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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

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: [email protected]


Everyting is known about bubbles

Everyting is known about bubbles

Clift, R., Grace, J.R. and Weber, M.E., 1978: Bubbles, Drops, and Particles. Academic Press, New York.

?


Classes of bubbles

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


Shape and rising velocity of bubbles

SIZE OF RISING BUBBLES

increasing volume


Shape and rising velocity of bubbles

LIQUID VISCOSITY

Low– and medium-viscosity …. Re > 50


Shape and rising velocity of bubbles

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 !!!


Focus of our interest

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


Shape and rising velocity of bubbles

LOWER DRAG (hypothetical)

Why not ??


Shape and rising velocity of bubbles

BUBBLE SHAPE

Surface tension

Hydrostatics


Shape and rising velocity of bubbles

SYMMETRIC OBLATE BUBBLE


Shape and rising velocity of bubbles

Our laboratories


Determination of the shape of bubbles

DETERMINATION OF THE SHAPE OF BUBBLES

Bubble levitating

in dowstream flow


Ideal oblate ellipsoid semiaxes a b

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)


Ideal oblate ellipsoid semiaxes a b1

IDEAL OBLATE ELLIPSOIDsemiaxes a, b

  • Improved procedure:

  • Determination of the object width, heightand inclination

    • In front view

    • In side view


Untreated data

Untreated data


Reynolds number

Reynolds number ?


Weber number

Weber number ?


E tv s number

Eötvös number


Static bubble profile under a wetted plate

Static bubble profile(under a wetted plate)

„Laplace length!“


Normalized semiaxes of rising bubbles theoretical prediction for static bubbles

Normalized semiaxes of rising bubblesTheoretical prediction for static bubbles


Rising velocity

RISING VELOCITY


Shape and rising velocity of bubbles

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


Rising velocity for medium contaminated bubbles

RISING VELOCITYfor medium contaminated bubbles

  • Effects of

  • Viscosity

  • Surface tension

  • Electrolyte


Our data compared with that of clift

Our data compared with that of Clift


Our data compared with that of tomiyama

Our data compared with that of Tomiyama


Rising velocity dimensional analysis

RISING VELOCITYdimensional analysis

  • Rising velocity

    • Bubble equivalent diameter

    • Gravity acceleration

    • Liquid density

    • Density difference

    • Liquid viscosity

    • Surface tension


Rising velocity effect of surface tension

RISING VELOCITYeffect of surface tension

Morton number

Dimensionless bubble diameter

Dimensionless bubble velocity

„Laplace velocity“

Viscosity cannot be neglected !!


Rising velocity classical variables

RISING VELOCITYclassical variables

Drag coefficient

Not very successful !!


Rising velocity effect of viscosity

RISING VELOCITYeffect of viscosity

Drag coefficient

Dimensionless bubble diameter

Dimensionless bubble velocity

There is still an effect of surface tension!!


Rising bubble

RISING BUBBLE

Oscillatory movement of a bubble Bubble front area isS = pa2New definition of the drag coefficient


New dimensionless variables

New dimensionless variables

OK !!!


Resulting formulas

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.


Shape and rising velocity of bubbles

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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