Chem.Eng,Comm., 192: 550-556, 2005
BREAKUP OF BUBBLES RISING IN LIQUIDS OF
LOW- AND MODERATE-VISCOSITY
WICHTERLE K.*, WICHTERLOVÁ J. , KULHÁNKOVÁ L.
VSB-Technical University of Ostrava,
70833 Ostrava Poruba, Czech Republic
Tel. 420 (69) 699 4304, Fax: 420 (69) 691 8647, e-mail: kamil.wichterle@vsb.cz
The breakup rate of bubbles was studied by observing them rising in water and in
glycerol solutions with μ=1-32 mPas. A levitating technique was applied with
bubbles seized in the downstream liquid flow of a diverging channel. Bubbles with
volumes VB=0.2-0.8 cm3 are generally spheroid but their shape pulsates. As they
wobble they have a tendency to split. The exponential decay of the number of
unbroken bubbles was found which has been characterized quantitatively by a halflife, t1/2. The rate of breakup increased significantly with the original size of the
bubble. By regression of experimental data, the proportionality t1/2 ~ VB–4 has been
determined. There is a significant effect of surface tension, while the effect of
viscosity on the process appeared to be negligible in the bubble Reynolds number
range of 60-3000 that was investigated.
Keywords: aeration, bubble, dispersion, multiphase flow, particle, stability
Introduction
Systems with bubbles in liquid are very common both in natural
environment and in process technologies. Bubbles can be used to induce
liquid flow in airlift systems, to agitate liquids, particularly the suspension of
solids and to contact liquid with gases, be it in distillation, absorption or
degassing to complex chemical reactions. The motion of bubbles plays an
important role also in heat transfer processes, particularly during liquid
boiling. Investigation of behavior of a single bubble is the first step to the
understanding of momentum, heat and mass transfer in gas-liquid processes.
Current knowledge of the subject is presented in the monograph by Clift,
Grace and Weber [1].
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BREAKUP OF BUBBLES RISING IN LIQUIDS OF LOW- AND MODERATE-VISCOSITY
Essentially, the bubble shape is determined by the ratio of gravity forces
deforming the bubble and the surface forces keeping its shape in a spherical
form. It is expressed for arbitrary liquid systems by the Eötvös number
d2  g
(1)
Eo  B

with equivalent diameter
6V
dB  3 B

(2)
The influence of viscosity on the shape of a bubble is characterized
by the Morton number
4 g
M  3 .
(3)
 
For low viscosity liquids with M <<10-3, there is no apparent viscosity effect
and a single value Eo controls the bubble shape. Small bubbles having
Eo<<1 are essentially spherical.
Numerous experimental and theoretical studies, including several
monographs dealing with bubbles, appeared during last two decades [2-8].
Unfortunately, these studies mostly pay attention to spherical bubbles in
viscous liquids and to small perturbations of this case.
However, larger bubbles rising at higher Reynolds numbers occur more
frequently, both in the nature as well as in industrial processes. Spheroid
bubbles are typical for the range of 1<Eo<40. They are kept stable by
hydrodynamic forces rather than by the surface tension. With increasing Eo,
they slowly lose their fore-and-aft symmetry and, at Eo>40, they acquire a
hemispherical or a spherical cap shape. Both the shape the motion of larger
bubbles are somewhat unstable, the bubbles wobble during their rise. Such
behavior is too complex to be studied theoretically. From an experimental
point of view, spheroid bubbles occur within the volume range of
0.01 cm3 <VB<2 cm3 in water and their rising velocity is within the range of
0.15-0.30 m/s. It appears that experimental investigation of such bubbles is
usually limited to the recording of their shape and velocity at a single instant.
A moving camera or a set of stationary cameras focused to selected points of
the column [9] may solve some problems. However, in the measuring
section of even large columns [10] (having the inside diameter up to 0.6 m
and the height of 4 m) bubbles spent only 10-20 s and a particular bubble can
be observed for only a very short period. This is insufficient to investigation
of such processes as breakup and coalescence. One possible solution is to
observe bubbles in the downstream flow of liquid in transparent channel
[11].
Time to time, large bubbles release smaller, daughter bubbles. A
class of medium size spheroid bubbles resulting from this breakup is
55
552
K.WICHTERLE ET AL.
extremely important in industrial gas-liquid processes [12-13]. We have
studied the probability of a breakup of large bubbles and the results are
presented in this paper.
Experimental
Recently, we applied a levitating technique that is a suitable way for
the long-term qualitative observation of the shape and its oscillation, of
wobbling, breakup and coalescence of bubbles under well-controlled
conditions [14-15].
The principal part of our equipment is an entrance region of a
diverging conical channel. When a bubble is placed in the downward
oriented diverging channel, it migrates to the position where its rising
Figure 1. Experimental setup
- liquid loop (Kavalier Glass 25 mm, PVC hoses 3/4", heat exchanger (copper)),
- centrifugal pump Wilo-Jet 401 (stainless steel, plastics), 0-50 dm3/min,
- calming section (Kavalier Glass 100/200 mm, with a system of slowly rotating baffles
(0-65 rpm),
- vertical rectangular transparent vessel 100×100×400 mm with a diverging conical
channel. In the presented experiments, the cone with entry diameter 47.5 mm, and
wall slope 2o was applied in this set of experiments.
- induction flowmeter Endress-Hauser,
- syringe system (Eppendorff) for injection of bubbles, usual dosage 10-1000 mm3,
- camera Panasonic DX100, VCR and TV Philips, PC Pentium, AD-DA transducer,
video-card National Instruments,
553
BREAKUP OF BUBBLES RISING IN LIQUIDS OF LOW- AND MODERATE-VISCOSITY
velocity is just compensated by the local liquid velocity. Thus, the liquid
flow rate need not be extremely carefully controlled like in the parallel
channel [11]. The Reynolds number for our pipe flow is between 300 and10.000. Thus, the assumption of an entrance region flow is plausible. It
means that a narrow boundary layer occurs close to the walls and that
essentially a plug flow characterizes the remaining flow profile. Bubbles are
maintained in the central region of the channel by the centrifugal force
induced by slowly rotating baffles upstream. The experimental setup is
shown schematically in Figure 1.
Tap water and glycerol solutions (viscosity 1-32 mPas) were used.
Liquids were saturated by air at 25-30oC. Liquid flow rate was adjusted by
the valve and measured by the flow-meter. Bubbles were released by a
syringe system. The motion of bubbles was recorded by a video and the
records were analyzed by PC. Smaller bubbles having volume up to 0.3 cm 3
break only rarely and one single bubble can be observed for hours. Life
periods of larger bubbles prior to their breakup are finite. This has been the
object of this study.
Results
Single bubbles of a given volume were released to the channel.
Experimental runs when the bubble broke just during its formation were
ignored. The number of released bubbles in time t=0 is N0 and number N of
bubbles surviving given time t is a function time N(t). The experimental data
obtained indicate an exponential decrease of the lifetime of bubbles as it can
be seen from the plot of log(N(t)/N0) versus t. From the interpretation of the
experimental data as shown in Fig.2 it can be clearly seen that, in water, the
number of bubbles of any initial volume decreases exponentially with time.
The same conclusion is found also for the aqueous solutions of glycerin of
1
N/N 0
0.1
3
V B = 450 mm
3
3
3
800 mm
3
700 mm
500 mm
600 mm
0.01
0
20
40
60
80
100
120
t [s]
Figure 2.
Decrease of the number of non-broken bubbles of various original volume
VB as a function of time in water
55
554
K.WICHTERLE ET AL.
varying viscosity. Therefore, the process can be characterized by a single
value, i. e. by the half-life t1/2 of a bubble

t 
 .
(4)
N  N0 exp   ln 2
t1 / 2 

The half-life of bubbles depends on the initial bubble size and on the
physical properties of the liquid (i. e. on the density, the viscosity and the
surface tension of the liquid.). Postulating that that the dimensionless
halftime can be expressed by a generalized formula Θ1/2 = f(Eo M), where
dimensionless half life is defined by
t  1/ 4 g 3 / 4
(5)
1 / 2  1 / 2 1 / 4

the regression of all experimental data for bubbles in water and two aqueous
solutions of glycerin leads to
Θ1/2 = 1.66×1010 Eo-6.05 M-0.04
(6)
2
(R = 0,93).
Clearly, the effect of the viscosity expressed here by the Morton number
within the investigated range of M=10-11-10-7 can be neglected and the
results plotted in Figure 3 may be satisfactorily interpreted by a simplified
power function
 Eo 
1 / 2  5900  
 10 
2
(R = 0,88).
6
(7)
The half-life (in seconds) for air bubbles in water is t1/2 = 0.7 VB-4 (when
volume is measured in cubic centimeters). Larger air bubbles in water during
10000
Water
 1/2
Glycerol 56%
Glycerol 76%
1000
100
10
15
Eo
20
Figure 3. Bubble half-life as a function of the volume of air bubbles that rise in water
and in aqueous solutions of glycerine.
Experimental data and power-law approximation (7)
BREAKUP OF BUBBLES RISING IN LIQUIDS OF LOW- AND MODERATE-VISCOSITY
555
their initial breakup will release usually just one small daughter bubble, its
volume being typically around 0.2 cm3. Bubbles smaller than 0.4 cm3, when
split, will form two similar daughter bubbles; however, bubbles of this size
are comparatively stable. Bubbles of the same size in glycerol solutions are
more prone to a breakage, e.g. for a 76% glycerol we have t1/2 = 0.3 VB-4.
This value results mainly from the lower surface tension while the effect of
viscosity seems to be negligible.
Conclusions
An experimental technique based on levitating bubbles makes it
possible to investigate rising bubbles at controlled conditions for large
periods of time.
The rate of bubble breakup evaluated from the experimental data has
been expressed by an exponential function of time. Half-life of bubbles
depends strongly on bubble size. It also depends on surface tension. On the
other hand, the effect of viscosity is minor. A dimensionless correlation has
been suggested for the generalization of the results.
Acknowledgments
We gratefully acknowledge financial support by the grants No.106/98/0050 and
104/01/0547 from the Grant Agency of the Czech Republic.
References
[1.]
R. Clift, J.R. Grace, M.E. Weber, Bubbles, Drops and Particles, (Academic Press
New York, 1978).
[2.]
L. van Wijngaarden, Mechanics and Physics of Bubbles in Liquids, ISBN 90-2472625-5, (Martinus Nijhoff Publ., The Hague, 1982)
[3.]
J.R. Grace and M.E. Weber, In: Handbook of Multiphase Systems, G. Hetsroni,
ed., (Hemisphere Publ. Co, New York, 1982), Part 1, pp.204-223
[4.]
Fan, L.-S. and K. Tsutschiya, Bubble Wake Dynamics in Liquids and Liquid-Solid
Suspensions, (Butterworth, Boston, 1990).
[5.]
R.P. Chabra and D. DeKee, Transport Processes In Bubbles, Drops And Particles,
(Hemisphere, New York, 1992)
[6.]
R.P. Chabra, Bubbles, Drops And Particles in Non/Newtonian Fluids, (CRC Press
Boca Raton, 1993). ISBN 0-8493-5718-2
[7.]
S.S. Sadhal, P.S. Ayyaswamy and J.N. Chang, Transport Phenomena with Drops
and Bubbles, (Springer, New York, 1997), ISBN 0-387-94678-0
[8.]
Z. Zapryanov and S. Tabakova, Dynamics of Bubbles, Drops and Rigid Particles,
(Kluwer Acad. Publ. Dordrecht, 1999), ISBN 0-7923-5347-1
[9.]
S. Hosokawa, A.Tomiyama and T. Hamada In: Two-phase flow modeling and
experimentation, Celata G.P et al. eds., (Edizioni ETS Pisa, 1999)
[10.] R. Krishna, M.I.Urseanu, J.M.van Baten and J. Ellenberger, Int. Commun. Heat
Mass Transfer 26, 781 (1999).
[11.] J.H.C.Coppus, K.Rietema, S.P.P. Ottengraf, Trans.Inst.Chem.Engrs 55, 122-129
(1977)
55
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K.WICHTERLE ET AL.
[12.] Y.T. Shah and W.D. Deckwer, In: Handbook of Fluids in Motion, N.P.
Cheremisinoff and R. Gupta, eds, (Science, Ann Arbor, 1983)
[13.] F. Kaštánek, J. Zahradník, J. Kratochvíl and J. Čermák Chemical Reactors for GasLiquid Systems. (Ellis Horwood, New York, (1993).
[14.] K. Wichterle, L.Kulhánková and J. Wichterlová, In: 14 th Congress CHISA,
(Process Eng.Publ., Prague, 2000), P1.38, ISBN80-86059-30-8
[15.] K. Wichterle, J. Wichterlová and L.Kulhánková, In: Sborník 46. konference
CHISA, (Process Eng.Publ., Prague, 1999), ISBN 80-86059-28-6
Notation
dB
Eo
g
M
N
N0
R2
t
t1/2
VB
v
x
θ1/2
μ
ρ
σ
equivalent diameter, (Eq.2)
Eötvös number, (Eq.1)
gravity acceleration
Morton number, (Eq.3)
number of unbroken bubbles
initial number of bubbles
correlation coefficient
time
the half-life of a bubble
bubble volume
axial velocity
axial distance from the channel inlet
dimensionless half-life, (Eq.5)
dynamic viscosity
density
surface tension