SHAPE AND RISING SHAPE AND RISING VELOCITY OF BUBBLESVELOCITY OF BUBBLES

VSB-Technical University of OstravaVSB-Technical University of Ostrava

Faculty of Metallurgy and Material EngineeringFaculty of Metallurgy and Material EngineeringDepartment of Chemistry, Department of Chemistry, 70833 Ostrava Poruba, CR 70833 Ostrava Poruba, CR Phone: 420 596 994 328, Fax: 420 596 918 647, e-mail: Phone: 420 596 994 328, Fax: 420 596 918 647, e-mail: kamil.wichterle@vsb.czkamil.wichterle@vsb.cz

36th Conference of Slovak Society of Chemical EngineeringMay 25 - 29, 2009 Tatranské Matliare

Kamil Wichterle, Kateřina Smutná, Marek VečeřKamil Wichterle, Kateřina Smutná, Marek Večeř

Everyting is known about bubbles Everyting is known about bubbles

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

?

Classes of bubblesClasses of bubbles

SmallSmall bubbles in bubbles in high-viscosityhigh-viscosity liquids liquids

SmallSmall bubbles in bubbles in low-viscositylow-viscosity liquids liquids

MediumMedium bubbles in bubbles in high-viscosityhigh-viscosity liquids liquids

MediumMedium bubbles in bubbles in purepure low-viscositylow-viscosity liquidsliquids

MediumMedium bubbles in bubbles in contaminedcontamined low-low-viscosityviscosity liquids liquids

LargeLarge bubbles bubbles

SIZE OF RISING BUBBLES

increasing volume

gd

Eo B

2

LIQUID VISCOSITY

BB Ud

Re

Low– and medium-viscosity …. Re > 50

PURE OR CONTAMINED LIQUID

NO QUANTITATIVE PARAMETER !!!

•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

Focus of our interestFocus of our interest

SmallSmall bubbles bubbles

MediumMedium bubbles in bubbles in purepure low-viscositylow-viscosity liquidsliquids

MediumMedium bubbles in bubbles in contamined contamined low-low-viscosityviscosity liquids liquids

LargeLarge bubbles bubbles

EASY EXPERIMENTS, SIMPLE THEORY Stokes (or Hadamard-Rybczinski) -law

COMPLICATED EXPERIMENTS

PULSATING BUBBLE SHAPE AND VELOCITY, FREQUENT BREAKUP

ELLIPSOIDAL BUBBLES, THE MOST COMMON IN BUBBLE COLUMNS

LOWER DRAG (hypothetical)

Why not ??

Hydrostatics

Surface tension

BUBBLE SHAPE

SYMMETRIC OBLATE BUBBLE

Our laboratories

DETERMINATION OF THE DETERMINATION OF THE SHAPE OF BUBBLESSHAPE OF BUBBLES

MIRROR FRONT

y x

zax

ay

LIQ

UID

FLO

W

Bubble levitating

in dowstream flow

IDEAL OBLATE ELLIPSOIDIDEAL OBLATE ELLIPSOIDsemiaxes semiaxes a, ba, b

-1,000

-0,800

-0,600

-0,400

-0,200

0,000

0,200

0,400

0,600

0,800

1,000

-1,000 -0,500 0,000 0,500 1,000

-1,000

-0,800

-0,600

-0,400

-0,200

0,000

0,200

0,400

0,600

0,800

1,000

-1,000 -0,800 -0,600 -0,400 -0,200 0,000 0,200 0,400 0,600 0,800 1,000

Standard procedure how to approximate the bubble:

•Determination of the projected bubble area

•Determination of perimeter (usually overestimated)

Calculated shape of a circle

1

1,5

2

2,5

3

3,5

4

0,1 1 10 100

Error in perimeter determination, %

Ap

pa

ren

t v

alu

e a

/b

Image analysis

IDEAL OBLATE ELLIPSOIDIDEAL OBLATE ELLIPSOIDsemiaxes semiaxes a, ba, b

-1,000

-0,800

-0,600

-0,400

-0,200

0,000

0,200

0,400

0,600

0,800

1,000

-1,000 -0,500 0,000 0,500 1,000

Improved procedure:

Determination of the object width, height and inclination•In front view

•In side view

Untreated dataUntreated data

0

2

4

6

0 2 4 6 8 10 12 14

a [mm]

b [

mm

]

waterwater-CaCl2glycerolbutanol

Reynolds number ?Reynolds number ?

1,01,11,21,31,41,51,61,71,81,92,0

1 10 100 1000 10000

Re

(2a/

d)2

w aterw ater-CaCl2glycerolbutanol

Weber number ?Weber number ?

1,01,11,21,31,41,51,61,71,81,92,0

1 10 100

We

(2a/

d)2

w aterw ater-CaCl2glycerolbutanol

LBB ud

eW2

Eötvös numberEötvös number

1,0

1,11,2

1,3

1,41,5

1,6

1,7

1,81,9

2,0

0,1 1 10 100

Eo

(2a/

d)2

w aterw ater-CaCl2glycerolbutanolstatic bubble

gd

Eo B

2

Static bubble profileStatic bubble profile(under a wetted plate)(under a wetted plate)

-3

-2

-1

0

0 1 2 3 4 5 6 7x/L

y/L

gL

„Laplace length!“

Normalized semiaxes of rising bubblesNormalized semiaxes of rising bubbles

Theoretical prediction for static bubblesTheoretical prediction for static bubbles

20for095.012 75.0

2

EoEod

a

0

1

2

3

0 1 2 3 4 5 62a/L

2b/L water

water-CaCl2glycerolbutanolWellek (drops)static bubble

RISING VELOCITYRISING VELOCITY

Rising velocity records for 7 bubbles of volume150 mm3 in water

0.21

0.22

0.23

0.24

0.25

0.26

0 200 400 600 800 1000 1200 1400

frame number (125 frame/s)

uB (m

/s)

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

RISING VELOCITYRISING VELOCITY for medium contaminated bubblesfor medium contaminated bubbles

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01

d , m

u m/s

H2O

CaCl2 1%

Glycerol 70%

Glycerol 73%

Butanol

Effects of

•Viscosity

•Surface tension

•Electrolyte

Our data compared with that of CliftOur data compared with that of Clift

H2O+CaCl2H2O

Our data compared with that of TomiyamaOur data compared with that of Tomiyama

H2O+CaCl2

H2O

RISING VELOCITYRISING VELOCITY dimensional analysisdimensional analysis

,,,,, gdfuRising velocity

•Bubble equivalent diameter

•Gravity acceleration

•Liquid density

•Density difference

•Liquid viscosity

•Surface tension

RISING VELOCITYRISING VELOCITY effect of surface tensioneffect of surface tension

41

g

W

21

41

Eo

MoeR

W

uU

2

1

21

EoL

d

g

dD

„Laplace velocity“

Dimensionless bubble diameter

Dimensionless bubble velocity

0.5

1.0

1.5

2.0

2.5

3.0

0 2 4 6 8 10 12 14 16 18 20

d/L

u/W

H2O

CaCl2 1%

Glycerol 70%

Glycerol 73%

Butanol

Viscosity cannot be neglected !!

Morton number

3

4gMo

RISING VELOCITYRISING VELOCITY classical variablesclassical variables

22 3

4

3

4

u

dg

u

dgCD

Drag coefficient

0.1

1

10

10 100 1000 10000Re

D

H2O

CaCl2 1%

Glycerol 70%

Glycerol 73%

Butanol

contaminated liquid

pure liquid

Not very successful !!

RISING VELOCITYRISING VELOCITY effect of viscosityeffect of viscosity

Dimensionless bubble diameter

Dimensionless bubble velocity

3

13

2

31

32

3

4DCeR

g

dD

22 3

4

3

4

u

dg

u

dgCD

Drag coefficient

31

31

3

4

DC

eR

g

uU

0

2

4

6

8

10

12

0 50 100 150 200 250D

U

Eo=1-2

Eo=2-3

Eo=3-4

Eo=4-5

Eo=5-7

Eo=7-10

Eo=10-20

There is still an effect of surface tension!!

RISING BUBBLERISING BUBBLE horizontal velocity

rising velocity

amplitude

Oscillatory movement of a Oscillatory movement of a bubble bubble

Bubble front area isBubble front area isSS = = aa22

New definition of the New definition of the drag coefficientdrag coefficient

2

2

2

23

4

2

a

d

u

gd

a

dCC DA

New dimensionless variablesNew dimensionless variables 3/2

2

a

dUU a

3/2

2

a

dDD a

0

2

4

6

8

10

12

14

0 50 100 150 200 250

Eo=1-2

Eo=2-3

Eo=3-5

Eo=5-10

Eo=10-20

D a

U a

OK !!!

RESULTING FORMULASRESULTING FORMULASCorrelation of the bubble shapeCorrelation of the bubble shape

Correlation of the bubble velocityCorrelation of the bubble velocity

20for095.012 75.0

2

EoEod

a

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.

30,201for

095.01365.0 75.0143.0

ReEo

EoeRCD

Thank you for your attentionThank 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.