I n d . Eng. Chem. Res. 1987,26, 1217-1222
= apparent viscosity of suspension at rotational speed 60 rpm, Pes d p = solid volume fraction of suspension
Literature Cited Bown, R. W. Trans.-Znst. Min. Metall., Sect. C 1966, C75, C173. Criado, J. M.; Gonzalez, M. Thermochim. Acta 1984, 79, 91. Heinicke, G. Tribochemistry; Akademie-Verlag: Berlin, 1984. Hess, W. Dissertation TH Karlsruhe 1980, p 154.
1217
Klimpel, T. Powder Technol. 1982,32, 267. Rumpf, H. Aufbereitungstech. 1973, 14, 59. Senna, M.; Kuno. H. J. Am. Ceram. SOC.1971,54, 259. Senna, M.; Schonert, K. Powder Technol. 1982, 31, 269. Sepulveda,J. L.; Herbst, J. A. Proc. Tech. Program: Int. Powder Bulk Solids Handl. Process. 1981, 10. Shinozaki, M.; Senna, M. Znd. Eng. Chem. Fundam. 1981, 20, 59.
Received for review June 3, 1986 Accepted February 27, 1987
Solubilization of Cresols by 1-Hexadecylpyridinium Chloride Micelles and Removal of Cresols from Aqueous Streams by Micellar-Enhanced Ultrafiltration Subray N. Bhat,+$George A. Smith,+§Edwin E. Tucker,?§Sherril D. Christian,*?§and John F. ScamehornlL Department of Chemistry, Institute f o r Applied Surfactant Research, and School of Chemical Engineering and Materials Science, University of Oklahoma, Norman, Oklahoma 73019
Willie Smith Halliburton Services, Duncan, Oklahoma 73536
In micellar-enhanced ultrafiltration (MEUF), solubilization of organic solutes in micelles, combined with ultrafiltration of these micellar solutions, leads to the removal of dissolved, low molecular weight organic compounds from water. T h e permeate from MEUF contains the organic solute a t concentrations equal to the unsolubilized solute concentration in the rejected (retentate) solution. Therefore, the equilibrium solubilization of the solute dictates the permeate purity or rejection of the solute by the membrane. T h e semiequilibrium dialysis method has been used to investigate the equilibrium solubilization of 0-,m-, and p-cresol by aqueous solutions of 1-hexadecylpyridinium chloride, throughout a range of concentrations of the cresols and the surfactant. The apparent solubilization constant, K = X,/ (concentration of unsolubilized cresol), has been correlated with X c , the mole fraction of cresol in the micelle. For each of the three cresol-1-hexadecylpyridinium chloride systems, K is found to vary nearly linearly with X c , throughout the range 0 < X c < 0.5. The removal of organic contaminants from aqueous streams, by the process called micellar-enhanced ultrafiltration (MEUF), has been shown to be effective for several types of organic compounds (Leung, 1979; Dunn et al., 1985,1986; Scamehorn and Harwell, 1986; Gibbs et al., 1986). In MEUF, a surfactant is added to the aqueous stream containing a dissolved organic contaminant, causing a large fraction of the solute to associate with the surfactant micelles. When the aqueous stream is passed through an ultrafilter having a molecular weight cutoff in the range 1000-20 000, most of the organic compound and the surfactant remain in the retentate solution. In a number of MEUF experiments, the effluent or permeate solution has been shown to contain organic solute at a very low concentration, approximately equal to the concentration of free organic molecules in the retentate solution. Research on the equilibrium solubilization of organic solutes by surfactant solutions is important, both in relation to practical problems such as detergency, enhanced oil recovery, or micelle-based separations and because detailed solubilization results can play a major role in increasing our understanding of the properties and structure of micellar solutions. There have been relatively Department of Chemistry. $On leave from the Department of Chemistry, North Eastern Hill University, Shillong 793003, India. f
Institute for Applied Surfactant Research. School of Chemical Engineering and Materials Science.
few solubilization studies yielding accurate information about the concentration dependence of the solubilization constant (or equivalently the activity coefficient of the solute in the intramicellar “solution”)(Doughertyand Berg, 1974; Goto and Endo, 1978; Valenzuela et al., 1984; Abuin et al., 1984). Typically, the extent of solubilization has been measured only at saturation of the surfactant solution by an organic solute, and it has commonly been assumed that the activity of the solute in aqueous solutions at fixed micellar concentration can be predicted by some form of ’ Henry’s law. However, several types of measurementsnotably solute vapor pressure results-have shown that adherence to Henry’s law in such systems is the exception, rather than the rule (Thomas and Christian, 1981; Christian et al., 1981, 1982, 1986; Tucker and Christian, 1982, 1985). Although vapor pressure studies (Christian et al., 1981; Tucker and Christian, 1982,1985)have probably provided the most accurate solubilization data for volatile organic solutes, methods for investigating the solubilization of solutes having vapor pressures of only a few torr or less are not so reliable. Recently, we reported the development of a new, generally applicable method for studying the equilibrium solubilization of almost any type of solute by aqueous surfactant solutions (Christian et al., 1985; Smith et al., 1986). Semiequilibrium dialysis (SED) is similar to MEUF in that it utilizes a membrane to separate a concentrated solution of solute and surfactant from a permeate solution containing only small amounts of either
0888-5885/87/2626-1217$01.50/00 1987 American Chemical Society
1218 Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987
species. In the SED studies, equilibrium is attained with respect t o transfer of the organic solute between the two compartments of the cell, approximately 16-24 h being required for this equilibration; however, during the time period of the experiment, very little of the surfactant passes through the membrane from the concentrated (retentate) side of the cell to the permeate side. Using phenol as a typical organic solute, we have been able to show that the solubilization constant and the activity coefficient of the solute in the intramicellar “solution” can be inferred from SED measurements made throughout wide ranges of concentration of solute and surfactant. The mathematical methods required to infer equilibrium solubilization results from SED data have been described previously (Christian et al., 1985; Smith et al., 1986). New SED results are reported here for three cresols, solubilized by aqueous solutions of 1-hexadecylpyridinium chloride (referred to as cetylpyridinium chloride or CPC). A somewhat simplified method of data analysis is developed for calculating activity coefficients of both the organic solute and the surfactant in t,he micelle-solubilizate pseudophase. By assuming that the equilibium solubilization results (obtained from SED experiments) may be used to calculate the concentrations of organic solutes transferred through the membrane in the MEUF process, we are able to determine the conditions required to remove the cresols from an aqueous stream by MEUF. Large reductions in cresol concentration are predicted for the separation process. Experimental Section Aldrich Gold-Label 0- and p-cresol were purified by vacuum sublimation, and m-cresol was purified by fractional distillation. Ultraviolet spectra of these compounds agreed well with literature spectra. SED experiments were performed as described previously (Christian et al., 1985; Smith et al., 19861, using regenerated cellulose membranes having a nominal molecular weight cutoff of 6000. The dialysis membranes were washed thoroughly in distilled water for approximately 15 min before use. Solutions containing surfactant and cresol at known concentrations were introduced into one side of each dialysis cell, and pure water was added to the other side. The cells were thermostated at 25.0 “C for 18-24 h, prior to analyzing the permeate solutions by UV spectroscopy. Concentrations of surfactant, [CPC], and of cresol, [C], in the permeate were inferred simultaneously by least-squares analysis of absorbance results at five or more wavelengths; retentate concentrations were obtained by correcting the original concentrations for the amounts of solutes t,ransferred into the permeate compartment. Table I includes all of the primary semiequilibrium dialysis results for 0-, m-, and p-cresol solutions; the data comprise experimental values of the concentrations of the components in the two cell compartments. We denote the concentrations by [CPC];:;, [CPC]?::, [CPCltz;, and [C];!: ret designating the retentate compartment, per designating the permeate, and tot indicating that these are total or analytical concentrations. Analysis of Semiequilibrium Dialysis Data We showed previously (Smith et al., 1986) that the total concentration of organic solute and of surfactant, respectively, in either compartment of the dialysis cell, may be expressed as and
[CPCI,, =
YCPC(1
- XC)C$PC + [CPCI,i,
(2)
where [CPCImi,denotes the molar concentration of surfactant in the micelle, Xc is the intramicellar mole fraction of organic (cresol),and yc and ycpc are activity coefficients, based on the pure-micelle standard state for the surfactant and the pure-component standard state for cresol. yepc is equal to ccpc/[c$pc(l - Xc)], where ccpc is the concentration of monomeric surfactant in the bulk aqueous phase and cgpc is the concentration of monomeric surfactant in the bulk phase in the absence of added cresol. y c is equal to c c / (c~X,),where cc is the concentration of monomeric cresol and c$ is selected to be approximately equal to the concentration of monomeric cresol a t which the partial pressure or fugacity of cresol equals that of pure cresol at the same temperature. If the activity coefficients for both components in the micelle were known explicitly as functions of Xc,it would be possible to solve eq 1and 2 simultaneously to calculate Xc and [CPCImi,for both the retentate and the permeate solutions. Previously, we used activity coefficient expansions consistent with the Gibbs-Duhem equation (Hansen and Miller, 1954) to correlate SED data and to infer the concentrations of the free and solubilized organic species in both the retentate and the permeate solutions (Smith et al., 1986). The data-fitting procedure based on the Hansen-Miller formalism, although satisfactory for correlating all of the SED data for phenol, is somewhat complex. We attempted, therefore, to simplify the analysis by making use of the observation that the solubilization constant K = Xc/cC
(3)
often varies linearly with Xc, throughout wide ranges of X c . When this occurs, K may be expressed as K = Ko(1 - bXc) (4) where KOis the value of the solubilization constant in the limit as Xc approaches zero and b is the negative of the slope of a plot of K vs. Xc, divided by KO. Previously, a linear dependence of K on Xc was observed for several systems (Dougherty and Berg, 1974; Goto and Endo, 1978), and we have observed an analogous linear dependence for many surfactant-polar organic solute systems studied with the SED and vapor pressure methods. “Note that the solubilization constant, defined in this work by eq 3, is not the same as that used in our earlier papers on the SED method (Christian et al., 1985; Smith et al., 1986); the solubilization constant used previously is larger than the K given here by the factor 1/(1- XC), although the two solubilization constants do approach the same value (viz., KO)in the limit as X c approaches zero.) The solubilization constant defined by eq 3 is quite simply related to the activity coefficient, yc, by the relation YC = 1/(Kc$
so that the observed linear dependence of K on Xc implies that the activity coefficient of cresol may be expressed as
Yc = a / ( l - bXc)
(5)
where a = l/(Koc$). By using the Gibbs-Duhem equation to calculate an expression for the activity coefficient of the surfactant in the intramicellar solution, we obtain In ycpc = (1/(1- b)](bIn (1 - X c ) - In (1 - bXC)J (6) which directly relates the change in ycpc to the value of the single parameter, b. Hence, the analysis of SED data can be performed by using eq 5 and 6 in place of the
Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 1219
T 0
-I
( 0 0
1
0.1
0.2
0.3
0.4
z
0
II)
0.5
0 0
0-CRESOL MOLE FRACTION IN MICELLE Figure 1. Dependence of the activity coefficients for o-cresol and 1-hexadecylpyridinium chloride on the composition of the micelle.
g E!
Y
3
0.1
0.2
0.3
0.4
0.5
0-CRESOL MOLE FRACTION IN MICELLE Figure 4. Dependence of the solubilization constant for o-cresol in 1-hexadecylpyridinium chloride on the composition of the micelle. Solid line calculated with least-squares parameters.
1.0
0.20
0.12
n H > I0 a
0.08
z H 0
75
Ia
;
50
h 0 0
0.:
0.2
0.3
0.4
0.5
P-CRESOL MOLE FRACTION IN MICELLE
Figure 2. Dependence of the activity coefficients for p-cresol and 1-hexadecylpyridinium chloride on the composition of the micelle. I-
B
0 V
I
0 I
0
0.1
0.2
0.3
0.'
0.5
P-CRESOL MOLE FRACTION IN MICELLE Figure 5. Dependence of the solubilization constant for p-cresol in 1-hexadecylpyridinium chloride on the composition of the micelle. Solid line calculated with least-squares parameters.
0.20
0
P 0
>
CH>
p
BP
150
$
125
I-
o.12
0 0.08
z
za
0
d
\
g 4
I-
N n
0.04
d
a 0
0.1
0.2
0.3
0.4
0.5
M-CRESOL MOLE FRACTION IN MICELLE
Figure 3. Dependence of the activity coefficients for m-cresol and 1-hexadecylpyridinium chloride on the composition of the micelle.
three-parameter Hansen-Miller equations for the activity coefficients (Smith et al., 1986). Table I1 lists the values of the least-squares parameters (KOand b ) derived by fitting all of the [C]El data for a given cresol with this model; also included in the table are values of c$ and c$pc employed in the analysis. Relative root-mean-square deviations in [C]El for each system are also tabulated, and the least-squares predicted values of [C]:! are listed in the final column of Table I. Figures 1-3 show the dependence of yc and ycpc on X C for the three CPC-cresol systems; activity coefficients of both the cresol and CPC are very similar for the different systems, as are the parameters in Table 11. Figures 4-6 are plots of K against X C ,the straight lines corresponding to the values of KOand b for each system. Also included in these figures are values of K calculated point by point by a method similar to that described previously (Smith et al., 1986). In order to compute the individual solubilization constants, we make the assumption bustified empirically by the present results and results for several polar
::
100 75
50
-
-
2 n o
0 1
0 2
0 3
0 6
0 5
M-CRESOL MOLE FRACTION IN MICELLE
Figure 6. Dependence of the solubilization constant for m-cresol in 1-hexadecylpyridinium chloride on the composition of the micelle. Solid line calculated with least-squares parameters.
solute-CPC systems (Smith et al., 1986; Smith, 1986)jthat the value of X c in the permeate solution is equal to that in the retentate. The retentate mole fraction is inferred for each data set by solving the equation obtained by substituting the expression for yc (eq 5) into eq 1. X c is calculation from this equation by using the least-squares values of KOand b from Table I and the experimental value of [C]::; [CPC]E:c is assumed to be equal to [CPC];:, as before. Then, using only the value of b from Table 11, we calculate ycpc for the permeate solution by means of eq 6. Finally, by applying eq 2 to the permeate solution (but using X c as inferred for the retentate solution), we calculate [CPC]g:c and calculate K from the equation derived previously:
K = (1- Xc)([Cli$ - [CIKl/ { [ c l g [ c P c l ~-~ c[cl~::[cPcl~l3 (7) The individual values of K in Figures 4-6 deviate more or
1220 Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 Table I. Results of Semiesuilibrium Dialysis Experiments for Cresols in 1-HexadecylDyridinium Chloride (CPC) at 25 ' C a b o-cresol into CPC a t 25 "C o-cresol into CPC a t 25 "C [o-cresollc: [CPC]e: [o-cresol];E [CPC]zt [o-cre~ol]E;~[o-cresol]c: [CPC]g: [o-cresol]i~~ [CPc];:: [o-cresol~~:~~ 6.93243-04 2.70943-03 4.49893-02 5.02993-01 6.72223-04 3.57713-03 9.86363-04 5.17103-02 1.09483-01 3.58963-03 5.91013-04 1.11303-03 1.28493-02 1.33233-01 5.57143-04 3.51313-03 7.96743-04 5.14373-02 1.05463-01 3.65713-03 5.48863-04 1.06183-03 1.28913-02 1.33283-01 5.54133-04 4.87503-03 2.37893-03 1.05753-01 2.18683-01 4.54623-03 5.81263-04 1.23723-03 1.81783-02 1.85883-01 5.84513-04 5.56083-03 4.00863-03 1.05073-01 2.17053-01 5.31233-03 5.78233-04 1.18103-03 1.81813-02 1.80543-01 5.97183-04 4.06593-03 9.83783-04 1.06563-01 2.20073-01 3.90363-03 6.43323-04 2.00653-03 4.99363-02 5.03693-01 6.80883-04 4.00473-03 9.03693-04 1.06633-01 2.20163-01 3.86753-03 6.93243-04 2.70943-03 4.98863-02 5.0299341 7.50083-04 4.02173-03 9.68503-04 1.06603-01 2.20093-01 3.89813-03 2.01293-03 2.40003-03 2.66403-02 1.03393-01 1.97493-03 3.97793-03 8.74723-04 1.06653-01 2.20183-01 3.85473-03 1.61763-03 7.88483-04 2.70323-02 1.05003-01 1.58413-03 4.68153-03 8.15593-04 5.21603-02 8.79303-02 4.79433-03 2.30173-03 2.88903-03 6.00483-02 2.27093-01 2.24123-03 4.63663-03 8.03623-04 5.22063-02 8.79463-02 4.79303-03 1.79963-03 1.03653-03 6.05503-02 2.28943-01 1.76583-03 4.70973-03 8.00693-04 4.90493-02 8.20183-02 4.79923-03 1.83733-03 1.18463-03 6.05123-02 2.28793-01 1.80403-03 4.52083-03 7.85673-04 4.92383-02 8.20333-02 4.81803-03 1.75103-03 9.06223-04 6.05993-02 2,2907341 1.73293-03 5.01903-03 9.05183-04 6.62593-02 1.10383-01 5.07233-03 2.40003-03 3.54193-03 5.99503-02 2.26443-01 2.41233-03 4.80203-03 6.60553-04 6.64753-02 1.10433-01 4.95843-03 3.22023-03 6.02913-03 1.19383-01 4.44313-01 3.15263-03 6.23703-03 6.67883-04 4.73833-02 7.39123-02 5.18043-03 3.67823-03 7.98073-03 1.18923-01 4.42323-01 3.67173-03 5.96383-03 6.40993-04 4.76563-02 7.39393-02 5.20913-03 3.11473-03 6.00373-03 1.19483-01 4.44293-01 3.14913-03 5.38933-03 7.28603-04 9.70843-02 1.57133-01 5.39703-03 3.01963-03 5.82613-03 1.19583-01 4.44473-01 3.10363-03 5.20553-03 7.20453-04 9.72673-02 1.57133-01 5.40863-03 2.89953-03 5.59393-03 1.19703-01 4.44703-01 3.04373-03 5.55213-03 9.70193-04 1.20063-01 1.95143--01 5.59453-03 2.66083-03 1.15593-03 2.18703-02 5.92003-02 2.46993-03 5.30193-03 1.02473-03 1.20313-01 1.95093-01 5.64813-03 2.23003-03 8.61133-04 2.23103-02 5.94963-02 2.41983-03 6.13383-03 6.63373-04 5.40223-02 7.46283-02 6.30703-03 2.59533-03 9.03793-04 3.39363-02 8.92063-02 2.59743-03 6.05643-03 6.33213-04 5.41003-02 7.46253-02 6.32433-03 2.58283-03 8.69423-04 3.39483-02 8.92403-02 2.58533-03 7.55213-03 6.91233-04 1.15103-01 1.54503-01 7.40733-03 2.97403-03 1.07753-03 6.75503-02 1.72323-01 2.90233-03 7.53043-03 6.99253-04 I ,15123-01 1.54493-01 7.41623-03 2.93513-03 1.08663-03 6.75933-02 1.72313-01 2.90853-03 p-cresol into CPC a t 25 "C p-cresol into CPC a t 25 "C [p-cresol]Ei [CPC]G [p-cresol]g: [CPC]z: [p-cre~ol]::~ [p-cresollr; [CPC]e; [p-cresollfzt [CPC]:,$ [p-cre~ol]~:~~ 4.93503-04 1.18533-03 7.48023-03 7.90333-02 5.09653-01 3.69303-03 2.04603-03 4.43003-02 9.55543-02 3.48043-03 5.05563-04 1.16143-03 7.3884343 7.75983-02 5.10103-04 4.94003-03 3.63003-03 9.16503-02 1.92573-01 4.47553-03 4.98713-04 1.11083-03 7.39533-03 7.76493-02 5.05763-04 4.28003-03 2.51003-03 9.22203-02 1.93693-01 3.96313-03 5.93053-04 1.20273-03 1.62273-02 1.66663-01 5.45943-04 4.28003-03 1.68003-03 4.94903-02 8.84903-02 4.18783-03 5.55733-04 1.16593-03 1.62643-02 1.66663-01 5.43783-04 4.23003-03 1.78003-03 4.95403-02 8.83903-02 4.25103-03 5.70173-04 1.42773-03 2.61153-02 2.66953-01 5.77173-04 5.1500343 2.25003-03 1.13753-01 1.97153-01 4.92363-03 1.52003-03 2.43003-03 1.97803-02 9.65303-02 1.42903-03 4.83003-03 1.93003-03 1.14073-01 1.97473-01 4.75323-03 1.45003-03 2.35503-03 1.98003-02 9.66003-02 1.41503-03 5.59203-03 1.76503-03 6.36103-02 9.68353-02 5.28273-03 1.79003-03 3.48003-03 4.12103-02 1.96323-01 1.72853-01 5.08903-03 1.77003-03 6.41103-02 9.68303-02 5.34273-03 1.71003-03 3.23003-03 4.12903-02 1.96573-01 1.67883-03 6.49003-03 2.26003-03 1.37913-01 2.03443-01 6.14033-03 1.56003-03 2.45003-03 2.28903-02 9.75103-02 1.66523-03 6.55003-03 2.38003-03 1.37853-01 2.03323-01 6.21993-03 1.50003-03 2.32003-03 2.29503-02 9.76403-02 1.63893-03 5.60003-03 1.27003-03 6.8400342 9.70303-02 5.49873-03 1.79003-03 3.30003-03 4.61103-02 1.92683-01 1.95263-03 5.39003-03 1.15503-03 6.86103-02 9.71403-02 5.43903-03 1.74003-03 3.12003-03 4.61603-02 1.92683-01 1.91313-03 6.05003-03 1.35003-03 1.42853-01 1.96453-01 6.12993-03 2.20003-03 1.21003-03 3.47003-02 9.77603-02 2.24893-03 6.92003-03 1.10003-03 5.56803-02 6.40003-02 6.92893-03 2.16003-03 1.13003-03 3.47403-02 9.78403-02 2.22323-03 6.79003-03 1.08003-03 5.58103-02 6.40203-02 6.93483-03 2.49003-03 1.54003-03 7.17103-02 1.9732341 2.51683-03 8.66003-03 1.41003-03 1.81243-01 1.96093-01 8.96573-03 2.37003-03 1.31003-03 7.18303-02 1.97553-01 2.43733-03 8.32003-03 1.19003-03 1.81583-01 1.96313-01 8.78313-03 3.84003-03 2.18003-03 4.41603-02 9.54203-02 3.53053-03 ___m-cresol into CPC at 25 "C m-cresol into CPC a t 25 OC [m-cresol]e: [CPC],P,e; [m-cresol];: [CPC];: [m-cresol]EL [m-cresol]f:l [CPC]g: [m-cresol]:$ [CPC]fzI [m-cresol]KL 4.07603-04 1.06003-03 7.41143-03 9.76503-02 4.11923-04 2.12003-03 8.96003-04 3.23503-02 9.82703-02 2.08933-03 3.94003-04 1.01003-03 7.42503-03 9.77003432 4.08913-04 2.38003-03 1.03003-03 6.71803-02 1.99103-01 2.28783-03 4.31003-04 1.28003-03 1.54203-02 1.98803-01 4.50483-04 2.33003-03 9.22003-04 6.72303-02 1.99203-01 2.25333-03 4.31003-04 1.32003-03 1.54203-02 1.98803-01 4.53503-04 5.42503-03 6.47003-04 6.71053-02 1.01253-01 5.33073-03 1.02003-03 8.09003-04 1.61303-02 1.01203-01 8.81383-04 5.06003-03 6.17003-04 6.74703-02 1.01303-01 5.35413-03 9.16003-04 9.26003-04 1.62343-02 1.01073-01 9.06723-04 6.19003-03 7.69003-04 1.45003-01 2.11603-01 6.10363-03 9.85003-04 1.12003-03 3.38553-02 2.06003-01 9.91073-04 6.18003-03 9.80003-04 1,45003-01 2.11403-01 6.25173-03 9.83003-04 1.17003-03 3.38603-02 2.05903-01 9.99753-04 'All concentrations in mol L-l. *Notation for values means times 10 to a certain power, e.g., 6.93243-04 is 6.9324
less randomly from the least-squares straight line, and the scatter of points provides an indication of the reproducibility of SED measurements in various ranges of X c . Although the analysis required to infer [CPC]sc, as described in the preceding paragraph, may appear to be rather complex, it is worthwhile noting that the concentration of CPC in the micellar form is usually very small. Consequently, the final term in the denominator of eq 7 is often negligible compared with the first term. Moreover, when Xc in the retentate can be estimated and equated to X C in the permeate, [CPC]sc can be inferred from eq 2 by using only the analytical concentration of CPC in the permeate solution, known constants, and the value of a
X
single parameter ( b ) . The other terms appearing in eq 7 are directly calculated from the analytical concentrations of cresol and CPC.
Micehr-Enhanced Ultrafiltration of Aqueous St~~am Containing s Cresols In utilizing the solubilization measurements to estimate the ability of MEUF to remove dissolved cresols from water, it is arbitrarily assumed that the feed solution contains 50 mM CPC and 1 mM cresol. The solution is then ultrafiltered until 80% of the volume of the solution is removed as permeate. If the water were to be recycled to the plant, this would indicate that the recycle ratio
Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 1221 Table 11. Least-Squares Parameters for Cresols in 1-Hexadecylpyridinium Chloride at 25 “C solute
KO/M-’
o-cresol m-cresol p-cresol
187 & 3 190 f 4 195 f 3
c,: M bb 1.68 f 0.02 0.24 1.62 f 0.04 0.206 1.49 f 0.02 0.18
c&, mM 0.88 0.88 0.88
RMSD,‘ 70 4.7 5.0 5.1
“Intercept of a plot of the solubilization constant, K , vs. the mole fraction of cresol in the micelle, Xc. (See eq 4.) *Parameters in eq 4. Root-mean-square deviation (relative) in cresol concentration in the permeate compartment, fitted with model described in text.
Table 111. Performance of MEUF in Removal of Cresols from Watern final concn (mM) in solute permeate retentate rejection, % o-cresol 0.0978 4.61 97.88 0.0961 4.62 97.92 m-cresol 0.0938 4.63 97.97 p-cresol “Feed: [cresol] = 1 mM, [CPC] = 50 mM. Permeate/feed = 0.8.
would be 80%. For these assumed conditions, the concentrations of cresol in the permeate and the retentate streams from the process are given in Table 111for the 0-, m-,and p-cresols. The “rejection”,a commonly used parameter in membrane science, is also listed in Table 111. For the conditions stated in Table 111, X C is equal to 0.018; in other words, the micelle contains a very small concentration of cresol relative to surfactant.
General Discussion Detailed investigations of the solubilization of organic compounds by surfactant micelles and the dependence of the solubilization equilibrium constant, K , and the activity coefficients, yc and ycpc, on the intramicellar composition can provide important information about the physical behavior of micelles and the nature of their interactions with solubilized species. There seems to be general agreement that highly polar solutes tend to solubilize in the vicinity of the micellar surface and that the polar groups interact strongly with the ionic and/or polar groups of the surfactant molecules (Szajdzinska-Pieteket al., 1986; Lianos et al., 1982). The fact that K varies linearly with X , throughout wide ranges of concentration suggests that a Langmuir-type adsorption of the polar solute may be taking place at the micellar surface. It has been shown (Dougherty and Berg, 1974) that the equation
K = Ko(1 - b X c ) is consistent with Langmuir’s equation in the form
where cc is the concentration of monomeric organic solute in the bulk aqueous solution. Treating eq 8 as a description of Langmuir adsorption, we can calculate that the value of cc at which half the surface “sites” are occupied is cc = l/(Kob). Extending this point of view, it may be reasonable to attribute the positive curvature of K vs. X c plots, which typically occurs as X c increases beyond 0.4 or 0.5 (Smith, 1986), to adsorption occurring at least partly within the micellar interior. A two-site adsorption model (Mukerjee, 1978, 1980) seems to be consistent with this interpretation. On the other hand, the size and shape of the micelles are undoubtedly altered considerably by the
incorporation of 40 or 50 mol 70 organic solubilizate, so that the simple Langmuir model might be expected to fail in any case. The solubilization of aliphatic hydrocarbon molecules in several ionic surfactants and the solubilization of benzene in sodium octylsulfate micelles cannot be forced into the Langmuir adsorption schema. For the hydrocarbon solutes, linear dependence of K on X c is observed throughout a limited region of X c , but the value of b required to fit data to eq 4 and 8 is negative, which would correspond to negative adsorption. On the other hand, solubilization data for benzene in aqueous solutions of cationic surfactants do seem to fit the linear K-vs.-Xc model (within a narrow range of X c ) with a slightly positive value of the parameter b, which may indicate that there is a moderately strong interaction between benzene and the positive surface groups of the micelles. It is known that benzene is solubilized to a greater extent by cationic surfactants than by anionic surfactants (Nagarajan et al., 1984; Rehfeld, 1971; Hirose and Sepulveda, 1981), so it is plausible to attribute part of this increase to an ion-induced dipole interaction. However, benzene as well as the aliphatic hydrocarbons is probably solubilized to a significant extent within the micellar interior at all values of Xc. All three cresols are strongly solubilized by aqueous solutions of CPC. As a result, a highly efficient separation of cresols from water can be achieved by MEUF in one pass. Under the conditions specified in Table 11, the permeate cresol concentration is 50 times smaller than that in the retentate product from the process and 10 times smaller than that in the feed. At a constant level of added surfactant, the ratio of the concentration of cresol in the permeate (which is equal to the concentration of unsolubilized cresol in the retentate) to the concentration of cresol in the feed is proportional to (1- X c ) / K . For the three cresols, K decreases so rapidly with increasing cresol concentrations, or X c , that the factor (1 - X c ) / K decreases also. Therefore, the ratio of the cresol concentration in the permeate to that in the retentate increases as the cresol concentration decreases; i.e., the separation efficiency becomes greater at lower cresol concentrations. This effect makes MEUF a particularly valuable separation method at low solute concentrations, because many other separation techniques become less efficient as the solute concentration decreases. The present study emphasizes the necessity of determining the value of K as a function of solubilization level (or mole fraction of solute in the micelle) in order to allow calculation of performance of MEUF in treating streams of arbitrary composition.
Acknowledgment The authors appreciate the financial support of the Office of Basic Energy Sciences, Department of Energy, Contract DE-AS05-84ER13175. Registry No. 4-H3CC6H40H,106-44-5;2-H3CC6H40H,95-48-7; 3-H3CC6H40H,108-39-4; 1-hexadecylpyridinium chloride, 123-
03-5.
Literature Cited Abuin, E. B.; Valenzuela, E.; Lis& E. A. J . Colloid Interface Sci. 1984, 101, 401. Christian, S. D.; Smith, L. S.; Bushong, D. S.; Tucker, E. E. J . Colloid Interface Sci. 1982, 89, 514. Christian, S. D.; Smith, G. A.; Tucker, E. E. Langmuir 1985, I, 564. Christian, S. D.; Tucker, E. E.; Lane, E. H. J . Colloid Interface Sci. 1981, 84, 23. Christian, S. D.; Tucker, E. E.; Smith G. A.; Bushong, D. S. J . Colloid Interface Sci. 1986, in press.
Ind. Eng. Chem. Res. 1987, 26, 1222-1227
1222
Dougherty, S. J.; Berg, J . C. J . Colloid Interface Sci. 1974,48, 100. Dunn, R. 0.;Scamehorn, J. F.; Christian, S. D. Sep. Sci. Technol. 1985, 20, 257. Dunn, R. 0.;Scamehorn. J . F.; Christian, S.D. Sep. Scz. Technol. 1986, in press. Gibbs, L. L.; Scamehorn, J . F.; Christian, S. D., submitted for publication in J . Membrane Sei. 1986. Goto, A,; Endo, F. J . Colloid Interface Sei. 1978, 66, 26. Hansen, R. S.; Miller, F. A. J . Phys. Chem. 1954, 58, 193. Hirose, C.; Sepulveda, L. J . Phys. Chem. 1981, 85, 3689. Leung, P. S. Ultrafiltration Membranes and Applications; Cooper, A. R., Ed.; Plenum: New York, 1979; p 415. Lianos, P.; Zana, R. J . Colloid Interface Sci. 1982, 88, 594. Mukerjee, P. Solution Chemistr3) of Surfactants; Mittal, K. L., Ed.: Plenum: New York, 1978. Mukerjee, P. Pure Appl. Chem. 1980, 52, 1. Nagarajan, R.; Chaiko, M. H.; Ruckenstein, E. J . Phys. Chem. 1984, 88, 2916. Rehfeld, S. J. J . Phys. Chem. 1971, 75. 3905.
Scamehorn, J. F.; Harwell, J . H. Surfactants and Chemical Engineering; Marcel Dekker: New York, 1986, in press. Smith, G. A. Ph.D. Dissertation, The University of Oklahoma, Norman, 1986. Smith, G. A.; Christian, S.D.; Tucker, E. E.; Scamehorn, J . F. J . Solution Chem. 1986, 15, 519. Szajdzinska-Pietek, E.; Maldonado, R.; Keran, L. J. Colloid Interface Sei. 1986, 110, 514. Thomas, D. C.; Christian, S. D. J . Colloid Interface Sci. 1981, 82, 430. Tucker, E. E.; Christian, S. D. Faraday Symp. Chem. SOC. 1982,17, 11. Tucker, E. E.; Christian, S. D. J . Colloid Interface Sci. 1985, 104, 562. Valenzuela, E.; Abuin, E.; Lissi, E. A. J . Colloid Interface Sci. 1984, 102, 46. Received for review J u n e 16, 1986 Accepted January 14, 1987
Constant-Pattern Behavior for Adsorption on the Wall of a Cylindrical Channel Charles D. Tereck,+Debra S. Kovach,t and M. Douglas Levan* Department of Chemical Engineering, University of Virginia, Charlottesville, Virginia 22901
Adsorption of solute on the wall of a cylindrical channel from a fluid in laminar flow is considered mathematically. A relation among concentrations for the constant-pattern profile is developed for arbitrary axially symmetric velocity profiles, isotherms, and partition ratios with mass transfer described by radial and axial diffusion. For Poiseuille flow, large partition ratios, and large Peclet numbers, an analytical solution, based on the Graetz series and in the form of an integral equation, is obtained for the shape of the constant-pattern profile. The solution is evaluated for Langmuir and Freundlich isotherms. Local Sherwood numbers calculated from the results show a dependence on both isotherm parameter and axial position. Constant-pattern solutions for adsorption in packed beds have been derived for various controlling mass-transfer resistance based on the assumption of plug flow within the packing (Vermeulen et al., 1984;Ruthven, 1984). Schweich (1983) has examined the role of residence-time distribution on the asymptotic behavior of breakthrough curves for favorable equilibrium. He showed that, for a given residence-time distribution of carrier fluid, the breakthrough curve is not uniquely defined. Residence-time distributions were assumed to be determined solely by convection and dispersion in the axial direction with degrees of mixing bounded by states of complete segregation and maximum mixedness (Zwietering, 1959). For a segregated nondispersive flow (independent flow trajectories in parallel), it was shown that the concentration profile did not approach a constant-pattern shape but broadened continuously. Given this result, Schweich concluded that the segregated nondispersive flow is not a realistic model because of the neglect of radial dispersion. We are in agreement with Schweich on the importance of developing a better understanding of adsorption in packed beds, allowance being made for deviations from plug flow. Packing nonuniformities, both at the wall and throughout the central core of the packing, lead to irregular velocity profiles which can greatly affect the shapes of
* Author t o whom correspondence
should be addressed. 'Present address: Union Carbide Corp., South Charleston Technical Center, South Charleston, WV 25303. Present address: Union Carbide Corp., Tarrytown Technical Center. Tarrytown, NY 10591.
*
0888-5885/87/2626-1222$01.50/0
role in damping out concentration fluctuations and can give rise to large observed bed-diameter effects for deep beds (LeVan and Vermeulen, 1984). In this paper we solve for the shapes of constant-pattern profiles for a system with a non-plug-flow velocity profile. We believe that this is the first direct development of such a solution. The problem considered is a simple one: fluid containing a trace of solute is fed at a constant rate into a cylindrical channel. Adsorption of the solute occurs on the wall of the channel, adsorption equilibria being described by a favorable isotherm. This geometry is an important one for establishing reasonable physical models for packed beds and, more generally, porous media. This is true especially for momentum transfer but also for heat and mass transfer. During the last decade, straight-tube-bundle models have been used to correlate extensive data for mass-transfer coefficients in packed beds at low Reynolds numbers (Schlunder, 1977; Fedkiw and Newman, 1982). This geometry also serves as the basis for more complicated models involving constricted tubes, randomly oriented tubes, and networks of interconnected tubes. Adsorption on the walls of a cylindrical channel has been considered previously by Sartory (1978), who was interested in the possible application of the geometry for laboratory and clinical purposes. Taking fluid to be in Poiseuille flow and assuming that the mole fraction of solute is small, that the partition ratio is large, and that diffusion in the axial direction can be neglected, he solved the transient problem, obtaining an exact solution based on the Graetz series for the irreversible isotherm and nubreakthrough curves. Radial dispersion plays an important 1987 American Chemical Society
