974
Ind. Eng. Chem. Process Des. Dev. 1986, 25, 974-978
Surface Effects and Mass Transfer in Bubble Column Jlann Jang Jeng, Jer Ru Maa," and Vu Min Yang Depaflment of Chemical Engineerlng, National Cheng Kung University, Tainan, Taiwan, R.O.C.
Absorption of C02 gas is carried out in a bubble column under a fixed gas flow rate. A small amount of surface-active additive in the column liquid has the effect of retarding the coalescence of gas bubbles, thus making the gas-liquid interfacial area, a , larger; it also has the effect of resisting the stretching or compression of the interface and reducing disturbance in the bulk fluids, therefore making the mass-transfer coefficient, k,, smaller. Because of these two opposing factors, the product k,a has a maximum value at a very low surfactant concentration. The surface activity of the cationidanionic binary surfactant solution may be considerably higher than that of the solution containing a single surface active component. The application of this synergistic effect may prove to be a very effective way of improving the operating efficiency of the bubble column.
A bubble column is a useful tool and widely used for various gas-liquid mass-transfer operations. In a bubble column, the gas phase is dispersed into small bubbles in order to increase its contact area with the liquid phase. The rising of the gas bubbles through the column liquid promotes convection in both the gas and the liquid phases and consequently enhances the mass-transfer coefficient. The effects of a small amount of surface-active additives in the column liquid on the mass-transfer coefficient and fluid flow behaviors were studied by Garner and Haycock (1957), Garner and Hammerton (1957), Zieminski and Lessard (1969),and Raymond and Zieminski (1971). Their results indicate that these additives often reduce the liquid-side mass-transfer coefficient, kL, but increases the gas-liquid interfacial area per unit volume, a, by retarding the coalescence of gas bubbles. The net effect of these additives on the operating efficiency of the bubble column, or the value of the product KLa,is rather complicated and further studies are desirable. The experiment of this work includes the study of the effect of a surface-active additive on bubble behaviors and mass-transfer coefficient in a bubble column by adding a small amount of it to the column liquid. Binary mixtures of cation/anion surfaceactive additives are also used to explore their synergistic effect on the improvement of the operating efficiency of the bubble column. Dynamic Surface Effect and Bubble Coalescence Mechanism Inhomogeneity in temperature or concentration on the liquid surface causes a local increase or decrease of surface tension and thus induces flow of the surface liquid. This is known as the Marangoni effect discussed by Scriven and Sternling (1960). In systems containing surface-active components, when the interface between phases is stretched at a certain rate, new surface area is created constantly and the surface-active components have to be supplied from the bulk liquid to the interface by diffusion in order to satisfy the need of adsorption. Their concentrations in the vicinity of the interface are lower than that in the bulk liquid because of limited rates of diffusion. The amounts of adsorptions of the surface-active components on the interface are in equilibrium with these lower concentrations and are therefore lower than that of the static case without stretching of the interface. Consequently, the interfacial tension of a stretching interface is higher than a static one, and the local increase in surface tension caused
* Author to whom correspondence should be addressed. 0196-4305/86/1125-0974$01.50/0
by the stretchw of the interface has the effect of retarding further stretching. When the interface between phases is compressed, the surface-active components have the similar effect of retarding further compression. These phenomena were also discussed by Gibbs (1960). This effect hampers the surface convection and the induced flow in the nearby fluids; the mass-transfer coefficient is thus reduced. This is the disadvantageous respect of the dynamic effect of the surface-active additive on the operating efficiency of the bubble column. The local change of surface tension can be expressed by eq 1 as shown by Andrew (1960) where C is the concen-
tration of the surface-active component in the bulk liquid, D is the diffusivity of this component, R is the gas constant, T is the temperature of the system, and S is the steady stretching rate of the interface (eq 2 where t is time and s = 1- -dA A dt A is the area of the interface between phases). Under constant system temperature, T, the denominator on the right side of eq 1is a group of constants. If we define the values in eq 3, then A B 0: Y,and the value of Y is a
YE.(%)
2
(3) measurement of the dynamic surface effect caused by the addition of the surface-active component (Andrew, 1960; Yang, 1983). When a small gas bubble is moving in a pure liquid, the bubble surface is dragged backward along with the liquid. In the front portion of the bubble, the surface is stretched and the new surface is constantly generated. In the rear portion, the bubble surface is compressed and disappears continuously. This forces surface convection and thus enhances the interfacial mass transfer. But when there is a small amount of surface-active additive in the column liquid, the expansion and compression of the bubble surface is retarded and the interfacial mass-transfer coefficient is thus reduced. A liquid film always forms between two gas bubbles in the process of their coalescence. When these two bubbles are getting closer, the liquid in the film flows outward. 0 1986 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 4, 1986
975
IO -
a-
C
b 6 .A
E
*
d E 2 -
E?
50
'0 x
2
I
0
3
kh
Figure 1. Plot of eq 4 and 7.
This causes the gas-liquid interface on both sides of the film to stretch. If the liquid contains a small amount of surface-active component, the dynamic surface effect retards the stretching of the bubble surface and makes the drainage of the film liquid slower, and consequently the coalescence of the gas bubbles becomes more difficult. Hence, the small amount of surface-active component increases the number of gas bubbles per unit volume, and consequently the gas-liquid interfacial area is increased. This is the advantageous respect of the dynamic effect of the surface-active additive on the operating efficiency of the bubble column. As two gas bubbles in dilute surfactant solution are approaching each other, a gradient of surface tension is created by the dynamic surface effect. The curvature of the bubble surface causes a difference between the inner and outer pressures. The van der Waals force also exists between the bubble surfaces on both sides of the liquid film. If we neglect the electrostatic force, a quasi-equilibrium thickness, h,, of the liquid film can be computed by a force balance, as shown by Marrucci (1969) and Sagert and Quinn (1976, 1978) in eq 4-6 where r is the bubble
-Qrk2 - -0
where
k =
kh,
(
!&$)'I3
+ (kho)2
(4)
(5)
radius, A , is the Hamaker London constant. The film thickness at the moment it breaks, hf, can be expressed by eq 7 as shown by Marrucci (1969) and Sagert and Quinn (1976, 1978). Figure 1 shows the relationship between (7)
Qrk2/oand kh. When Qrk2/ois larger than 1.89, ho > hf, it requires a period of time for the thickness of the liquid film to reduce from hoto hf before the two bubbles coalesce. But if Qrk2/a is less than 1.89, they coalesce instantly. Hence, the value of Qrk2/uis very important to the coalescence of bubbles. If we define eq 8, under isothermal condition, we can write eq 9. One can use the
value of M to express the degree of easiness for two gas
401 30
t
i \\\
-5
','u
:
-4
-3 -2 Log conc. Figure 2. Variation of surface tension with concentration (mol/L) of the following SDBS/DTMAC ratios: ( 0 )1/0;(0) 0/1; (49/1; (A) I/% (@ 1/1. -6
bubbles in dilute surfactant solution to coalesce.
Synergistic Effect in Binary Surfactant Solutions When a small amount of surface-active solute is added to a liquid, the interfacial tension decreases substantially because of the adsorption at the interface. The relationship between the adsorption, r, and the variation of surface tension with respect to bulk concentration can be expressed as eq 10. The surface activity of a binary solution
r=--1
da
2RT d In C of two surface-active components may be remarkably different from that containing only one of them; its surface tension may decrease much more rapidly. This synergistic effect is negligible when both of the surface-active solutes are nonionic, becomes rather significant in ionic/nonionic binary solution, and is very prominent when the solutes are a cationic/anionic pair. This phenomenon has been studied in depth by Goralczyk (1980), Goralczyk and Waligora (1981), Lucassen-Reynders et al. (1981), and Rosen and Zhu (1984). The cationic and anionic surfactants used in this work are, respectively, sodium dodecylbenzenesulfonate(SDBS, Cl2H,,CGH,SO3Na) and dodecyltrimethylammonium chloride (DTMAC, C12H25N(CH3)3C1). Figure 2 shows the surface tensions of aqueous solutions determined by the pendant drop method, as shown by Adamson (1982), for various SDBSIDTMAC ratios as a function of surfactant concentration. This figure indicates that the synergistic effect is significant when the surfactant concentration is low; the surface tension of the binary solution is lower than that of the single solute of the same concentration. The synergistic effect weakens gradually as the concentration increases. I t disappears entirely and precipitation starts to appear in the cationic/anionic binary surfactant solution when an upper concentration limit is reached. Experimental Method and Apparatus Figure 3 is a schematic diagram of the experimental setup of this work. C02 gas from bottle A and regulator Q is saturated with water vapor by bubbling through two
076
Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 4, 1986 k6&
Q
I
+Figure 3. Apparatus.
flasks, B, containing distilled water. Water droplets carried in the gas stream, if any, are removed by a trap C. The COzflow rate is adjusted by a needle valve E and measured by a rotameter F before it enters the bubble column H. D is a self-adjusting bypass with the functions of preventing the pressure before E becomes too high and making the flow through E more steady. The COPgas can be released to the outside of the system through three-way valve 0 during the stage of adjusting its flow rate. When the C 0 2 flow is steady at the desired rate, it is led to the bubble column through gas distributor G. The bubble column is made of Plexiglas, with a 6 X 6 cm square cross section and a height of 95 cm. The liquid height in this column is 60 cm. Two different gas distributors were used in this work. The one made of steel has 21 holes of 1-mm diameter; another one is made of sintered 100-pm glass powder. When the bubble column is in operation, the volume fraction of gas bubbles in the column, e, can be computed from the heights of liquid levels in the manometer N as shown in Figure 3 (eq 11). The diameters of the gas E = (2, - ZZ)/Z, (11) bubbles are determined by taking photographs using a close-up lense. The diameter of each bubble is measured on the photograph and a volume-surface mean bubble diameter or Sauter mean diameter is computed by eq 12. The gas-liquid interfacial area per unit volume of the bubble column is defined in eq 13. d,, = (Enid:)
/ (Cn&)
a = 6~/d,,
(12)
(13)
In this work, the acidity of the solution in the bubble column is determined by a pH meter J with an electrode I inserted in the column. It is also recorded by recorder K. The concentration of dissolved COz in the column liquid, C, can therefore be computed from the pH value. Because of the constant agitation by the gas bubbles, we can assume that the column is well mixed. Because the gas is pure COB,the gas-phase mass-transfer resistance is negligible. Only the liquid-phase resistance is influential to the rate of mass transfer. Hence, the variation of the concentration of the dissolved C 0 2 in the column liquid can be expressed as eq 14 where k L is the liquid-phase dC (1- t) - = kLa(C* - C) (14) dt mass-transfer coefficient and C* is the saturated concentration in equilibrium with the gas phase. Because when t = 0, C = Co, eq 14 can be integrated to give eq 15. If
we plot the experimentally determined (C* - C)/(C* - Co) vs. time on semilog paper, the slope of the resulting straight
conc. x I $ , mole I_' Figure 4. kL, a , and kLa as functions of concentrations for SDBS solution (electric conductivity of water sample: 10.5 pR/cm; steel gas distributor).
-
1-01
CWC. x i o " , mote )_I Figure 5. kL, a, and kLa as functions of concentration for solutions of SDBS/DTMAC = 1/9 (electric conductivity of water sample: 10.5 pR/cm; steel gas distributor).
line is -KLa/[2.303(1 - e)]; the value of KLa is thus obtained. Results and Discussion Experimental results verify that the addition of a small amount of surfactant to the liquid phase in a bubble column has the effect of retarding the coalescence of the gas bubbles. This makes the number of gas bubbles per unit volume larger, their size smaller, their terminal rising velocity slower, their residence time in the column liquid longer, and consequently the volume fraction occupied by the gas phase, E , and the interfacial area per unit volume larger. Figure 4 is a set of typical experimental results. The bubble size decreases and the a value increases as the concentration of the surfactant is increased. The masstransfer coefficient, kL, is not only a function of the rigidity of the interface but also a function of bubble size. The larger the bubble size the smaller the value of kL as shown by Baird and Davidson (1962). The kL value is low at zero surfactant concentration because of the large bubble size. It reaches a maximum a t a low surfactant concentration and decreases monotonically as the concentration is further increased. Consequently, the product kLa has also a maximum as indicated in this figure. When the cationiclanionic binary mixture of surfactants is used, the position of the maximum of kLa moves leftward to a lower concentration because of the synergistic effect, as shown in Figure 5 for the case of SDBS/DTMAC = 1/9. The experimental results in Figure 6 show that in the case of SDBS/DTMAC = 1/1, the a value also has a maximum.
Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 4, 1986 977
conc. x l a 4 , mole ? Figure 6. kL, a , and kLa as functions of concentration for solutions of SDBS/DTMAC = 1/1(electric conductivity of water sample: 10.5 pQ/cm; steel gas distributor).
,
7
'
, ' - " ' I
* ' " ' ' ' I
'
"
'
'
7
'
mole
L$C
I
0"
i"1
Y'
Figure 8. kLa and Y as functions of concentration (mol/L) for solutions of SDBS/DTMAC = 1/9. Symbol, electric conductivity of water sample (pQ/cm), gas distributor; 0,10.5,steel; 0,1.0, steel; A, 2.8, sintered glass. I
'
.
,
,
,
'
'
I
I
li61..1 I
as
'
'
"""'
'
I
a5
' ' ' a , . , '
I t4
'
'
J I
o3
0
Figure 7. Effect of water purity on the k ~ value a (Kis the electric conductivity, pQ/cm).
conc. x 10" . mole I-' Figure 9. a and M as functions of concentration for solutions of SDBS/DTMAC = 9/1.
The cause for the a value to decrease is the reaction between the cationic and the anionic surfactants with the formation of precipitation. Experiments were carried out using water samples of different quality without the addition of surfactant. Figure 7 shows the resulting kLa as function of the electric conductivity of the water sample. This figure indicates that water quality or impurity content influences the kLa value greatly. A variation of several hundred times is observed within the experimental range of this work. When the experiments are carried out using water samples of high electric conductivity, such as tap water, the impurity creates a large resistance to mass transfer. Before the addition of any surface-active additive, the kLa value is already low and the system is on the right side of the maximum of the kLa curve. Hence, from the results of the experiments using various surfactant concentrations, no maximum of the kLa curve as shown in Figures 4-6 or any improvement of the operating efficiency of the bubble column is observed. Figure 8 shows the kLa values as a function of surfactant concentration for the absorption of C02 in the bubble column. Experiments of this figure were carried out using two different gas distributors and three kinds of water samples. The surface-active additive is a binary mixture of SDBS/DTMAC = 1/9. A curve for the Y values is also plotted in this figure for the purpose of comparison. The value of Y is a measurement of the damping effect of
surface perturbation caused by the addition of the surface-activecomponent as indicated by eq 1-3 and discussed by Andrew (1960) and Yang (1983). On the basis of the curves in Figure 8, we can conclude that the kLa value is higher and the maximum of the kLa curve is closer to that of the Y curve if water of higher purity is used and/or if the gas bubbles are divided smaller. This is reasonable because in the computation of the Y values no impurity other than the added surfactant is taken into consideration and for the same volume fraction the smaller the gas bubbles the higher the coalescence frequency; the interfacial mass transfer is more closely related to the dynamic surface effect which is quantitatively measured by the Y value. Cases for surface-active additives of SDBS/ DTMAC = 1/0,0/1,1/1, and 9/1 were also studied. The results are not presented because they are similar to those of Figure 8. The value of M measures the degree of difficulty of the coalescence of gas bubbles. The gas bubbles are difficult to coalesce when the M value is large; they coalesce easily when the M value is small. Figure 9 shows the experimentally measured a value (gas-liquid interfacial area per unit volume) for the absorption of COz in the bubble column with the binary surface-active additive of SDBS/DTMAC = 9/1 and the computed M value for the same system as a function of additive concentration. The similarity between these two curves verifies that the M value is a measurement of the difficulty of bubble coa-
K , uu cm"
978
Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 4, 1986
lescence. Cases for surface-active additives of SDBS/ DTMAC = 1/0,0/1 and 1/9 were also studied. The results are not presented because they are similar to those of Figure 9. Precipitation was observed in the case of SDBS/DTMAC = 1/1.
Conclusion Proper use of surface-active additives is an effective means of improving the operating efficiency of bubble columns. A small amount of surface-active component has the effect of retarding the coalescence of gas bubbles and, thus, makes the gas-liquid interfacial area larger; it also has the effect of resisting the stretching and compression of the interface, therefore reducing the disturbance in the bulk fluids, and making the resistance to mass transfer larger and consequently the mass transfer coefficient smaller. Because of these two opposing factors, the product kLu has a maximum value at a very low surfactant concentration. The surface activity of cationic/anionic binary surfactant solution may be considerably higher than that of the solution containing a single surface-active component. This synergistic effect has strong influence to the coalescence of the gas bubbles and the gas-liquid interfacial masstransfer coefficient. It has been shown to be an effective way of improving the operating efficiency of the bubble column. If the purity of the water used in the bubble column is too low, the impurity creates a large resistance to mass transfer. Before the addition of the surface-active additive, the kLu value is already low and the system is on the right side of the maximum of the kLu curve. Hence, addition of the surface-active additive will not give any improvement of the operating efficiency of the bubble column. The value of Y is a measurement of the dynamic surface effect or the damping effect of surface perturbation caused by the addition of the surface-active component. The trend of Y as a function of additive concentration agrees satisfactorily with the experimentally measured k,u values. Nomenclature A = area, cm2 A. =*Hamaker London constant, erg a = interfacial area per unit volume, cm-' C = concentration, g-mol/cm3 Co = initial concentration, g-mol/cm3
C* = equilibrium concentration, g-mol/cm3 D = diffusivity, cm2/s di = diameter of bubbles of size i , cm d, = volume-surface mean bubble diameter, cm h = film thickness, cm hf = film thickness at break, cm ho = quasi-equilibrium film thickness, cm K = electric conductance of water sample, cm-' k = defined by eq 5, cm-' kL = liquid-phase mass-transfer coefficient, cm s-l M = defined by eq 8, (dyn ~ m )g-mol-' ~ / ~ ni = number of bubbles of size i R = gas constant, erg/K Q = defined by eq 6, dyn r = bubble radius, cm S = stretching rate of the interface, s-l T = temperature, K t = time, s Y = defined by eq 3, dyn2 cm/g-mol Zo,Z,, Z2 = liquid levels in the manometer, cm Greek Letters r = adsorption at the interface, g-mol cm-2 t = volume fraction of gas bubbles in column a = surface tension, dyn/cm Registry No. COz, 124-38-9.
Literature Cited Adamson, A. W. phvsical Chemistry of Surfaces, 4th ed.;Wiley: New York, 1982. Andrew, S.P. S. Proceedings of the International Symposiumon DisHyatbn; Rottenburg, P. A., Ed.; Instltute of Chemlcal Englneers: London, 1960; p 73. Balrd, M. H. I.; DavMson, J. F. Chem. E r g . Sci. 1962, 17, 87. Garner, F. H.; Hammerton, D. Chem. Eng. Scl. 1057, 3 , 1. Garner, F. H.; Haycock, P.J. Roc. R. Soc.London 1957, 252. 457. Glbbs, J. W. The Scient/fic Papers; Dover: New York, 1960; Vol. 1, pp 302-303. Goralcryk, D. J . Colbld Interface Sci. 1980, 78, 68. Goralczyk, D.; Wallgora, 6. J . colloid Interface Sci. 1081, 82, 1. Lucasaen-Reynders, E. H.; Lucassen, J.; Gibs, D. J . Colbld Interface Sci. 1081, 81, 150. Marruccl, G. Chem. Eng. Sci. 1060. 2 4 . 975. Raymond, D. R.; Zbminskl, S. A. AI&€ J . 1071, 17(1), 57. Rosen, M. J.; Zhu. 6. Y. J . CoHold Interface Sci. 1984, 99(2), 427. Rosen, M. J.; Zhu, 8. Y. J . ColloM Interface Sci. 1084, 99(2). 435. Sagert, N. H.; Qulnn, M. J. Can. J . Chem. Eng. 1976, 5 4 , 392. Sagert, N. H.; Qulnn. M. J. Chem. Eng. Sci. 1978, 33, 1087. Scrlven, L. E.; Sternling, C. V. Netwe (London) 1980, 287(4733), 186. Yang, Y. M. Ph.D. Thesis, National Cheng Kung Unlverslty, Tainan, Taiwan, R.O.C., 1983. Zlemlnski, S. A.; Lessard, R. 2nd. Eng. Chem. Process Des. D e v . 1960. 8(1), 69.
Receiued for reuiew September 17, 1985 Accepted April 21, 1986
