shape and rising velocity of bubbles vsb-technical university of ostrava faculty of metallurgy and...
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![Page 1: SHAPE AND RISING VELOCITY OF BUBBLES VSB-Technical University of Ostrava Faculty of Metallurgy and Material Engineering Department of Chemistry, 70833](https://reader035.vdocuments.mx/reader035/viewer/2022062519/5697bfbc1a28abf838ca13ad/html5/thumbnails/1.jpg)
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: [email protected]@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
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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.
?
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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
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SIZE OF RISING BUBBLES
increasing volume
gd
Eo B
2
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LIQUID VISCOSITY
BB Ud
Re
Low– and medium-viscosity …. Re > 50
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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
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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
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LOWER DRAG (hypothetical)
Why not ??
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Hydrostatics
Surface tension
BUBBLE SHAPE
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SYMMETRIC OBLATE BUBBLE
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Our laboratories
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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
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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
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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
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Untreated dataUntreated data
0
2
4
6
0 2 4 6 8 10 12 14
a [mm]
b [
mm
]
waterwater-CaCl2glycerolbutanol
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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
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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
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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
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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!“
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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
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RISING VELOCITYRISING VELOCITY
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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)
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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
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Our data compared with that of CliftOur data compared with that of Clift
H2O+CaCl2H2O
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Our data compared with that of TomiyamaOur data compared with that of Tomiyama
H2O+CaCl2
H2O
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RISING VELOCITYRISING VELOCITY dimensional analysisdimensional analysis
,,,,, gdfuRising velocity
•Bubble equivalent diameter
•Gravity acceleration
•Liquid density
•Density difference
•Liquid viscosity
•Surface tension
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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
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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 !!
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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!!
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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
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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 !!!
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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
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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.
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