Ind. Eng. Chem. Res. 1987,26,907-911
907
Effects of Surface-Active Agents on Drop Size, Terminal Velocity, and Droplet Oscillation in Liquid-Liquid Systems A. H. P. Skelland,* Sally Woo, and George G. Ramsay School
of
Chemical Engineering, Georgia Institute
of
Technology, Atlanta, Georgia 30332
Drop size, terminal velocity, and the onset of oscillation of chlorobenzene drops falling through water were determined in systems containing anionic, cationic, or nonionic surfactants. Surfactant concentration, nozzle diameter, and nozzle velocity were varied to cover the range of most industrial applications of drop formation from circular orifices in the nonjetting region. Existing correlations for drop size and terminal velocity in uncontaminated systems are shown to be adequate in the presence of surfactants (SAA) when used with the diminished value of interfacial tension due to the SAA. The applicability of criteria for the onset of oscillation in pure systems to those containing surfactants is examined. Much effort has been spent studying drops in liquidliquid systems. Most of this work, however, has been with “pure” or “nearly pure” components, whereas actual applications often contain significant contamination that results in uncertainty about applying laboratory correlations to industrial systems. The purpose of this paper is to develop some ”rules of thumb” about the effectiveness of some of these correlations in the presence of surfactants
(SAA). Because the surface area available for mass transfer is so important, the sizes of drops formed in the presence of surfactants are compared with those predicted by Scheele and Meister’s (1968) correlation for uncontaminated systems. It has long been known that surfactants decrease terminal velocity (and mass transfer) by inhibiting internal circulation (Garner and Skelland, 1955). The present study attempts to quantify this effect by comparing the terminal velocities of contaminated drops with predictions from the equations of Klee and Treybal (1956). Schroeder and Kintner (1965) showed that drop oscillation greatly increases the rate of heat and mass transfer. Criteria for the onset of oscillation are given in Hu and Kintner (19551, Klee and Treybal (19561, Johnson and Braida (1957), Edge and Grant (1971), and Grace et al. (1976). The applicability of these criteria in the presence of surfactants is investigated. Drop sizes studied here are in the range commonly encountered in spray and perforated plate extraction columns.
Experimental Work The experimental apparatus included a constant-head 50-mL buret, fitted with various sizes of glass nozzles via a ground glass joint. The tip of the nozzle was submerged in a solution of water and surfactant, contained in a 2.25-in.-i.d. glass column. Chlorobenzene was placed in the buret and allowed to form drops at the inner edge of the nozzle tip. A constant flow rate was maintained by using a Marriotte bottle device, formed by placing a narrow glass tube down most of the length of the buret and tightly sealing the top with a rubber stopper. (See, for example, Skelland and Wellek (1964), for further experimental details.) Eleven nozzles were used with internal diameters ranging from 0.0064 to 0.5527 cm. Drop formation times ranged from 1.05 to 117 s. The anionic surfactant was dodecyl sodium sulfate, the cationic surfactant was dodecyl pyridinium chloride, and the nonionic surfactant was
phenoxypolyethoxyethanol; each was dissolved in turn in the aqueous phase. Figure 1shows the effects of concentration of surfactant on interfacial tension, as measured by Harkins and Brown’s (1919) drop-weight method. Drop size was determined by counting the drops formed from a known volume of disperse phase, and terminal velocities were measured by timing the fall of drops over a height of 65 cm, preceded and followed by 20 cm of untimed fall. The onset of droplet oscillation was determined both visually and by the location of the maxima in the plots of terminal velocity ut vs. drop diameter d,. The latter criterion is well-known [see, e.g., Clift et al. (1978),Davies (1972), Hu and Kintner (1955), Klee and Treybal(1956), Johnson and Braida (1957),Schroeder and Kintner (1965), and Thorsen et al. (1968)] and is in accordance with our visual observations on all systems.
Discussion Drop volumes were predicted by using the diminished values of interfacial tension (due to the presence of surfactant) in Scheele and Meister’s equation,
4 4
(
.“.)pdugc]”3) 4gAp
(1)
Data for the pure system showed good agreement with eq 1,except when d o was below the range used by Scheele and Meister (0.0813-0.688 cm). For doless than about 0.06 cm, eq 1 showed an increasing tendency to underpredict as d o became smaller and even gave a negative value for V , when do was 0.0064 cm. Also, the only two runs with do of 0.0137 cm, using the anionic surfactant, gave negative predicted drop volumes. In order to make an accurate evaluation of eq 1, data outside the range of d o used by Scheele and Meister were not included in the analysis. Because the interfacial tension at the edge of the nozzle during rapid drop formation is probably higher than that measured when the surfactant concentration at the interface has reached equilibrium, it may be anticipated that predictions of such drop volumes from eq 1 using equilibrium values of u would be lower than the measured values. The mean deviation, defined as C ( V c d - V e x , ) / n V e x p , and the mean absolute deviation, defined as C l V , , V e x p l / n V e xwere p , used to evaluate the results. Analysis
0888-58851871 2626-0907$01,5010 0 1987 American Chemical Society
908 Ind. Eng. Chem. Res., Vol. 26, No. 5, 1987
35
30
25 D
~- 11
20
(dyne/cm)
15
! J
i 0 01 0 01
0 0
2
4
c
6 (WI)
8
12
12
Figure 1. Diminished value of interfacial tension due to the presence of surface-active agents (SAA): anionic SAA ,).( cationic SAA (M), nonionic SAA (VI.
of Scheele and Meister's original data showed a mean deviation of +6.3% from eq 1, which indicates a tendency to overpredict, whereas our 219 runs in the presence of surfactants had a mean deviation of -5.0%, indicating a tendency to underpredict. The original authors had a mean absolute deviation of 11.0%, whereas our mean absolute deviation in the presence of surfactants was 11.5%. These results are shown in Figure 2. A statistical analysis of variance on our 219 runs was unable to detect differences in drop volume due to differences between the surfactants used. Whether small differences between the effects of various SAA's would be statistically detectable with more data is currently being studied. The criterion developed by Klee and Treybal(l956) for critical drop diameter at the beginning of droplet oscillation is d PC =
0.33pc4.14~p4.4 PC3O.3Ocr0.24
(2)
The terminal velocity ut is given by them as Ut = 3 8 . 3 p c - 0 . 4 5 ~ p 0 . 5 8 cCL*'.lldP0 70 d, < d,,
(3)
and Ut
= 17.6pc-0.55&,0.28PCo.10cro.18
d,
> d,,
(4)
Equations 2-4 were developed experimentally by Klee and Treybal (1956) by using "some technical-grade materials without special purification". They may thus embody a built-in accommodation for some degree of surface-active contamination commonly present in industrial systems. Indeed, Skelland and Vasti (1985), using presumably "purer" systems, found their terminal velocities to be all higher than predicted by eq 3 and 4 but (mostly) lower than calculated from the correlation for very pure systems given by Grace et al. (1976). Since "generalized" accommodation for the effects of unknown industrial contaminants is the object here, this explains the selection of Klee and Treybal's equations for comparison with the present data. The diminished values of interfacial tension due to the presence of surfactants were used in comparing eq 2-4 with our measurements in Figure 3. For eq 3 the mean absolute deviation of ut in the presence of surfactants was 5.43%, whereas the mean absolute deviation for Klee and Treybal's data was 4.15%. Our 34 runs for which this equation is applicable were not suffi-
I
01 V a , (c")
1
Figure 2. Comparison between drop volumes predicted by the Scheele and Meister eq 1and experimental data: anionic SAA (01, cationic SAA ( O ) , nonionic SAA (A).
11
l2
I
i
./
/ . l
6
7
'
'
i '
l
8
9 u,
'
I
'
10
t
11
"
'
12
13
(cm/s)
Figure 3. Comparison between terminal velocities predicted by Klee and Treybal's correlations (eq 2-4) and experimental data: anionic SAA ( O ) , cationic SAA (a),nonionic SAA (V).
cient to draw any statistical conclusions about differences between the effects of the different surfactants, but they appear to be slight. It is interesting to note that eq 3 does not contain any term that completely accommodates the effects of SAA since, for given values of pc, Ap, and bc,d, depends on u, and do as well as on u, as shown by eq 1. Thus it is the interplay between d,, d, and cr that causes eq 3 to function as well as it does here. To illustrate this point, consider a d, of 0.6 cm in Figure 4a; routine preliminary application of eq 2-which contains cr-confirms what the figure shows, namely, that only the top three curves would correspond to use of eq 3 for estimation of ut. The shift of the peak in the curve to smaller d, as SAA concentration increases means that preliminary application of eq 1 would lead to use of eq 4 for this d, in the bottom 7 curves (eq 4 again contains a). For d, of 0.6 cm, the top three curves of Figure 4a correspond to a spread in ut of 11.25-12.56 cm/s or f5.5% about the mean value of 11.91 cm/s. This, of course, is well within the "average deviation of less than 10 percent" claimed later for eq 3 by Treybal (1963). It is these considerations that explain the horiin Figure 3 and zontal distribution of ut,erpfor a given which lead to the (acceptable) mean absolute deviations in the presence of SAA reported above. Since, in the
Ind. Eng. Chem. Res., Vol. 26, No. 5, 1987 909 10.7511,~ 1050
-
10.25
-
10.00
-
9.75
-
9.50
I
.
I
.
,
.
( 4 s ) 9 25
-
9.00-
1
8.751
h
8 50 03
04
0.5
06 07 d. (cm)
08
09
Figure 4. Terminal velocity, drop size, and the onset of droplet oscillation in the presence of (a, left) anionic SAA, (b, middle) cationic SAA, and (c, right) nonionic SAA.
industrial situation, the surface-active impurities would be unknown, there seems to be little point in recorrelating ut so as to just fit the specific SAA's used here. This is because generalized "rules of thumb" are perhaps the best that can be hoped for at present. For eq 4, the mean absolute deviation in the presence of surfactants was 4.45% for our 191 runs, whereas the mean absolute deivation for Klee and Treybal's data was 2.82%. Analysis of variance indicated that the type of surfactant had no effect on the terminal velocity. Parts a-c of Figure 4 show that, to the right of the peak, ut falls between 3% and 8% with increasing d,. This observation is common, the curves normally becoming roughly horizontal after the initial drop in ut (Hu and Kintner, 1955; Klee and Treybal, 1956; Johnson and Braida, 1957). The effect is somewhat magnified here by the enlarged scales of the ordinates. However, the peak velocities and the corresponding lowest values to the right of the peak differ at most by about 8% in parts a-c of Figure 4, which is well within the 15% accuracy subsequently claimed for eq 4 by Treybal (1963). The mean deviations for eq 3 and 4 were -4.13% and -3.05%, respectively. This shows a slight additional reduction in terminal velocity beyond the accommodation provided by use of the diminiihed interfacial tension values due to SAA in eq 2-4. The results are shown in Figure 3. Next, the onset of droplet oscillations in the presence of surfactants will be compared with several proposed criteria for pure systems, using the diminished values of n due to the SAA throughout. Hu and Kintner (1955) proposed that oscillations begin when Nwe > 3.58 (5) Figure 5 shows "least-squares" lines through our data points; the transition Weber number at which oscillation starts increases as the concentration of surfactant increases and then passes through a maximum. For eq 5, the mean deviation was -23.4% and the mean absolute deviation was 25.9%. Klee and Treybal's criterion for the onset of oscillation is eq 2, and experimental results are compared with this in Figure 6. For the pure system, eq 2 underpredicts the critical drop diameter. As the concentration of surfactant increases, the discrepancy between predicted and experimental values stays about the same for the nonionic but decreases for the anionic and cationic surfactants. For eq 2, the mean deviation was -36.8% and the mean absolute deviation was 37.3%.
" I
1
0
2
4
6
c (do
8
1
0
1
2
Figure 5. Weber number at the onset of droplet oscillation, computed from the maxima in the curves in Figure 4: anionic SAA (e), cationic SAA (B), nonionic SAA (v).
0.2
0
2
6
4
c
8
(do
1 0 1 2
Figure 6. Drop diameter at the onset of oscillation: anionic SAA (O),cationic SAA ( O ) , nonionic SAA (v). Corresponding solid symbols denote values predicted by Klee and Treybal's eq 2. The horizontal line at d, = 0.52 cm represents Edge and Grant's predicted value.
Johnson and Braida (1957) proposed that oscillation starts when The results compared with this criterion are shown in Figure 7; at higher concentrations of anionic and cationic surfactant, eq 6 overpredicts the critical drop diameter. Underprediction prevails at all concentrations for the nonionic surfactant. For eq 6, the mean deviation was
910 Ind. Eng. Chem. Res., Vol. 26, No. 5, 1987
24 26
loo
,
,
.,’:.,,:
,
,
,
,
16
0
2
4
c
6 (g/l)
8
10
,
1 12
Figure 7. Johnson and Braida’s criterion for the onset of droplet oscillation (NRa/Npo.ls= 20) compared with experimental data: pure system (o),anionic SAA (e),cationic SAA (W, nonionic SAA (W.
-10.9% and the mean absolute deviation was 16.0%. Allowance should be made for the enlarged scale of the ordinate when evaluating Figure 7, which exhibits the least error here in correlating the onset of droplet oscillation. Edge and Grant (1971) proposed that d,, = 0.162(~d/Ap)~’~ (7) This is the only criterion for critical drop diameter that does not contain interfacial tension. Therefore, for all concentrations of surfactants, this equation predicted a critical drop diameter of 0.518 cm. Although the range of error is fairly large, eq 7 seems to lie near the middle of that range, as shown in Figure 6 and by its mean deviation of -0.6% and mean absolute deviation of 23.2%. Grace et al. (1976) give a criterion for the onset of oscillation as 4 H > 59.3; H = -NflM4.14’(p c / P w )-0.14 (8) 3 The results of using eq 8 are illustrated in Figure 8. This correlation is actually similar to Klee and Treybal’s eq 2, as shown by its dimensional form = 0.36~,4‘.15~~-0.43~ 0.30,0.28 C (Pc/Pw)0.07 (9) Pc but gives better results than the equation of Klee and Treybal, as indicated by its mean deviation of -16.3% and mean absolute deviation of 20.2%. In the past, workers have been intrigued by maxima or minima in various two-phase phenomena at intermediate SAA concentrations. Examples include the following: (1) minimum mass-transfer rates from falling drops (Garner and Hale, 1953; Garner and Skelland, 1956; Farmer, 1950; Skelland and Caenepeel, 1972), (2) minimum mass-transfer rates across plane interfaces between two stirred liquids (Gordon and Shemood (1953) as examined by Garner and Hale (1953), Davies (1963), and Davies and Rideal(1961), (3) minimum mass-transfer rates during droplet formation and coalescence (Skelland and Caenepeel, 1972), and (4) maximum damping of waves on a liquid surface (Davies and Vose, 1965; Emmert and Pigford, 1954; Tailby and Portalski, 1961; Kafesjian et al., 1961). In this vein there are indications of maxima in the transition Weber number a t intermediate SAA concentrations in Figure 5 and of minimum ut at some intermediate concentration at the onset of oscillation in parts a and b of Figure 4. Some may see maxima in the three respective sets of data points in Figures 7 and 8. Further study is needed on this question. It should, of course, be understood that the purpose of the present work is not to recorrelate drop volume, terminal velocity, and oscillation criteria in terms peculiar to the particular species of surface-active contaminants
H
I. 1
-.ii 6o
171 40
,
0
, 2
.,
;
.,
4
c
,
6 (9/1)
, 8
,
,
,1‘
1 0 1 2
Figure 8. Grace et a1.k criterion for the onset of droplet oscillation (H = 59.3) compared with experimental data: pure system (O), anionic SAA (e),cationic SAA (m), nonionic SAA (v).
used here. Instead, the surfactants are intended to simulate some of the impurities encountered industrially, which are usually unknown with regard to number of species, structure, and concentration. The object, then, is to ascertain whether characterization of their effects by measurement of a single property, (r, is adequate for purposes of predicting the quantities under consideration via existing correlations, without further modification.
Conclusions (1) New data are presented on the effects of anionic, cationic, and nonionic surface-active agents on drop size, terminal velocity, and the onset of oscillation in liquidliquid systems. (2) Using the diminished value of interfacial tension due to the presence of surfactants in Scheele and Meister’s eq 1 for drop size gives results with an accuracy comparable to that for pure systems. Data from 219 runs were insufficient to detect differences in drop volume due to differences between the surfactants used. (3) Klee and Treybal’s eq 2-4 for determining droplet terminal velocity seem to be roughly adequate when the diminished value of interfacial tension due to the presence of surfactants is used. The type of surfactant seems to have no effect on terminal velocity. (4)The effect of surfactant type on the onset of droplet oscillation is also small, if any. Generally, as the concentration of surfactant increased, the observed d, decreased faster than the predicted value. Johnson and Braida’s criterion for the onset of oscillation (using diminished a) gave the least error but requires ut,which may have to be estimated in practice. Grace et a1.k criterion, using the diminished value of u due to the presence of surfactant, otherwise seems to be the best, with a mean absolute deviation of 20.2%. This is probably the result of the large amount of data upon which it is based. Acknowledgment This work was partially supported by National Science Foundation Grants CPE 80-19617 and CPE82-03872. Nomenclature C = concentration of surfactant, g/L CD = drag coefficient = 4Apdg/3pCu: do,d,, dw = diameters of nozzle or orifice, droplet, and droplet at the onset of oscillation, cm F = Harkins and Brown’s correction factor
Ind. Eng. Chem. Res. 1987,26, 911-921 g = gravitational acceleration, cm/sz g, = conversion factor, g.cm/(dyn.s2)
n = number of runs NEo= Eotvos number gd,2Ap/u = (3/4)Nw& N M = Morton number, gp:Ap/p:u3 = 3C&w,3/4Nk4 N = O3p:/gp:Ap = (NM)-l = Reynolds number, dppcut/p, Nwe = Weber number, dPu,2pJu SAA = surface-active agent (i.e., surfactant) uo,ut = velocity of fluid through orifice or nozzle, terminal
dk
velocity, cm/s V,, Vex,, V,, = volume of droplet, experimental value, value calculated from eq 1using diminished u due to SAA, cm3 Greek Symbols ,I p, = viscosity of continuous phase and of water, P P d , p,, Ap = density of dispersed phase, continuous phase, and the difference between the two, g/cm3 u = interfacial tension, dyn/cm
Literature Cited Clift, R.; Grace, J. R.; Weber, M. E. Bubbles, Drops, and Particles, Academic: New York, 1978; pp 172-188. Davies, J. T. In Advances in Chemical Engineering; Drew, T. B., Hoopes, J. W., Jr., Vermeulen, T., Eds.; Academic: New York, 1963;Vol. 4,p 33. Davies, J. T. Turbulence Phenomena; Academic: New York, 1972; p 313. Davies, J. T.; Rideal, E. K. Znterfacial Phenomena, 1st ed.; Academic: New York, 1961;pp 318, 335-337.
911
Davies, J. T.; Vose, R. W. Roc. R. SOC.London, Ser. A 1965,A286, 218. Edge, R. M.; Grant, C. D. Chem. Eng. Sci. 1971,25,1001. Emmert, R. E.; Pigford, R. L. Chem. Eng. h o g . 1954,50,87. Farmer, W.S. Unclassified Report ORNL 635, 1950; Oak Ridge National Laboratory, Oak Ridge, TN. Garner, F. H.; Hale, A. R. Chem. Eng. Sci. 1953,2,157. Garner, F. H.; Skelland, A. H. P. Chem. Eng. Sci. 1955, 4, 149. Garner, F. H.;Skelland, A. H. P. Ind. Eng. Chem. 1956,48, 51. Gordon, K. F.; Sherwood, T. K. Paper presented at American Institute of Chemical Engineers Meeting in Toronto, April 1953 (Cited as their ref 10 in Garner and Hale, 1953). Grace, J. R.; Wairegi, T.; Nguyen, T. H. Trans. Znst. Chem. Eng. 1976,54, 167. Harkins, W. D.; Brown, F. E. J. Am. Chem. SOC.1919,41,499. Hu, S.; Kintner, R. C. AIChE J. 1955,I , 42. Johnson, A. I.; Braida, L. Can. J. Chem. Eng. 1957,35,165. Kafesjian, R.; Plank, H.; Gerard, E. R. AZChE J . 1961,7,463. Klee, A. J.; Treybal, R. E. AZChE J. 1956,2,444. Scheele, G. F.; Meister, B. J. AZChE J . 1968,14,9. Schroeder, R. R.;Kintner, R. C. AZChE J. 1965,11,5. Skelland, A. H. P.; Caenepeel, C. L. AZChE J. 1972,18,1154. Skelland, A. H. P.; Vasti, N. C. Can. J. Chem. Eng. 1985,63,390. Skelland, A. H. P.; Wellek, R. M. AZChE J . 1964,10,491. Tailby, S.R.; Portalski, S. Trans. Znst. Chem. Eng. 1961,39,328. Thorsen, G.; Stordalen, R. M.; Terjesen, S. G. Chem. Eng. Sci. 1968, 23,413. Treybal, R. E. Liquid Extraction, 2nd ed.; McGraw-Hik New York, 1963;pp 184-185.
Receiued for reuiew April 16,1984 Accepted October 8,1986
Evolution of Pore Surface Area during Noncatalytic Gas-Solid Reactions. 1. Model Development Girish Ballal and Kyriacos Zygourakis* Department of Chemical Engineering, Rice University, Houston, Texas 77251
Novel random pore models are developed to predict the evolution of internal pore surface area during noncatalytic gas-solid reactions. These models can treat porous solids having micro- and macropores of different shapes and exhibiting widely ranging pore-size distributions. Pores are visualized as overlapping geometrical entities randomly interspersed in the solid matrix. Probabilistic arguments are used to correlate the changes in pore volumes and surface areas to the conversion of the solid reactant in the kinetic control regime. Surface area losses due to coalescence of adjacent pores are rigorously accounted for and the model parameters are obtained from measurable physical properties of the unreacted solid. Numerical computations show a strong effect of the size distribution of the micro- and macropores on the predicted surface area-vs.-conversion curves. The problem of noncatalytic reactions between fluids and porous solids is considered in this study. These reactions take place on the walls of the internal pores of the solids, and in the absence of intraparticle diffusional limitations and heterogeneities in the chemical structure of the solid, their rates may be assumed to be proportional to the internal surface area. Since the solid reactant is consumed, however, the surface area and hence the gasification rate will vary continuously with the extent of reaction. The gasification reactions of char particles formed by devolatilizing parent coals are prime examples of such systems. The char particles exhibit bimodal pore-size distributions with many large macropores and a micropore network that usually results in high values for the internal surface area. The pores are randomly oriented and may be of many different shapes. In the case of some highranked coals (anthracites), the pores resemble slits or cracks rather than cylinders. Thus, the modeling of the
* Author to whom
all correspondence should be addressed.
0888-5885/87/2626-0911$01.50/0
evolution of the internal surface area (or equivalently of the gasification rate) with conversion is a complex task for such systems. One of the earliest attempts to model such reactions was that by Petersen (1957). He solved the reaction-diffusion problem in a single pore and in an assembly of cylindrical pores of uniform size. However, he neglected the intersection of new reaction surfaces, which is the dominant factor after the initial stages of gasification. Szekely and Evans (1970)used Petersen’s formulations to obtain the reaction rate-vs.-conversion relationship. Recently, Ramachandran and Smith (1977)also considered a structural model, assuming cylindrical pores of uniform radius and neglecting intersection of new reaction surfaces during gasification. Another approach to this problem is by using population balance techniques. Hashimoto and Silveston (1973) adopted this approach to account for pore-size distribution and coalescence of pores as they grow due to reaction: However, their model contains numerous parameters which need to be fitted in order to obtain the reaction 0 1987 American Chemical Society
