- Email: [email protected]
A new method for measuring the size distribution of gas bubbles in aqueous media
A New Method for Measuring the Size Distribution of Gas Bubbles in Aqueous Media H I R O S H I SASAKI,* H I D E O M A T S U K A W A , * S H I N N O S U K E USUI,* AND E G O N M A T I J E V I C t *Research Institute of Mineral Dressing and Metallurgy, Tohoku Univei'sity, Katahira, Sendai 980, Japan, and "~Department of Chemistry and Institute of Colloid and Surface Science, Clarkson University, Potsdam, New York, 13676
Received August 29, 1985; accepted January 20, 1986 A simple and rapid method for the determination of the size distribution of gas bubbles in aqueous media is described which is, in principle, analogous to the size analysis of solid particles in a liquid by sedimentation. The procedure involves the measurement of the liquid column height as a function of time that elapsesafter the bubbling of gas has been discontinued. A pressure transducer, placed at a fixed position below the meniscus of the liquid, is used in these experiments. The size distribution of argon bubbles (0.1-1.5 mm in diameter) in aqueous solution of sodium hexadecyl sulfate (1 × 10-6 and 1 × 10-5 mole dm-a) was evaluated and the results compared with those obtained by the photographic method. © 1986 Academic Press, Inc. INTRODUCTION The photographic method has been widely used for measuring the size distribution of gas bubbles in liquid media (1). While the visual sizing of bubbles on the photograph is rather tedious, an image analyzer combined with a computer makes the procedure m u c h simpler (2). However, this procedure gives the information only for a selected cross section and it can not be used for systems contained in opaque vessels. In the present study a new method is described for the measurement o f the size distribution of finely divided gas bubbles ascending in a water column. The change in the liquid volume is established as a function of time, caused by successive disappearance of bubbles from the top of the liquid after the bubbling is discontinued. A pressure transducer is used in these measurements. PRINCIPLE OF MEASUREMENTS The principle by which the size distribution of gas bubbles is obtained is the same as that
of the sedimentation size analysis for solid particles in a liquid m e d i u m (3, 4). The only difference is that the terminal velocity o f rising bubbles does not obey the Stokes law. In the case of solids, particles settle on a weighing sensor and the weight of sedimented solids is recorded as a function of time; the larger the size the faster the sedimentation. By differentiating the cumulative weight curve with respect to time, the size distribution of solid particles is obtained with the aid of the Stokes law. In the case of bubbles, the larger the size the faster the rising velocity. The bubbles reaching the top leave the liquid, whereby the liquid volume is decreased when no further bubbling is permitted at the bottom. Thus, the decrease of the meniscus height of the liquid column is measured as a function o f time elapsed after the bubbling is interrupted. The height of the liquid column is recorded using a pressure transducer placed at a fixed position below t h e meniscus. Differentiation of the height recorded with respect to time permits the evaluation of the size distribution of bub500
0021-9797/86 $3.00 Copyright © 1986 by Academic Press, Inc. All rights of reproduction in any form reserved.
Journal of Colloid and Interface Science, VoL 113, No. 2, October 1986
SIZE DISTRIBUTION OF GAS BUBBLES IN AQUEOUS MEDIA bles, if the relation between the rising velocity of bubbles and their size is established.
501
,xP = pHz. ,XH/(Ho + ,XH)
or ,xP = pHz. ZXH/Ho,
EXPERIMENTAL Figure 1 represents the schematic drawing of the experimental setup for measuring the size distribution of finely divided gas bubbles ascending in a liquid column. Argon gas was introduced into the solution through a gas disperser (fritted glass sphere) at the bottom of the cell, which is 80 cm long and has an inner diameter of 2.6 cm. The bubbling cell of Pyrex glass is the same as used in the measurements of the Dorn potential of bubbles (5) except for the side tube (diameter 6 mm) to which a pressure transducer (Type PG-50 GC, Kyowa Co., Tokyo, Japan) was connected. When argon gas is introduced into the cell, the height of the liquid column increases from H0 to Hf in a steady state. Conversely, when the bubbling is stopped the liquid column height decreases from Hf to Ho. The pressure difference, AP, measured by the pressure transducer placed at a position Hz can be given as
AmO'i",rl Recorder
~ Stopcock
Gas
disperser
Ho>>(Hf-Ho)=AH
[1]
where p is the density of the liquid. The pressure difference, AP, is recorded as a function of time. A rectangular cell is fixed at the middle part of the column for taking the photographs of bubbles. Approximately 1000 bubbles were sized in each case. The bubble size was varied by using flitted glass spheres of different pore size (Nos. 1 to 4, where increasing number indicates smaller pore size). The bubbles were generated in aqueous solutions containing 1 × 10-5 and 1 × 10-6 mole dm -3 sodium hexadecyl sulfate (SHS) at room temperature, which varied between 21 and 25°C. RESULTS AND DISCUSSION In order to obtain the size distribution of bubbles from the AH vs t curve, it is necessary to know the relationship between the ascending velocity and the bubble diameter. Rising bubbles are photographed and the velocity determined by tracing their trajectory. Figure 2 shows that the ascending velocity, u, of bubbles in 1 × 10 -6 and 1 × l0 -5 mole dm -3 SHS aqueous solutions depends linearly on the bubble diameter. The proportionally constant k is found to be 125 s-~ when u and D are given in m m s-1 and mm, respectively. The linear relationship between rising velocity of bubbles and their diameter has been reported by several investigators (6-8). In Fig. 3, AH is plotted against t for the 1 × 10 -6 mole dm -3 SHS aqueous solution using bubbler No. 4. AHi and AH(i+~) represent the intercepts of tangential lines drawn at ti and t(i+l). The difference, AH~ - AH~i+~), corresponds to the fraction of bubbles having the diameter between Di and D(i+I), where D i is given by ti = Hf/ui = Hf/(kDi)
- -
[2]
Argon gas
Glasscolumn apparatus used in measurements of gas bubble size distributions. FIG. 1.
for
and ui is the ascending velocity of bubble of diameter Di. The differentiation of the AH vs t curve was carried out by a computer. Journal of Colloid and Interface Science, Vol. 113, No. 2, Oc~ber 1986
502
SASAKI ET AL. 300
i%o
,5 !
-~
200
o •
SHS I x l O ' r M SHS IxlO-SM
/
°Ooo o
o
o ° ~ e
0
i
8 U
u
o
I00
10
°
= k "D k = 125/s
i I D ,rnm
4
I
o)
J 2
I
t
B
15
i 2
FIG. 2. The relationship between gas bubble diameter (D) and ascendingvelocity(u) in aqueoussolutions of sodium hexadecyl sulfate (SHS): 1 × 10-s mole dm-3 (e) and 1 × 10 -6 mole dm-3 (0).
k
] 2
u ,ram
FIG. 4. Size distribution of argon gas bubbles measured
by the pressure transducer method (A, upper) and the photographic method (B, lower). As an example, the size distribution histogram of argon bubbles obtained by the pressure transducer method in 1 X 10 -5 mole dm -3 SHS is shown in the upper part (A) of Fig. 4, and compared to the results of the photographic method (lower part, B), with the corresponding median diameters (D50 and D~,med). Figure 5 illustrates the relationship between the median diameter by the pressure transducer method, Ds0, and that by the photographic method, Dv,m~. Solid and open circles
represent the results for 1 × 10 -6 and 1 × 10 -5 mole dm -3 SHS aqueous solutions, respectively. At both concentrations, values of Ds0 appear to be somewhat larger for larger bubbles, which effect could be due to the coalescence of bubbles that takes place during their ascending in the liquid column. The opposite trend is seen, with small bubbles. In the latter case the bubbler of small pore size continues to generate fine bubbles even after dosing the gas inlet stopcock, which makes the size dis-
1.5
/ / E E
&Hi
E E
£
/
AHi.H 0
d
/
0.5
/
9~
// • 0
//
2O
/
310 see.
(Di) (Di+l) Time
FIG. 3. The liquid column height vs time curve for a 1 × 10-6 mole dm-3 SHS aqueous solution and for bubbler No. 4. Journal of Colloid and Interface Science, Vol. 113, No. 2, October 1986
•
//0
1.0
<]
I
/
/
•
/
/
/
/
/
o15
,Io
I x IO'~M SHS I x 10-SM SHS
,15
D50 ~mlTt FIG. 5. The relationship between the median diameter obtainedby the pressuretransducermethod, Ds0, and the photographic method, Dv,m~.
SIZE DISTRIBUTION OF GAS BUBBLES IN AQUEOUS MEDIA t r i b u t i o n curve shift t o w a r d the s m a l l e r size. This s h o r t c o m i n g m a y b e r e m e d i e d b y m i n i m i z i n g the space v o l u m e b e t w e e n the gas disperser a n d the s t o p c o c k o f gas inlet. It has b e e n r e p o r t e d t h a t the D o r n effect o f b u b b l e s is quite different f r o m t h a t o f solid particles (9, 10) a n d t h a t it d e p e n d s o n the b u b b l e size (1 1). F o r this reason, t h e new m e t h o d d e s c r i b e d in this p a p e r will b e useful, p a r t i c u l a r l y in c o n c u r r e n t m e a s u r e m e n t o f b u b b l e size in the study o f the D o r n effect o f bubbles. REFERENCES 1. Cassel, E. A., Kaufman, K. M., and Matijevir, E., WaterRes. 8, 1017 (1975). 2. Kamiwano, M., Sato, R., Oshima, N., and Motoyoshi, T., Kagaku Kogaku Ronbunshu (Japan) 5, 199 (1979).
503
3. Orr, C., Jr., and Dallavalle, J. M., "Fine Particle Measurement." MacMillan Co., New York, 1959. 4. Allen, T., "Particle Size Measurement," 3rd ed., Chap. 10. Chapman & Hall, London/New York, 1981. 5. Usui, S., and Sasaki, H., J. Colloid Interface Sci. 65, 36 (1978). 6. Fuerstenau, D. W., and Wayman, C. H., Trans AIME 211, 694 (1958). 7. Klassen, V. I., and Mokrousov, V. A., in "Theory of Flotation" (J. Leja and G. W. Poling, Transl.), p. 468. Butterworths, London, 1963. 8. Anfruns, J. P., and Kitchener, J. A., in "Flotation-A. M. Gaudin Memorial Volume" (M. C. Fuerstenau, Ed.), Vol. 2, Chap. 23, p. 625. AIME Inc., New York, 1976. 9. Dukhin, S. S., in "Research in Surface Forces" (B. V. Derjaguin, Ed.), Vol. 2, p. 54. Consultant Bureau, New York, 1966. 10. Dukhin, S. S., Colloid J. USSR (Engl. Transl.) July, 46 (1983), translated from Kolloidn. Zh. 45, 22 (1983). 11. Usui, S., Sasaki, H., and Matsukawa, H., J. Colloid Interface Sci. 81, 80 (1981).
Journal of Colloid and Interface Science, Vol. 113, No. 2, October 1986
Received August 29, 1985; accepted January 20, 1986 A simple and rapid method for the determination of the size distribution of gas bubbles in aqueous media is described which is, in principle, analogous to the size analysis of solid particles in a liquid by sedimentation. The procedure involves the measurement of the liquid column height as a function of time that elapsesafter the bubbling of gas has been discontinued. A pressure transducer, placed at a fixed position below the meniscus of the liquid, is used in these experiments. The size distribution of argon bubbles (0.1-1.5 mm in diameter) in aqueous solution of sodium hexadecyl sulfate (1 × 10-6 and 1 × 10-5 mole dm-a) was evaluated and the results compared with those obtained by the photographic method. © 1986 Academic Press, Inc. INTRODUCTION The photographic method has been widely used for measuring the size distribution of gas bubbles in liquid media (1). While the visual sizing of bubbles on the photograph is rather tedious, an image analyzer combined with a computer makes the procedure m u c h simpler (2). However, this procedure gives the information only for a selected cross section and it can not be used for systems contained in opaque vessels. In the present study a new method is described for the measurement o f the size distribution of finely divided gas bubbles ascending in a water column. The change in the liquid volume is established as a function of time, caused by successive disappearance of bubbles from the top of the liquid after the bubbling is discontinued. A pressure transducer is used in these measurements. PRINCIPLE OF MEASUREMENTS The principle by which the size distribution of gas bubbles is obtained is the same as that
of the sedimentation size analysis for solid particles in a liquid m e d i u m (3, 4). The only difference is that the terminal velocity o f rising bubbles does not obey the Stokes law. In the case of solids, particles settle on a weighing sensor and the weight of sedimented solids is recorded as a function of time; the larger the size the faster the sedimentation. By differentiating the cumulative weight curve with respect to time, the size distribution of solid particles is obtained with the aid of the Stokes law. In the case of bubbles, the larger the size the faster the rising velocity. The bubbles reaching the top leave the liquid, whereby the liquid volume is decreased when no further bubbling is permitted at the bottom. Thus, the decrease of the meniscus height of the liquid column is measured as a function o f time elapsed after the bubbling is interrupted. The height of the liquid column is recorded using a pressure transducer placed at a fixed position below t h e meniscus. Differentiation of the height recorded with respect to time permits the evaluation of the size distribution of bub500
0021-9797/86 $3.00 Copyright © 1986 by Academic Press, Inc. All rights of reproduction in any form reserved.
Journal of Colloid and Interface Science, VoL 113, No. 2, October 1986
SIZE DISTRIBUTION OF GAS BUBBLES IN AQUEOUS MEDIA bles, if the relation between the rising velocity of bubbles and their size is established.
501
,xP = pHz. ,XH/(Ho + ,XH)
or ,xP = pHz. ZXH/Ho,
EXPERIMENTAL Figure 1 represents the schematic drawing of the experimental setup for measuring the size distribution of finely divided gas bubbles ascending in a liquid column. Argon gas was introduced into the solution through a gas disperser (fritted glass sphere) at the bottom of the cell, which is 80 cm long and has an inner diameter of 2.6 cm. The bubbling cell of Pyrex glass is the same as used in the measurements of the Dorn potential of bubbles (5) except for the side tube (diameter 6 mm) to which a pressure transducer (Type PG-50 GC, Kyowa Co., Tokyo, Japan) was connected. When argon gas is introduced into the cell, the height of the liquid column increases from H0 to Hf in a steady state. Conversely, when the bubbling is stopped the liquid column height decreases from Hf to Ho. The pressure difference, AP, measured by the pressure transducer placed at a position Hz can be given as
AmO'i",rl Recorder
~ Stopcock
Gas
disperser
Ho>>(Hf-Ho)=AH
[1]
where p is the density of the liquid. The pressure difference, AP, is recorded as a function of time. A rectangular cell is fixed at the middle part of the column for taking the photographs of bubbles. Approximately 1000 bubbles were sized in each case. The bubble size was varied by using flitted glass spheres of different pore size (Nos. 1 to 4, where increasing number indicates smaller pore size). The bubbles were generated in aqueous solutions containing 1 × 10-5 and 1 × 10-6 mole dm -3 sodium hexadecyl sulfate (SHS) at room temperature, which varied between 21 and 25°C. RESULTS AND DISCUSSION In order to obtain the size distribution of bubbles from the AH vs t curve, it is necessary to know the relationship between the ascending velocity and the bubble diameter. Rising bubbles are photographed and the velocity determined by tracing their trajectory. Figure 2 shows that the ascending velocity, u, of bubbles in 1 × 10 -6 and 1 × l0 -5 mole dm -3 SHS aqueous solutions depends linearly on the bubble diameter. The proportionally constant k is found to be 125 s-~ when u and D are given in m m s-1 and mm, respectively. The linear relationship between rising velocity of bubbles and their diameter has been reported by several investigators (6-8). In Fig. 3, AH is plotted against t for the 1 × 10 -6 mole dm -3 SHS aqueous solution using bubbler No. 4. AHi and AH(i+~) represent the intercepts of tangential lines drawn at ti and t(i+l). The difference, AH~ - AH~i+~), corresponds to the fraction of bubbles having the diameter between Di and D(i+I), where D i is given by ti = Hf/ui = Hf/(kDi)
- -
[2]
Argon gas
Glasscolumn apparatus used in measurements of gas bubble size distributions. FIG. 1.
for
and ui is the ascending velocity of bubble of diameter Di. The differentiation of the AH vs t curve was carried out by a computer. Journal of Colloid and Interface Science, Vol. 113, No. 2, Oc~ber 1986
502
SASAKI ET AL. 300
i%o
,5 !
-~
200
o •
SHS I x l O ' r M SHS IxlO-SM
/
°Ooo o
o
o ° ~ e
0
i
8 U
u
o
I00
10
°
= k "D k = 125/s
i I D ,rnm
4
I
o)
J 2
I
t
B
15
i 2
FIG. 2. The relationship between gas bubble diameter (D) and ascendingvelocity(u) in aqueoussolutions of sodium hexadecyl sulfate (SHS): 1 × 10-s mole dm-3 (e) and 1 × 10 -6 mole dm-3 (0).
k
] 2
u ,ram
FIG. 4. Size distribution of argon gas bubbles measured
by the pressure transducer method (A, upper) and the photographic method (B, lower). As an example, the size distribution histogram of argon bubbles obtained by the pressure transducer method in 1 X 10 -5 mole dm -3 SHS is shown in the upper part (A) of Fig. 4, and compared to the results of the photographic method (lower part, B), with the corresponding median diameters (D50 and D~,med). Figure 5 illustrates the relationship between the median diameter by the pressure transducer method, Ds0, and that by the photographic method, Dv,m~. Solid and open circles
represent the results for 1 × 10 -6 and 1 × 10 -5 mole dm -3 SHS aqueous solutions, respectively. At both concentrations, values of Ds0 appear to be somewhat larger for larger bubbles, which effect could be due to the coalescence of bubbles that takes place during their ascending in the liquid column. The opposite trend is seen, with small bubbles. In the latter case the bubbler of small pore size continues to generate fine bubbles even after dosing the gas inlet stopcock, which makes the size dis-
1.5
/ / E E
&Hi
E E
£
/
AHi.H 0
d
/
0.5
/
9~
// • 0
//
2O
/
310 see.
(Di) (Di+l) Time
FIG. 3. The liquid column height vs time curve for a 1 × 10-6 mole dm-3 SHS aqueous solution and for bubbler No. 4. Journal of Colloid and Interface Science, Vol. 113, No. 2, October 1986
•
//0
1.0
<]
I
/
/
•
/
/
/
/
/
o15
,Io
I x IO'~M SHS I x 10-SM SHS
,15
D50 ~mlTt FIG. 5. The relationship between the median diameter obtainedby the pressuretransducermethod, Ds0, and the photographic method, Dv,m~.
SIZE DISTRIBUTION OF GAS BUBBLES IN AQUEOUS MEDIA t r i b u t i o n curve shift t o w a r d the s m a l l e r size. This s h o r t c o m i n g m a y b e r e m e d i e d b y m i n i m i z i n g the space v o l u m e b e t w e e n the gas disperser a n d the s t o p c o c k o f gas inlet. It has b e e n r e p o r t e d t h a t the D o r n effect o f b u b b l e s is quite different f r o m t h a t o f solid particles (9, 10) a n d t h a t it d e p e n d s o n the b u b b l e size (1 1). F o r this reason, t h e new m e t h o d d e s c r i b e d in this p a p e r will b e useful, p a r t i c u l a r l y in c o n c u r r e n t m e a s u r e m e n t o f b u b b l e size in the study o f the D o r n effect o f bubbles. REFERENCES 1. Cassel, E. A., Kaufman, K. M., and Matijevir, E., WaterRes. 8, 1017 (1975). 2. Kamiwano, M., Sato, R., Oshima, N., and Motoyoshi, T., Kagaku Kogaku Ronbunshu (Japan) 5, 199 (1979).
503
3. Orr, C., Jr., and Dallavalle, J. M., "Fine Particle Measurement." MacMillan Co., New York, 1959. 4. Allen, T., "Particle Size Measurement," 3rd ed., Chap. 10. Chapman & Hall, London/New York, 1981. 5. Usui, S., and Sasaki, H., J. Colloid Interface Sci. 65, 36 (1978). 6. Fuerstenau, D. W., and Wayman, C. H., Trans AIME 211, 694 (1958). 7. Klassen, V. I., and Mokrousov, V. A., in "Theory of Flotation" (J. Leja and G. W. Poling, Transl.), p. 468. Butterworths, London, 1963. 8. Anfruns, J. P., and Kitchener, J. A., in "Flotation-A. M. Gaudin Memorial Volume" (M. C. Fuerstenau, Ed.), Vol. 2, Chap. 23, p. 625. AIME Inc., New York, 1976. 9. Dukhin, S. S., in "Research in Surface Forces" (B. V. Derjaguin, Ed.), Vol. 2, p. 54. Consultant Bureau, New York, 1966. 10. Dukhin, S. S., Colloid J. USSR (Engl. Transl.) July, 46 (1983), translated from Kolloidn. Zh. 45, 22 (1983). 11. Usui, S., Sasaki, H., and Matsukawa, H., J. Colloid Interface Sci. 81, 80 (1981).
Journal of Colloid and Interface Science, Vol. 113, No. 2, October 1986