FOAM SEPARATION OF SOLUTIONS CONTAINING TWO IONIC SURFACE-ACTIVE SOLUTES ELIEZER RUBIN AND JACOB JORNE Department of Chemical Engineering, Technion-Israel Institute of Technology, Haifa, Israel
A theoretical and experimental investigation shows that foam techniques may be applied to separate two surface-active solutes. The relative distribution of the two solutes, preferentially adsorbed A and B, between bulk solution and the surface at equilibrium is defined by the relative distribution coefficient, C AB = r A C B / r B C A . ~ ) / ( E B - 1). The experimental For equilibrium foam separation this definition reduces to C Y A B = (EA results indicate that for the system studied C AB is not necessarily constant, that its value reduces considerably at and above the critical micelle concentration (CMC), and that for maximum separation between solutes it is best to operate just below the CMC, where its value is maximal. Theoretical derivations for estimation of CYAB based on the Gibbs equation, the Langmuir isotherm, and long-chain ions isotherm are presented and their agreement with experimental results is discussed.
-
URING the last decade there has been a rise of interest in the separation or removal of components from solutions using the foam separation or foam fractionation technique. This technique is based on the tendency of surface-active solutes to concentrate at gas-liquid interfaces. The generation and collection of controlled foams serve as an effective means for obtaining high solute concentrated gas-liquid interfaces. A variety of foam separation equipment has been used and studied, including batch, continuous single-stage, and multistage columns (Brunner and Lemlich, 1963; Fanlo and Lemlich, 1965; Haas and Johnson, 1965; Rubin and Gaden, 1962). The technique has been applied to concentration and removal of various surface-active solutes (Brunner and Stephan, 1965; Grieves et al., 1964; Kishimoto, 1963; Rubin and Everett, 1963), metal ions (Rubin et al., 1962; Schnepf et al., 1959; Schoen et al., 1962), nonsurface-active anions (Grieves et al., 1965; Ponchka and Karger, 1965), and colloids (Grieves and Bhattacharyya, 1965). The behavior of foams has also been studied theoretically and experimentally (Haas and Johnson, 1967; Leonard and Lemlich, 1965; Rubin et al., 1967). These studies have been limited almost exclusively to solutions containing only one surface-active solute. Actual solutions, however, may contain in many cases several surface-active solutes. I n such cases, selective adsorption a t the gas-liquid interface may be expected. Several studies on selective adsorption, using the radiotracer technique, have been reported (Aniansson, 1951; Nilsson, 1957; Sobotka, 1954; Wilson et al., 1957). These studies were concerned, however, with static plane gas-liquid interfaces and only the concentrations of the selectively adsorbed solutes were measured. The present work was undertaken realizing that the potential applicability of foam separation could be extended considerably if it could be applied to separate two or more surface-active solutes. The main objectives of the present work were to determine the effect of concentrations on the relative separation of two surface-active solutes and to examine the possibility of predicting the relative separation from experimental data obtained with solutions containing the single solutes. Probably the only studies on separation between two 474
l&EC
FUNDAMENTALS
surface-active solutes using a foam separation apparatus were reported by Shinoda et al. (Shinoda and Kinoshita, 1963; Shinoda and Mashio, 1960; Shinoda and Nakanishi, 1963). They conducted batch experiments with several pairs of surface-active solutes a t a constant total solute concentration below the critical micelle concentration (CMC), and a relatively narrow range of solute concentration ratio. A radiotracer technique was used for the determination of concentrations in the bulk liquid and the collapsed foam (foaniate). Defining selective adsorptivity by a=
Xads
(1 - X b u l k )
(1 - X a d s )
Xbulk
(1)
they concluded, from their experimental results, that a is constant for a given surfactants pair, but presented no theoretical analysis. Moreover, since their experiments were conducted in batch, their reported a’s do not necessarily represent equilibrium values and may depend on experimental conditions. Theory
In a solution containing several surface-active solutes, all the solutes tend to adsorb at the gas-liquid interface. Selective adsorption of one solute relative to the other depends on the molecular structure, properties of the hydrophilic and hydrophobic parts of the molecules, valence, ionic dissociation, and hydrolysis a t the surface. Borrowing from other separation processes a relative distribution coefficient for two surface-active solutes may be defined as the ratio of their individual distribution coefficients:
The distribution coefficient, Fi/C;, is the ratio of the concentration of solute i a t the gas-liquid interface and in the bulk solution. It is analogous to the distribution coefficient in extraction or the volatility in distillation. CYAB, as defined in Equation 2, is essentially identical to a of Equation 1, and is analogous to the relative volatility in distillation. For the case of foam separation with stable foams, under equilibrium conditions, CYAB depends only on the solutes concentration in the bulk liquid, and is independent of foam properties.
Several theoretical models may be utilized for the estimation of CYAB. I n the theoretical derivations presented below expressions for CYAB are obtained using the Gibbs equation, the Langmuir isotherm, and the long-chain ions isotherm. I n addition, the ideal foam model is extended to cover the case of two surface-active solutes, resulting in a simple expression for CYAB which enables its prediction from foam separation experiments. CYABAccording to Gibbs Equation. An expression for the surface excess of each surface-active solute in a multicomponent solution may be obtained from the Gibbs equation. I n an aqueous solution of two ionic surface active solutes. NaA and NaB,
+ AN a B e Na+ + B-
NaA e Na+
Assuming complete dissociation of the two solutes, the Gibbs equation for all the ions present in solution is:
+ rA-(')dpA-' + rB-(')dpB-"
-dy = rNa+(')dpsa+'
(4 )
Because of electrical neutrality a t the surface phase, u,
rhTa+(l) = rA-C + rE-K
Because of equilibrium between the bulk liquid phase, CY, and the surface phase, u : @Na+' PNa+'
+ +
/LA-u = /.LNa+a PB-'
(9b ) Equations 9a and 9b indicate that the determination of the surface excess of one solute requires the determination of the surface excess of the other solute, even if the concentration of the latter is constant. However, in the presence of excess Na+ (by adding an electrolyte such as NaC1) CN~+>>CACB- and the surface excess of each solute can be determined from the slope of its surface tension-concentration curve when the concentration of the other solute is constant and a t a constant excess of electrolyte:
+
(3)
In writing Equation 3 the Guggenheim approach is used (RIoilliet et al., 1961)-i.e., the liquid phase is divided into two phases: a bulk liquid phase, CY, and a surface phase, u. I?,(') denotes surface excess of solute i when the surface excess of the solvent is zero (this is the original Gibbs convention for surface excess). It may be considered as a shorthand notation for [I',(G) - I'8(G)N,/N8] which is obtained in the Guggenheim approach. p l ic: the chemical potential of component i defined by p , = p U o +RTlna,
can be expressed in the following form:
For solutions containing only one nonionic or ionic surfaceactive solute with excess electrolyte Equations 10a and 10b reduce to the well-known form of the Gibbs equation:
Equations 9 indicate that for solutions containing only one ionic surface-active solute without excess electrolyte the denominator on the right of Equation 11 should include a '(factor 2." The relative distribution coefficient can be calculated from Equations 2, 9a, and 9b:
(12) or in the presence of excess Na+ from Equations 2, loa, and lob:
+
(13)
= pXa+
Equation 5 can therefore be written:
(6)
For dilute solutions the activity coefficient may be assumed constant; then dpi = RTd In Ci (7 1
Equations 12 and 13 indicate that CYAB is not necessarily constant. LYAB According to Langmuir Adsorption Isotherm. The Langmuir adsorption isotherm was found applicable for nonionic surface-active solutes, or for ionic surface-active solutes at very low concentrations when the potential of the electric double layer is very small. For solutions containing only one surface-active solute, the Langmuir isotherm is (Davies and Rideal, 1961) :
C
r = -1
k' (1
By substituting Equation 7 in Equation 6
+ A,C/L')
(14)
or in a linearized form:
-dy
RT
- ra-"'d In (CNa"
CA-)
+
rB-(')&
hl (CNa"
CE-)
Two special cases pertaining to Equation 8 are worth mentioning. Noting that C N ~= + CA- CB-, the surface excess of one solute a t a constant concentration of the other solute
+
1
(8)
-r =
k'
AO+z
Constants A, and k' can therefore be determined from the straight line of a correlation of l/r os. 1/C. r for such a correlation can be calculated either from surface tensionVOC.
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concentration curves using Equation 11 or from foam separation experiments using Equation 30. For a solution containing two surface-active solutes, assuming no interactions between the solutes, the Langmuir isotherm applicable to each solute is (Rubin and Gaden, 1962) : CA
1
FA
= kA'
rB= -,1
(1 -k
(1
+
AO,cA/kA'
+
&,CB/kB')
CE AO,CE/~B')
A,,CA/kA'+
(16a)
(16b)
The relative distribution coefficient is obtained from Equations 16a, 16b, and 2 :
According to Equation 17, the relative distribution coefficient is constant and equal t o the inverse ratio of the desorption coefficients of the two solutes. It is possible to obtain the constants of the Langmuir equations directly from surface tension-concentration data by combining the Gibbs and Langmuir isotherms (Butler and Ockrent, 1930). For a solution containing one surfaceactive solute, combining Equations 11 and 14, yo-v=
Ay= R T
k' (1
+
C dln C A,C/k')
Equation 18 can be used to calculate k ~ and ' kA', and hence according to Equation 17, from surface tension-concentration curves of solutions containing the single solutes. CYAB According to Adsorption Isotherm for Long-chain Ions. The adsorption isotherm for long-chain ions-i.e., alkyl aryl sulfonates or alkyl sulfates-considers the effects of the potential of the electrical double layer and the cohesion forces at the gas liquid interface, not accounted for in the Langmuir adsorption isotherm. The potential of the electrical double layer reduces the adsorption particularly at higher surface concentrations, whereas the cohesion forces between adsorbed molecules affect the adsorption energy. The adsorption isotherm for solutions containing a single long-chain solute has been derived and discussed (Davies and Rideal, 1961). The surface excess is given by
WE
and
In Equation 19, B1 and B2 are constants which depend on the hydrodynamics of the diffusion process at the surface. However, their ratio, B1/B2, is an independent constant (Davies and Rideal, 1961). In Equations 19 and 20, W is expressed per molecule and A is expressed in square angstroms per molecule at the surface. Equation 19 reduces t o the Langmuir isotherm a t very low concentrations-Le., when A >> A,. For the present work, Equation 19 can be rewritten in a more useful form:
Substituting W from Equation 20 in Equation 22, and taking the logarithm from both sides:
1200 X 7750m 2.3kT
rl,z
(23 )
The left-hand side of Equation 23 can be calculated using experimental F d u e s of I'-i.e., from foaming experimentsand $, values calculated from Equation 21. The value of m can be calculated from the slope of the straight line obtained by correlating the left-hand side of Equation 23 us. P I 2 , and B2/B1 can be calculated from the intercept of the line. If the surface-active molecule is not linear (Davies, 1952, 1956), m is the effective number of -CH2- groups, and does not necessarily yield information about the molecular structure. It is possible to extend the adsorption isotherm for longchain ions to solutions of two solutes. At equilibrium, and assuming no interaction between the solutes, the following equations may be written:
for solute A , and
where for solute B. The left-hand side of these equations represents the rate of adsorption and the right-hand side the rate of desorption. Solving Equations 24a and 24b for and I'D:
476
ILEC
FUNDAMENTALS
The relative distribution coefficient is obtained from Equatioris 25a, 2Sb, and 2:
Writing Equation 20 for each of the solutes and substituting in Equation 26 yields :
where -1 15 the average area per niolecule a t the surface. A can be replaced by F, the total wrface excess of the two solutes. using the relation
Equation 27 therefore becomes a . 4 ~=
521 K exp ( n t ~ mn) (RT
[
+ 1200kXT 7750 rl/B
The values of n i and ~ ~ 7 ~ can 2 ~ be obtained from experiments with solutions containing the single solutes, A or B , through Equation 23 as described above. Equation 29 indicates that CYAB is not necessarily constant. Ideal Foam Model for Two-Solute Systems. The relation between surface escess, r, and the variables in foam separation of a single solute under equilibrium conditions is given by Rubin and Gaden (1962) r(1) -
Cz
jd 6
( E - 1)
(30 )
It can be easily shown that, for a two-solute system, Equations similar to 30 can be written for each solute:
Froin Equations 31a, 31b, and 2: ffAB =
EA - 1 EB - 1
Equation 32 can be used to calculate ffAB from equilibrium foam separation experiments. Equations 12, 13, 17, and 29 may not be applicable above the CMC, since the effects of micelles formation were not considered in their derivation. The idea of expressing selective adsorption by the relative distribution coefficient can be extended to solutions containing more than two solutes, as i n other unit operations. Some of the derivations may be easily simplified for the case of nonionic surface-active solutes-for example, in Equation 23 the term containing ll.o will equal zero for nonionic burface-active solutes.
Concentrations of samples containing only XaDBS were determined directly by ultraviolet absorbance measurements using a Beckman DB spectrophotometer connected to a Sargent Model SRL recorder. ,Ibsorbance readings were taken at. a wavelength of 223 or 260 microns. Concentratious of samples containing only KaLS were determined by the methylene blue method (American Public Health Association, 1955). Samples containing both NaDBS and KaLS were analyzed by the methylene blue method, which is general for sulfates and sulfonates. This gave the concentration of both NaDBS and NaLS. The same samples were also analyzed by direct absorbance measurements, as described above, yielding the concentration of XaDBS. The concent,ration difference obtained by the two methods gives the concentrat'ion of NaLS in the mixt'ure.
Purification of Solutions. Surface tension measurements indicated minima in the surface terisioii-coiicentratioii curves, indicative of highly surface-active impurities (Rrady, 1949; Niles and Shedlovsky, 1944; Moilliet et al., 1961). These impurities may be, among others, hydrolysis products forming sloivly in aqueous solutions of surfactants. XaDBS and S a L S solutions were therefore purified for each day's experiments by foaming in batch. Relatively concentrated (just below the CMC) solutions of each surfactant were foamed and the collapsed foam was removed until no further shifts in t,he surface tension-concentration curves were observed. After a few purifications it was found that, with the available foaming apparatus at t8heexperiment,al air flow rate, removal of 20 to 257, of the solution in the form of foam removed all the impurities. The purified solutions were diluted or mixed as necessary. Foam Separation. single-stage continuous circulatory type foam system identical (except for dimensions) t o the one described by Rubin et al. (1967) was used. This system enables the determination of equilibrium bulk liquidfoarnate concentrations. It consisted of a 3.62-cm. i.d. glass column on top of a 4-liter glass liquid chamber, a mechanical foam breaker, and a recycle line (Rubin et al., 1967, Figure 1 ). Filtered, COz-free, and humidified air was introduced through a spinnerette-type (125 holes of 0.008-ern. diameter each) sparger, and the foam produced passed from the foam column int'o the mechanical foam breaker, where it was collapsed. The collapsed foam liquid was recycled into the bottom of the liquid chamber. For purification of surfactant solutions, the system was operated as a batch unit by discoiiiiecting the recycle line and directing the foamate into a container. The experiment,al procedure involved placing approxiniat'ely 4 liters of a solution of one or of both surface-active solutes in the liquid chamber. Air was continuously bubbled at a flow rate measured with a rotameter. After steady-state conditions were obtained, samples for analysis were taken from t'he liquid chamber and the collapsed foam. All the experiments were conducted with completely stable foams. The lowest concentrations used in the foam separation experiments were dictated by foam stability considerations. Foam ratio (cubic centimet,ers of liquid/cubic centimeters of foam) was calculated from air and collapsed foam flow rates. Pictures for measurement of bubble diameter were taken in each experiment with a single-lens refles camera equipped with an extension t'ube. Actual bubble diameters were measured from enlarged prints. Average bubble diam eters were calculated according to t,he equation ~
Experimental
Materials and Analysis. Two surface-active solutes were used in all experiments: a 98.57, pure sodium lauryl sulfate (SaLS) and 97.5y0 pure sodium dodecylbenzene sulfonate (XaDBS), supplied under the trade names Quolac OK-WD and Quolac -4TE-DS-IO, respectively, by Lnibasic, Inc.
(331 The average bubble size range was 1.1 to 2.2 mm. Surface Tension Measurements. Surface tensions were measured with a semiautomatic ring type Tensiomat (Fisher Tensiomat, Model 21) accurate to within f 0 . 1 dyne per cm. VOL.
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1 9 6 9
477
80-
I
I
~
l
l
I
60-
e! a
U
'f
50-
40
-
)
I
1
1
1
1
1
I
,
I 1 1 1 1 1 1
I
I
I 1 1 1 1 1 1
Results and Discussion
The experimental work involved surface tension measurements and foam separation experiments, both conducted with solutions containing the single solutes and solutions containing both solutes. Solutions
Containing
One
~
1
~ I
I 1 1 1 1 1 1 1 ~
I I I I I I I )
1
1
-
-
-
30
6
j :
70
2
1
Surface-Active
Solute.
The surface tension data for solutions containing either NaLS or NaDBS (Figures 1 and 2) indicate that purification of the original solution removes highly surface active impurities. The fact that the slopes of the curves, before and after purification, hardly change, indicates that the areas per molecule, A , of the impurities and main component are almost equal. The minimum surface areas per molecule, A,, calculated from Figures 1 and 2 using Equations 11 and 28, are 51.2 and 55.0 sq. A. for NaLS and 61.5 and 57.8 sq. A. for NaDBS before and after purification, respectively. On the strength of previous observations (Davies, 1952; Moilliet et al., 1961) the Gibbs equation was used without "factor 2," although according to theory this factor should have been used. Figures 3 and 4 show surface excess-concentration curves calculated from foam separation data and Equation 30. The
I
I
I l l l l l l
I
I 1 1 1 1 1 1 1
I ,
scatter of experimental points in Figures 3 and 4 (as well as in Figures 10 and 11) is due primarily ta two sources of experimental error. One is the average bubble diameter, which could be determined only to within f15'%. Another source, inherent in Equations 30, 31a, and 31b, is the factor E - 1. For values of E close to 1, relatively small errors in sample analysis may result in relatively large errors in the calculated values of I?). The minimum surface areas per molecule, A,, calculated from Figures 3 and 4 and Equation 28 are 34.6 sq. A. for NaLS and 45.0 sq. A. for NaDBS. Surface tension and foam separation are two fundamentally different methods for estimating surface excess. Surface tension-concentration curves, which may be affected by factors such as molecular orientation a t the surface, are only an indirect method for estimating the surface excess, whereas foam separation experiments yield surface excess directly. The agreement between the values of A , calculated from surface tension-concentration curves and foam separation experiments may therefore be considered reasonable. There is, however, a large discrepancy between the values of surface excess for A > A , (or equivalently r < r,) ob-
70 5.0
60
I
I "
h
I
I
9
10
4.0
? Y
3.0
50
U h
* 40
Y
2D 1.0
30
;o*
IOS
1L?
0
1d
1
2
3
Vj2
5
4
c,
7
6
8
(rnolllltIxl03
C (molllit1
Figure 2.
Surface tension curves of NaDBS solution 0 Original solutions
A
Purified solution Temperature 25" C.
A78
I&EC
FUNDAMENTALS
Figure 3. Adsorption isotherm for NaLS solutions with and without NaCl 0 Without NaCl With 0.01 M NaCl
A
Temperature 20-28'
C.
V
3 2.0
E
1.0
0
0
2
4
6
8
10
14
12
16
18
20
C, (rnot/lit)xd Figure 4. Adsorption isotherm for NaDBS solutions with arid without NaCl 0
0 A
Without N a C l With 0.01 M N a C l Temperature 23-27" C.
tained by the two methods. Such a discrepancy was also observed by other investigators (Banfield et al., 1966; Davies, 1952). Since foam separation is the direct method for estimating surface excess, it may be assumed that the values obtained from foam separation experiments are the more reliable. On the other hand, the break in surface tensionconcentration curves is probably the best indication for the CMC. Thus, the CMC according to Figures 1 and 2 is 2.2 X 10-3JI for NaLS and NaDBS and the corresponding surface excesses, read from Figures 3 and 4, are 2.7 X lo-'' and 3.0 X mole per sq. cm., respectively. The data obtained from foam separation experiments (Figures 3 and 4) indicate that identical values of ro,or A,, are obtained with and without added NaCl. On the other hand, excess XaC1 increases d r / d C below F0. Similar observations were reported by Newson (1966), based on measurements of surface excess by the radiotracer technique, and by Matsuura et aZ. (1962) based on surface tension determinations. This effect of NaCl on d r / d C can be explained easily by the long-chain ions model. The presence of excess NaCl reduces the surface potential of the solution, 4, in Equation 21, and therefore increases the surface excess (Equation 19). It is possible now to calculate the constants later used for calculating ( Y A B . LANGMUIR ISOTHERM. The constants in the Langmuir equation can be obtained from surface tension-concentration data using Equation 18, or from foam separation data using Equation 15. A correlation of exp (7, - r ) A / ( R T ) - 1 us. C, in accordance with Equation 18, is shown in Figure 5. The correlation is based on surface tension data for purified NaLS and NaDBS shown in Figures 1 and 2. From Figure 5 it was calculated that for NaLS solutions
- y = 7.65 In
+ 1);
(7.25 X 103C k'NaLS
= 4.5 X io5sq. cm./liter
(34)
and for NaDBS solutions yo - y = 7.25 In (5 X 104C 4- 1 ) ; ~ ' N ~ B =S6.74 X
(rnol/lit)xd
Test of combined Gibbs and Langmuir equations Calculation of k'
10
0
5
10
20
Figure 6. Test of Langmuir equation for foam separation experiments Without N a C l
obtained from the straight-line portion of the curves in Figure 6, are: k'NaLs
= 1.0 X IO6 sq. cm./liter
~ ' N ~ D B= S
0.4 X lo6 sq. cm./liter
(36 )
From the straight-line portion of the curves in Figure 6 it can be calculated that the Langmuir isotherm is applicable for r < 0.6r0. LONG-CHAIN IONS ISOTHERM. A correlation in accordance with Equation 23 is shown in Figure 7. It is based on the curves shown in Figures 3 and 4. The straight-line portions of the curves in Figure 7 indicate that the long-chain ions isotherm is applicable for r < 0.85r0. The slopes of the straight-line portions yield m, the effective number of -CH2groups, and the intercepts a t r = 0 constants B1/B2. The values obtained are : liter/sq. cm.;
(35)
-4 correlation of l/r us. 1/C, in accordance with Equation 15, is shown in Figure 6. It is based on the smoothed experimental data presented in Figures 3 and 4. The values of k',
15
(IC (1it/rnol)x16~
(BI/B2)NaLS = 1.15 X lo4sq. cm./liter
15
10
c Figure 5.
yo
5
mNaLg
= 11.6
(37)
(BiIB2)NaDBS = 1.62 x lo-' liter/sq. Cm.;
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50
50t
45
4.0
u, ?
35
3.0
30
1i5
2 .o
10'
1i4
1c2
NaLS (mol/lit)
Figure 8. Surface tension curves of NaLS solutions with constant concentrations of NaDBS 0
10
0 C N ~ D B B= 4 X 10-'M C N ~ D B B= 2 X lO-'M
A
20
Temperature 25" C.
Figure 7.
50
Test of adsorption equation of long-chain ions Foaming experiments without NaCl
45
Solutions Containing Both Surface-Active Solutes. Surface tension-concentration curves for .solutions containing both NaLS and NaDBS are shown in Figures 8 and 9. The minimum in the curves of NaLS in the presence of small concentrations of NaDBS (Figure 8) stems from the preferential adsorption of NaDBS from solutions with NaLS. NaDBS acts as a highly surface-active impurity. The minimum in Figure 8 is a t the same concentration as the minimum in the surface tension-concentration curve of unpurified NaLS (Figure 1). No minimum is evident in the curves of NaDBS in the presence of small concentrations of NaLS. NaLS is not adsorbed preferentially to NaDBS, it does not act as a highly surface-active impurity, and therefore no minimum is visible. Surface excess-concentration curves calculated from foam separation experiments with solutions containing both NaLS and NaDRS are shown in Figures 10 and 11. The outstanding phenomenon in Figure 10 is the maximum in the Values of rNaDBS. This phenomenon, also obtained a t other concentration ratios, stems from the preferential adsorption and solubilization of NaDBS a t the air-water interface and in the micelles, respectively. Increasing the NaDBS concentration (accompanied by a proper increase in NaLS concentration, since the concentration ratio was kept constant) results in a rapid increase of rN&Bs because of its preferential adsorption. When the total concentration reaches a certain value, micelles start to form. At this concentration rNaDBB starts to fall because of its preferential solubilization in the micelles. h still further increase in the total concentration results in a constant value of rNaDBs because of its distribution between the micelles and the gas-liquid interface. In most of the foam separation experiments with mixtures, the concentration ratios of NaDBS to NaLS were below unity. Therefore, NaDBS may be considered as a highly surface-active impurity. Peaks in adsorption isotherms in the presence of "artificial impurities" which constituted 1% 480
l h E C
FUNDAMENTALS
€U
e 40
z
2,
'0
*
u
35
30 N.aDBS (molllit)
Figure 9. Surface tension curve of NaDBS solutions with constant Concentration of NaLS C N ~ L B= 4 X 1O-'M Temperature 25' C.
of the total concentration were also reported by Nilsson (1957)and Aniansson (1951). The calculated values of the relative distribution coefficient according to the various models are given below. The determination of CYAB according to the Gibbs equation requires an exceptionally large number of surface tension-concentration measurements which were not carried out in the present investigation. LANGMUIR ISOTHERM. Substituting the values of k' calculated from surface-tension data of the single solutes, Equation 34 and 35,into Equation 17:
6.7 (39) Substituting the values of k', calculated from foam separation experiments (Equation 36) into Equation 17: QINBDBS,N~LS =
(40) LONG-CHAIN IONS ISOTHERM. Substituting the values of m and Bl/Bz given in Equations 37 and 38 into Equation 29: Q I N ~ D B S , N ~ L= S
QIN&BS,N~LS=
2.5
3.07 exp (20,500r1'2)
(411
1.0
0.2
z
0 X
0
-sX h
NE Y a E v
"E
V
5.
-E
0.1
0.5
VI
g
m
0 CI
z
L2
a r-4
0.0
0
30
20
10
40
NaDBS (rnol/lit)x105 Figure 10.
Adsorption isotherm for NaDBS from mixture with NaLS
0 C N ~ D B E ~ C N= ~ L0.03 B
A
I
o v0
CNaDBB/CNaLB = 0.09
" I
10
20
30
I
40
NaLS (mOl/lit)xlO' 0
Figure 1 1 . Adsorption isotherm for NaLS from mixtures with NaDBS
-24 a,
CNsDBdCNaL8 = 0.09
A correlation of log a us. F1/*, in accordance with Equation 41,is shown in Figure 12. The lines satisfying Equations 39 and 40 are also shown. The experimental points mere calculated according to Equation 32, using data obtained from foam separation of solutions containing both NaLS and NaDBS, whereas the solid lines are based on theory and data obtained from experiments with solutions containing the single solutes. The horizontal lines in Figure 12 represent the Langmuir model. Line 1 is based on foam separation experiments and line 3 is based on surface tension measurements. The difference between the two lines stems from the discrepancy in the surface excess values obtained by the two methods, as discussed above. At very low concentrations the Langmuir and long-chain ions models should yield identical results. As seen in Figure 12, lines 1 and 2, both based on foam separation experiments with the single solutes, are close to each other a t = 0. The small difference between the intercepts stems from, and is within the range of, the experimental error. Lines 1 and 3 were drawn up to about the CMC, since the Langrnuir model is not Epplicable to higher concentrations. Line 2 was drawn up to A = 71 sq. A. (P2 = 1.53 X lo+'), the theoretical limit of the long-chain ions model (Davies and Rideal, 1961).
1
1.0
20
r112(mol/crn2)112x105 Figure 12. Selective adsorption coefficient vs. total surface excess for mixtures of NaLS and NaDBS
0 Without NaCl
A
With 0.01 M NaCl 1 . langmuir model (foaming experiments) 2. long-chain ions model 3. Langmuir model (surface tension)
Figure 12 indicates that up to F1I2= 1.5 X there is a good agreement between the experimental points and the long-chain ions model. At this surface excess a sharp decrease in the experimental a's is evident. This decrease in CY is in accordance with the decrease in the surface excess of NaDBS, in the presence of excess NaLS, as mentioned above. It stems from the same reasons-i.e., the preferential solubilization of NaDBS in the mixed micelles. Indeed, the sharp decrease in a starts at F = 2.3 X which is very close to the surface excess a t which micelles start to form. The values of the relative distribution coefficients for the system NaLS-NaDBS obtained in the present work are smaller VOL.
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3
AUGUST
1 9 6 9
481
by approximately an order of magnitude than the values reported by Shinoda and Mashio (1960) for the same system. I n our opinion this difference stems from the fact that Shinoda et al. conducted their experiments in a batch system, where the volume of foam was much larger than the volume of the original solution. They report considerable changes in the concentrations of their original solutjons in the course of foaming. For calculations they used the logarithm averages of concentration of their bulk solution (without justification). No correction was made for changes in concentrations in the foamate nor for the large holdup in the foam.
2 = valence of ion a,CZAB = relative distribution coefficient of A relative to B y = surface tension, dynes/cm. yo = surface tension of pure solvent, dynes/cm. e = electronic charge r = surface excess, moles/sq. cm. F = over-all surface excess of several surface-active solutes I’i(‘) = surface excess of component i, when surface excess of the solvent is zero, moles/sq. cm. riCG)= total number of moles of component in surface phase per unit area, according to Guggenheim’s model, moles/sq. cm. = surface excess at complete coverage in monomolecular layer, moIes/sq. cm. I.( = chemical potential = electrical potential of surface relative to the bulk solution, mv.
r0
Conclusions
Foam separation techniques may be huccessfully applied to separate surface-active solutes. The following conclusions, applicable to solutes similar to those used in the present work, may be reached: Determination of surface excess for solutions Containing a bingle surface-active solute from surface tension-concentration data does not necessarily yield results obtainable by foam separation. Surface tension measurements may serve, however, as a good indicator for the CMC. The relative distribution coefficient is not necessarily constant. Its value increases with concentration below the CMC and reduces drastically at and above the CMC of the solution. Thus, to obtain maximum separation between surface-active solutes it is advantageous to work just below the CMC, where CYABhas its maximum value. The experimental results indicate that, as might be expected none of the theoretical derivations presented applied above the CMC. Below the ClllC calculated values of CYAB based on equilibrium foam separation experiments with solutions containing the single solutes and the long-chain ions isotherm are in good agreement with experimental values obtained with solutions containing the two solutes. Calculations based on the Langmuir isotherm may be used for a conservative estimation of OLABat very low concentrations.
+.
SUBSCRIPTS A , B = surface active solutes
8 X
y
= solvent, water = bulk solution in foam = foamate (collapsed foam)
literature Cited
American Public Health Association, New York, “Standard Methods for Examination of Water and Sewage,” 11th ed., 1960.
Aniansson, G., J . Phys. Colloid Sci. 66, 1286 (1951). Banfield, D. L., Simpson, M. P., Xewson, I. H., Alder, P. J., United Kingdom Atomic Energy Authority, Rept. AERER6124 (1966).
Brady, A. P., J . Phys. Colloid Ckem. 63, 56 (1949). Brunner, C. A., Lemlich, It., IND.ENG.CHEM.FUNDAMENTALS 2, 297 (1963).
Brunner, C. A., Ste han, D. G., Ind. Eng. Chem. 67, 40 (1965). Butler, J. A. V., Ocfrent, C., J . Phys. Chem. 34, (1930). Ilavies, J. T., J . Colloid Sci. 11, 377 (1956). Ilavies, J. T., Trans. Faraday SOC.48, 1052 (1952). navies, J. T., Riedeal, E. K., “Interfacial Phenomena,” Academic Press, New York, 1961. Fanlo, S., Lemlich, R., A.I.Ch.E.-I. Chem. E. Symp. Ser. 9, 75 (1965).
Grieves, R. B., Bhattacharyya, D., A.1.Ch.E. J . 11, 274 (1965). Grieves. R. B.. Crandall. C. J.. Wood, R. K., Intern. J . Air
Nomenclature
A A,
= area per molecule, sq. cm./mole
A
= average area per molecule in mixture of surface-
a
= activity
Bi
= adsorption constant, liters/sq. cm.
Wate; Pollution 8, 501 (1964).‘
= area per molecule, surface completely covered with
monomolecular layer, sq. cm./mole active solutes, sq. cm./moIe sec.
CZ CY
= concentration in foamate (collapsed foam), moles/
D
= dielectric constant of medium
C
moles/liter liter
-a
= bubble diameter
E
= enrichment ratio, C,/Cz
f
= foam ratio, ml. of liquid/ml. of foam
K IC’
= constant, (&/&)A/ (BI/&)B = desorption constant in Langmuir equation, sq. cm./
k
= Boltsmann constant
173
= effective number of -CHr groups in molecule = mole fraction = number of bubbles of diameter -ai
liter
N ni
R
T M.’
= gas constant, cal./niole O K . = temperature, OK. = desorption energy, cal./mole
Xade Xbulk
= mole fraction of solute in adsorbed layer
482
I&EC
= mole fraction of solute in bulk liquid FUNDAMENTALS
820 (1965).
Haas, P. A., Johnson, H. F., A.I.Ch.E. J . 11, 319 (1965). Haas. P. A.. Johnson, H. F., IND.ENG.CHEM.FUNDAMENTALS 6, 225 (1967).
= desorption constant, set.+ = concentration, moles/liter = concentration in bulk solution (in foam separation),
B2
Grieves, R. B., Wilson, T. E., Shik, K. Y., A.I.Ch.E. J . 11,
Kishimoto, H., Kolloid 2.192, 66 (1963). Leonard, R. A., Lemlich, R., A.I.Ch.E. J . 11, 18 (1965). Matsuura, R., Kimizuka, H., Matsubara, A., Matsunobu, K., Matsuda, T., Bull. Chem. SOC.Japan 36, 552 (1962). Miles, G. D., Shedlovsky, L. I., J . Phys. Chem. 48, 57 (1944). Moilliet. J. L.. Collie,, B.,, Black, W., “Surface Activity,” Spon, London, 1961. Newson, I. H., J . Appl. Chem. 16, 43 (1966). Nilsson, G., J . Phys. Chem. 61, 1135 (1957). Ponchka, It. P., Karger, B. L., Anal. Chem. 37, 422 (1965). Rubin, E., Everett, R., Jr., Ind. Eng. Chem. 66, 44 (1963). Rubin, E., Gaden, E. L., “New Chemical Engineering Separation Techniques, H. M. Schoen, ed., Interscience, New York, 1962. Rubin, E., Lamantia, C. R., Gaden, E. L., Chem. Eng. Scz. 22, 1117 (1967).
ltubin, E., Schoenfeld, E., Everett, R., Jr., Oak Ridge National Laboratory Rept. RAI-104 (October 1962). Schnepf, R. W., Gaden, E. L., Mirocnik, E., Schonfeld, E., Chem. Eng. Progr. 66, 42 (1959).
Shinoda, K., Kinoshita, K., J . Colloid Sci. 18, 174 (1963). Shinoda, K., Mashio, K., J . Phys. Chem. 64, 54 (1960). Shinoda, K., Nakanishi, J., J . Phys. Chem. 67, 2547 (1963). Schoen, H. &Rubin, I., E., Ghosh, D., J . Water Pollution Control Fed. 34, 1026 (1962).
Sobotka, H., “Monomolecular Layers,” American Association for the Advancement of Science, Washington D. C., 1954. Wilson, A., Epstein, M. B., Rose, J., J . Colloid Sci. 12, 345 (1957).
RECEIVED for review January 12, 1968 ACCEPTED January 6, 1969
