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Electro-osmosis of water through liquid membranes
Electro-Osmosis of Water through Liquid Membranes R. C. SRIVASTAVA AND SAROJ YADAV Department of Chemistry, Birla Institute of Technology and Science, Pilani-333031, Rajasthan, India Received October 3, 1978; accepted November 15, 1978 The experiments on hydraulic permeability, electro-osmotic velocity, streaming potential and current reported in this paper lend support to Kesting's liquid membrane hypothesis according to which when a surfactant like PVME is added to water or aqueous solutions flowing through a membrane, a surfactant layer at the interface between the membrane and the aqueous solution or water is formed which acts as a fiquid membrane in series with the solid membrane. The data have revealed that the water flux through the poly(vinyl methyl ether) liquid membrane does not vary proportionally with the applied pressure difference, instead a nonproportional exponential type of relationship has been shown to describe the hydraulic permeability data. In the case of electroosmotic velocity and streaming current, however, the usual proportional relationships between fluxes and the respective driving forces have been found to be valid. The analysis for mosaic membrane model has been utilized to demonstrate that when concentration of the surfactant is half its critical micelle concentration (CMC) the area of supporting membrane covered with the liquid membrane is half the area covered at CMC. At CMC the supporting membrane is fully covered with the liquid membrane. The analysis also indicates the possibility of formation of multilayers of the liquid membrane when concentration of the surfactant exceeds its CMC value. INTRODUCTION
Martin (1) observed that the addition of small amounts, of the order of a few parts per million, of surfactants like poly(vinyl methyl ether) (PVME) to saline feed in reverse osmosis effects a large increase in the salt retention capacity of cellulose acetate membranes with but a small decrease in the flux of desalted water. The explanation of the increased permselectivity was given by Kesting et al. (2-4) based on the hypothesis of the existence of a surfactant layer liquid membrane at the interface between the cellulose acetate membrane and the saline solution. The experiments of Kesting et al. (4) also demonstrated that as the concentration of the surfactant is increased, the cellulose acetate m e m b r a n e gets progressively covered with the surfactant layer liquid membrane and at the critical micelle concentration
(CMC) the coverage of the cellulose acetate membrane with the surfactant layer is complete. The experiments on hydraulic permeability, electro-osmotic velocity, streaming potential, and current reported in this paper lend further support to Kesting's liquid membrane hypothesis (2-4). The transport data have been utilized to estimate the fraction of total area of the supporting membrane covered with the liquid membrane when the concentration of surfactant is lower than its CMC value, and it has been concluded that when the concentration of the surfactant is half its CMC value the area covered by the liquid membrane is half the area covered at the critical micelle concentration. The data also indicate the possibility of the formation of multilayers of the liquid membrane as the concentration of the surfactant is increased beyond its CMC value. 280
0021-9797/79/050280-07502.00/0 Copyright © 1979 by Academic Press, Inc. All rights of reproduction in any form reserved.
Journal of Colloid and lnterJaee Science, Vol. 69, No. 2, April 1979
ELECTRO-OSMOSIS EXPERIMENTAL
Materials. Poly(vinyl methyl ether) (Aldrich MW 71,000) sodium chloride (BDH A.R. Grade), and distilled water distilled once over potassium permanganate in an all glass still were used in the present studies. Apparatus and procedures. For the measurements of hydraulic permeability, electroosmotic velocity, and streaming potentials a slightly modified version of the all glass apparatus described earlier (5) was used. The apparatus is diagrammed in Fig. 1 which has been well labeled to make it serf-explanatory. The all glass cell (Fig. 1) was separated into two compartments by a Sartorius cellulose acetate microfiltration membrane (Cat. No. 11107) of thickness 1 x 10-4 m and area 0.95 x 10-4 m2, which in fact acted as a support for the liquid membrane. For measurements of both hydraulic permeability and electro-osmotic velocity aqueous solutions of PVME of various concentrations ranging from 0 to 12 ppm filled compartment C on the right-hand side of the microfiltration membrane S (Fig. 1), and distilled water filled compartment D. Since value of the critical micelle concentration for the aqueous solutions of PVME is 6 ppm (4) the concentration
281
ranges from 0 to 12 ppm were purposely chosen in order to obtain data on both the lower and the higher side of the CMC, at which the supporting membrane is expected to be completely covered with the liquid membrane. The procedure followed for the measurement of hydraulic permeability, electro-osmotic velocity, and streaming potentials has already been described in earlier publications (5-7). For hydraulic permeability measurements known pressures were applied to compartment C containing the PVME solution, and electrodes E1 and E2 were short-circuited. Electrical potential differences needed for the measurement of electro-osmotic velocity were tapped from an electronically operated stabilized dc power supply (Bentronix, electrophoresis power supply Model No. E.P.-101). Streaming potentials were measured using a V.T.V.M. (Phillips Model GM 6009/90) of least count 0.01 mV. During the measurement of streaming potentials a correction was made for the asymmetry potential of the electrodes. Resistances of the systems were measured using a Leitffihigkeitsmesser conductivity meter. Streaming currents were calculated using Ohm's law, from the values of streaming potentials and resistances thus obtained.
L[
L2
TO PRESSURE HEAD
TI
T2
Q[
Q2
C
RI
EI~
D
,,//
~___~--\__/--
AI
~
\~/-
~
R2
A2
FIG. 1. The electro-osmotic cell. T1 and T2 are stop cocks, M~ and M2 are magnetic stirrers. S, cellulose acetate millipore filter, pore size 0.2 /xm. L~L2, capillary tube of length 18 cm and diameter 0.38 z 10-4 m. Volume of compartments C and D, 96 and 86 ml, respectively. A1 and A2 are B-19 glass joints. Q1 and Q2 are B-14 glass joints. Ej and E2 are bright platinum electrodes. R1R2, glass tubes containing mercury. Journal of Colloid and Interface Science, Vol. 69, No. 2, April 1979
282
SRIVASTAVA AND YADAV
The volume flux was measured by noting the rate of advancement of the liquid meniscus in the capillary L1L2 with a cathetometer of least count 0.001 cm and a stop watch of least count 0.1 secs. During the volume flux measurements the solutions in the two compartments were well stirred using magnetic stirrers M~ and Ms. All measurements were made at constant temperature by placing the apparatus (Fig. 1) in a thermostat set at 40 _ 0. I°C.
2 to 5. The usual linear phenomenological equations, i.e., + LI~Ar,
[1]
I = L21AP + L~2AqS,
[2]
Jv = LllAP
obtained using the nonequilibrium thermodynamic treatment (8) for the simultaneous transport of water and electricity, predict the following linear relationships. For hydraulic permeability (Jv)a*=0 = Lll ~p-
RESULTS AND DISCUSSION
For electro-osmotic velocity
The data on hydraulic permeability, electro-osmotic velocity, streaming potential, and streaming current for different concentrations of PVME is plotted in Figs.
(Jv)ae=o = L12A~b.
(A~b/AP)l=o = - L J L 2 2 ,
1.5
T 1.0
0 l:,< >
0.5
O_Ap0_~ 5
I0
15 AP X 10- 2
20
25
30
Nn~ 2
FIG. 2. The hydraulic permeability data. Curves I, II, III, IV are for 0, 3, 6, 12 ppm PVME, respectively; ©, experimental points; ×, theoretical points as predicted by the Eq. [8]. Journal of Colloid and Interface Science, Vol. 69, No. 2, April 1979
[4]
For streaming potential
2.0
,=:
[3]
[5]
ELECTRO-OSMOSIS
283
0.3
To
0.2
E o ><
> --)
0.1 lv"
o
i
I
I
I
IO
15
20
25
Adp~
30
35
VOLTS
FIG. 3. T h e Electro-osmotic velocity data. Curves I, II, III, IV are for 0, 3, 6, and 12 p p m o f P V M E , respectively.
and for streaming current (/)~,=0 = L21AP.
[6]
In Eqs. [1] to [6] Jv stands for the volume flux of water, ! stands for the flow of electricity, AP and A~b are the pressure difference and the electrical potential difference, respectively, and L~k is the phenomenological coefficient. The equality L12 = L21
[7]
holds among them because of Onsager's theorem. As is apparent from Figs. 2 to 5 the linear relationships [4] to [6] predicted from Eqs. [11 and [2] hold good in all cases (Figs. 3 to 5). Equation [3] however does not hold good for the hydraulic permeability data in presence of PVME (Fig. 2, curves II, III, IV). The water flux (Jr) versus pressure difference (AP) curves in all cases where PVME concentration is greater than zero (Fig. 2, curves II, III, IV) start from the origin, bend upward, then approach straight lines which
extrapolate to intercepts AP0 on the AP axis. The following equation was found to fit in the hydraulic flow data in all such cases. F Jv = L11[AP - AP0
When zXP assumes such high values that the term exp(-AP/Z~0) becomes much smaller than unity Eq. [8] simplifies to Jv = Lll[zIP - AP0]
[9]
which represents the straight line parts of the curves II to IV in Fig. 2. Since water flow through the cellulose acetate microfiltration membrane obeys the linear relationship [3] (Fig. 2, curve I) this kind of nonideal behavior (Eq. [8]) appears to be the result of the flow through the PVME liquid membrane formed in series with the cellulose acetate microfiltration membrane as Journal of Colloid and Interface Science, Vol. 69, No. 2, April 1979
284
SRIVASTAVA AND YADAV 15
I0
-
o >
O X
"0<3
5
--
0 ~
0
5
I0 Ap
15 x
Io-2
20
2,5
30
Nm- z
FIG. 4. The streaming potential data. Curves I, II, III, IV are for 0, 3, 6, and 12 ppm o f PVME, respectively.
hypothesised by Kesting et al. (2-4). A more definite indication of the formation of the liquid membrane can be had from the gradation in the values of the coefficient L~a as the concentration of PVME is increased from 0 to 12 ppm. Values of the coefficients L n for various concentrations of PVME, as estimated from the slopes of the straight line portions of the curves in Fig. 2, have been given in Table I. Values of the coefficients L~2, L21, and L22 estimated from the slopes of the straight lines in Figs. 3 to 5, for various concentrations of PVME, are also given in Table I. Values of the coefficient L~I which measure conductivity to volume flow of water, show a progressive decrease as the concentration of PVME is increased from 0 to 6 ppm (the CMC value). When the concentration of PVME is increased further the value of Lla also decreases but this decrease is less pronounced than the decrease which is observed up to 6 p p m - - t h e CMC value for aqueous PVME. Similar trends can be seen Journal of Colloid and lnterJace Science, VO]. 69, No. 2, April 1979
in the values of L12 and L21- These trends are in keeping with the liquid membrane hypothesis of Kesting et al. (2-4) according to which as concentration of the surfactant (PVME in the present case) is increased, the supporting membrane (the cellulose acetate microfiltration membrane in the present case) gets progressively covered with the surfactant layer liquid membrane, and at the CMC the coverage is complete. The decrease in the values of Lll beyond the CMC was ascribed by Kesting et al. (4), to increasing density of the liquid membrane which at the CMC is fully developed and completely covers the supporting membrane. There is, however, another possibility which must be looked into, viz, the possibility of formation of multilayers of the liquid membrane? The data on electrical resistances of the system (Table I) can be utilized to check this possibility. Since at 1 We gratefully acknowledge that our attention was drawn to this possibility by Dr. R. E. Kesting himself.
285
ELECTRO-OSMOSIS 35
30--
<
2o
~) o
×
[5
Io
5
0
0
5
io
L5
2o
25
AP
x 10- 2
Nrn 2
~,.
30
F1G. 5. The streaming current data. Curves I, II, III, IV are for 0, 3, 6, and 12 p p m of P V M E , respectively.
CMC (6 ppm) the liquid membrane completely covers the supporting membrane, the total membrane at 6 ppm can be viewed as the cellulose acetate millipore filter membrane plus the PVME liquid membrane in a series arrangement. Therefore the electrical resistance at 6 ppm can be written as
R1 stands for the resistance of the liquid membrane. At 12 ppm concentration, which is twice the CMC value for PVME, another layer of the liquid membrane would be formed in series. Hence the electrical resistance at 12 ppm concentration would be given by
R6 = R0 + R1,
Rlz = Ro + 2Rl,
[10]
[11]
where R0 and R6 represent the values of the resistances at 0 and 6 ppm of PVME and
where R12 stands for the value of R at 12 ppm concentration of PVME. From Eqs. [10] and [11] we can write
TABLEI
R12 = 2R6 - R0.
Values of the P h e n o m e n o l o g i c a l Coefficients L~,, L,2, L21, L22, and the E l e c t r i c a l R e s i s t a n c e at Various C o n c e n t r a t i o n s of P V M E
The value of R~2 computed from Eq. [i2] using the experimentally determined values of Ro and R6 (Table I), comes out to be equal to 0.495 × 106 ohm which matches very well with the experimentally determined value (Table I). This clearly indicates the formation of multilayers of the liquid membrane at surfactant concentrations higher than the CMC. According to the liquid membrane hypothesis (2-4), partial liquid membranes
Concentration of PVME (pprn) LH x 107 m 3 N - ' sec -~ L,2 × 106 m A J - ' L~, x 106 m A J - ' L22 × l0 S o h m - ' m -2 Resistance × 10 ~ ohm
0
3
6
12
0.486 0.936 0.925 2.36
0.38 0.63 0.62 2.33
0.246 0.44 0.45 2.23
0.212 0.37 0.36 2.14
0.445
0.45
0.47
0.49
[12]
Journal of Colloid and Interface Science, Vol. 69, No. 2, April 1979
286
SRIVASTAVA AND YADAV
exist below and c o m p l e t e liquid m e m b r a n e s at or a b o v e the critical micelle concentration o f the surfactant. Utilizing the analysis for mosaic m e m b r a n e s (9-11) it is possible to estimate f r o m the transport data r e p o r t e d in this p a p e r (Figs. 2 - 5 ) , the fraction o f the total a r e a of the supporting m e m b r a n e , c o v e r e d with the liquid m e m b r a n e , at concentrations lower than the CMC. F o r this let us consider the hydraulic permeability data (Fig. 2) corresponding to P V M E concentrations equal to 0, 3, and 6 ppm. F o r simplicity of calculation we will focus attention only on the linear region o f the curves (Fig. 2). Since at concentrations l o w e r than the C M C the supporting m e m brane is only partially c o v e r e d with the liquid m e m b r a n e , the w a t e r flux for such a case would be given by the equation (A s + A C ) J v = L l l S A S A p + LI~CAC(Ap - AP0)
[13]
which on transformation can be rewritten as Jv :
[ t l l S ( A s A SA ) +c
+ LnC(AsA--~-Ac)]AP - Ln c
( ×
Ac As + Ac
) APo,
[14]
w h e r e the superscripts S and C stand for the supporting m e m b r a n e and the supporting m e m b r a n e c o v e r e d with the liquid m e m brane, respectively, and A represents the area of the m e m b r a n e denoted by the superscripts. Llx s and Lllc r e p r e s e n t the values o f La~ denoted b y the superscripts. Since at 6 p p m (the C M C value) concentration of P V M E the supporting m e m b r a n e is fully c o v e r e d with the liquid m e m b r a n e it is logical to expect that at 3 p p m concentration the fraction of the total area c o v e r e d with the liquid m e m b r a n e will be equal to half. Thus the slope o f the straight line
Journal of Colloid and Interface Science, Vol. 69, No. 2, April 1979
part of the Jv versus flap curve for 3 p p m concentration of P V M E (Fig. 2) should be equal to ((Lll s + LuC)/2), where Lla s and Lll c, respectively, are values of the slopes corresponding to 0 and 6 p p m concentrations of P V M E . Value of the slope thus computed c o m e s out to be equal to 0.366 × 10 -7 which m a t c h e s with the experimental value o f La~ for 3 p p m concentration of P V M E (Table I). Similar conclusions can be arrived at f r o m the analysis of the electro-osmotic velocity and streaming current data. ACKNOWLEDGMENTS This work forms a part of the project sponsored by the Indian Council of Agricultural Research New Delhi. We are grateful to Professor N. Lakshminarayaniah of Thomas Jefferson UniverSity, Philadelphia, Pa., for the generous gift of poly(vinyl methyl ether). REFERENCES 1. Martin, F., private communication to R. Kesting, March 1963. See also: Hwang, S. T., and Kammermeyer, K., "Membranes in Separation," Chap. VIII, p. 173. Wiley, New York, 1975. 2. Kesting, R., Vincent, A., and Eberlin, J., OSW R&D Report No. 117, Aug. 1964. 3. Kesting, R. "Reverse osmosis process using surfactant feed additives," OSW, Patent application SAL 830, Nov. 3, 1965. 4. Kesting, R., Subcasky, W. J., and Paton, J. D., J. Colloid Interface Sci. 28, 156 (1968). 5. Srivastava, R. C., and Abraham, M. G., J. Colloid Interface Sci. 57, 58 (1976). 6. Srivastava, R. C., and Avasthi, P. K., Kolloid Z. Z. Polym. 250, 253 (1972). 7. Srivastava, R. C., and Avasthi, P. K., J. Hydrol. 20, 37 (1973). 8. Katchalsky, A., and Curran, P. F., "NonEquilibrium Thermodynamics in Biophysics," p. 244. Harvard Univ. Press, Cambridge, Mass., 1965. 9. Spiegler, K. S., and Kedem, O., Desalination 1, 311 (1966). 10. Sherwood, T. K., Brain, P. L. T., and Fischer, R. E., Ind. Eng. Chem. Fundam. 6, 2 (1967). 11. Harris, F. L., Humphreys, G. B., and Spiegler, K. S., in "Membrane Separation Processes," (P. Meares, Ed.), Chap. 4. Elsevier, Amsterdam/New York, 1976.
Martin (1) observed that the addition of small amounts, of the order of a few parts per million, of surfactants like poly(vinyl methyl ether) (PVME) to saline feed in reverse osmosis effects a large increase in the salt retention capacity of cellulose acetate membranes with but a small decrease in the flux of desalted water. The explanation of the increased permselectivity was given by Kesting et al. (2-4) based on the hypothesis of the existence of a surfactant layer liquid membrane at the interface between the cellulose acetate membrane and the saline solution. The experiments of Kesting et al. (4) also demonstrated that as the concentration of the surfactant is increased, the cellulose acetate m e m b r a n e gets progressively covered with the surfactant layer liquid membrane and at the critical micelle concentration
(CMC) the coverage of the cellulose acetate membrane with the surfactant layer is complete. The experiments on hydraulic permeability, electro-osmotic velocity, streaming potential, and current reported in this paper lend further support to Kesting's liquid membrane hypothesis (2-4). The transport data have been utilized to estimate the fraction of total area of the supporting membrane covered with the liquid membrane when the concentration of surfactant is lower than its CMC value, and it has been concluded that when the concentration of the surfactant is half its CMC value the area covered by the liquid membrane is half the area covered at the critical micelle concentration. The data also indicate the possibility of the formation of multilayers of the liquid membrane as the concentration of the surfactant is increased beyond its CMC value. 280
0021-9797/79/050280-07502.00/0 Copyright © 1979 by Academic Press, Inc. All rights of reproduction in any form reserved.
Journal of Colloid and lnterJaee Science, Vol. 69, No. 2, April 1979
ELECTRO-OSMOSIS EXPERIMENTAL
Materials. Poly(vinyl methyl ether) (Aldrich MW 71,000) sodium chloride (BDH A.R. Grade), and distilled water distilled once over potassium permanganate in an all glass still were used in the present studies. Apparatus and procedures. For the measurements of hydraulic permeability, electroosmotic velocity, and streaming potentials a slightly modified version of the all glass apparatus described earlier (5) was used. The apparatus is diagrammed in Fig. 1 which has been well labeled to make it serf-explanatory. The all glass cell (Fig. 1) was separated into two compartments by a Sartorius cellulose acetate microfiltration membrane (Cat. No. 11107) of thickness 1 x 10-4 m and area 0.95 x 10-4 m2, which in fact acted as a support for the liquid membrane. For measurements of both hydraulic permeability and electro-osmotic velocity aqueous solutions of PVME of various concentrations ranging from 0 to 12 ppm filled compartment C on the right-hand side of the microfiltration membrane S (Fig. 1), and distilled water filled compartment D. Since value of the critical micelle concentration for the aqueous solutions of PVME is 6 ppm (4) the concentration
281
ranges from 0 to 12 ppm were purposely chosen in order to obtain data on both the lower and the higher side of the CMC, at which the supporting membrane is expected to be completely covered with the liquid membrane. The procedure followed for the measurement of hydraulic permeability, electro-osmotic velocity, and streaming potentials has already been described in earlier publications (5-7). For hydraulic permeability measurements known pressures were applied to compartment C containing the PVME solution, and electrodes E1 and E2 were short-circuited. Electrical potential differences needed for the measurement of electro-osmotic velocity were tapped from an electronically operated stabilized dc power supply (Bentronix, electrophoresis power supply Model No. E.P.-101). Streaming potentials were measured using a V.T.V.M. (Phillips Model GM 6009/90) of least count 0.01 mV. During the measurement of streaming potentials a correction was made for the asymmetry potential of the electrodes. Resistances of the systems were measured using a Leitffihigkeitsmesser conductivity meter. Streaming currents were calculated using Ohm's law, from the values of streaming potentials and resistances thus obtained.
L[
L2
TO PRESSURE HEAD
TI
T2
Q[
Q2
C
RI
EI~
D
,,//
~___~--\__/--
AI
~
\~/-
~
R2
A2
FIG. 1. The electro-osmotic cell. T1 and T2 are stop cocks, M~ and M2 are magnetic stirrers. S, cellulose acetate millipore filter, pore size 0.2 /xm. L~L2, capillary tube of length 18 cm and diameter 0.38 z 10-4 m. Volume of compartments C and D, 96 and 86 ml, respectively. A1 and A2 are B-19 glass joints. Q1 and Q2 are B-14 glass joints. Ej and E2 are bright platinum electrodes. R1R2, glass tubes containing mercury. Journal of Colloid and Interface Science, Vol. 69, No. 2, April 1979
282
SRIVASTAVA AND YADAV
The volume flux was measured by noting the rate of advancement of the liquid meniscus in the capillary L1L2 with a cathetometer of least count 0.001 cm and a stop watch of least count 0.1 secs. During the volume flux measurements the solutions in the two compartments were well stirred using magnetic stirrers M~ and Ms. All measurements were made at constant temperature by placing the apparatus (Fig. 1) in a thermostat set at 40 _ 0. I°C.
2 to 5. The usual linear phenomenological equations, i.e., + LI~Ar,
[1]
I = L21AP + L~2AqS,
[2]
Jv = LllAP
obtained using the nonequilibrium thermodynamic treatment (8) for the simultaneous transport of water and electricity, predict the following linear relationships. For hydraulic permeability (Jv)a*=0 = Lll ~p-
RESULTS AND DISCUSSION
For electro-osmotic velocity
The data on hydraulic permeability, electro-osmotic velocity, streaming potential, and streaming current for different concentrations of PVME is plotted in Figs.
(Jv)ae=o = L12A~b.
(A~b/AP)l=o = - L J L 2 2 ,
1.5
T 1.0
0 l:,< >
0.5
O_Ap0_~ 5
I0
15 AP X 10- 2
20
25
30
Nn~ 2
FIG. 2. The hydraulic permeability data. Curves I, II, III, IV are for 0, 3, 6, 12 ppm PVME, respectively; ©, experimental points; ×, theoretical points as predicted by the Eq. [8]. Journal of Colloid and Interface Science, Vol. 69, No. 2, April 1979
[4]
For streaming potential
2.0
,=:
[3]
[5]
ELECTRO-OSMOSIS
283
0.3
To
0.2
E o ><
> --)
0.1 lv"
o
i
I
I
I
IO
15
20
25
Adp~
30
35
VOLTS
FIG. 3. T h e Electro-osmotic velocity data. Curves I, II, III, IV are for 0, 3, 6, and 12 p p m o f P V M E , respectively.
and for streaming current (/)~,=0 = L21AP.
[6]
In Eqs. [1] to [6] Jv stands for the volume flux of water, ! stands for the flow of electricity, AP and A~b are the pressure difference and the electrical potential difference, respectively, and L~k is the phenomenological coefficient. The equality L12 = L21
[7]
holds among them because of Onsager's theorem. As is apparent from Figs. 2 to 5 the linear relationships [4] to [6] predicted from Eqs. [11 and [2] hold good in all cases (Figs. 3 to 5). Equation [3] however does not hold good for the hydraulic permeability data in presence of PVME (Fig. 2, curves II, III, IV). The water flux (Jr) versus pressure difference (AP) curves in all cases where PVME concentration is greater than zero (Fig. 2, curves II, III, IV) start from the origin, bend upward, then approach straight lines which
extrapolate to intercepts AP0 on the AP axis. The following equation was found to fit in the hydraulic flow data in all such cases. F Jv = L11[AP - AP0
When zXP assumes such high values that the term exp(-AP/Z~0) becomes much smaller than unity Eq. [8] simplifies to Jv = Lll[zIP - AP0]
[9]
which represents the straight line parts of the curves II to IV in Fig. 2. Since water flow through the cellulose acetate microfiltration membrane obeys the linear relationship [3] (Fig. 2, curve I) this kind of nonideal behavior (Eq. [8]) appears to be the result of the flow through the PVME liquid membrane formed in series with the cellulose acetate microfiltration membrane as Journal of Colloid and Interface Science, Vol. 69, No. 2, April 1979
284
SRIVASTAVA AND YADAV 15
I0
-
o >
O X
"0<3
5
--
0 ~
0
5
I0 Ap
15 x
Io-2
20
2,5
30
Nm- z
FIG. 4. The streaming potential data. Curves I, II, III, IV are for 0, 3, 6, and 12 ppm o f PVME, respectively.
hypothesised by Kesting et al. (2-4). A more definite indication of the formation of the liquid membrane can be had from the gradation in the values of the coefficient L~a as the concentration of PVME is increased from 0 to 12 ppm. Values of the coefficients L n for various concentrations of PVME, as estimated from the slopes of the straight line portions of the curves in Fig. 2, have been given in Table I. Values of the coefficients L~2, L21, and L22 estimated from the slopes of the straight lines in Figs. 3 to 5, for various concentrations of PVME, are also given in Table I. Values of the coefficient L~I which measure conductivity to volume flow of water, show a progressive decrease as the concentration of PVME is increased from 0 to 6 ppm (the CMC value). When the concentration of PVME is increased further the value of Lla also decreases but this decrease is less pronounced than the decrease which is observed up to 6 p p m - - t h e CMC value for aqueous PVME. Similar trends can be seen Journal of Colloid and lnterJace Science, VO]. 69, No. 2, April 1979
in the values of L12 and L21- These trends are in keeping with the liquid membrane hypothesis of Kesting et al. (2-4) according to which as concentration of the surfactant (PVME in the present case) is increased, the supporting membrane (the cellulose acetate microfiltration membrane in the present case) gets progressively covered with the surfactant layer liquid membrane, and at the CMC the coverage is complete. The decrease in the values of Lll beyond the CMC was ascribed by Kesting et al. (4), to increasing density of the liquid membrane which at the CMC is fully developed and completely covers the supporting membrane. There is, however, another possibility which must be looked into, viz, the possibility of formation of multilayers of the liquid membrane? The data on electrical resistances of the system (Table I) can be utilized to check this possibility. Since at 1 We gratefully acknowledge that our attention was drawn to this possibility by Dr. R. E. Kesting himself.
285
ELECTRO-OSMOSIS 35
30--
<
2o
~) o
×
[5
Io
5
0
0
5
io
L5
2o
25
AP
x 10- 2
Nrn 2
~,.
30
F1G. 5. The streaming current data. Curves I, II, III, IV are for 0, 3, 6, and 12 p p m of P V M E , respectively.
CMC (6 ppm) the liquid membrane completely covers the supporting membrane, the total membrane at 6 ppm can be viewed as the cellulose acetate millipore filter membrane plus the PVME liquid membrane in a series arrangement. Therefore the electrical resistance at 6 ppm can be written as
R1 stands for the resistance of the liquid membrane. At 12 ppm concentration, which is twice the CMC value for PVME, another layer of the liquid membrane would be formed in series. Hence the electrical resistance at 12 ppm concentration would be given by
R6 = R0 + R1,
Rlz = Ro + 2Rl,
[10]
[11]
where R0 and R6 represent the values of the resistances at 0 and 6 ppm of PVME and
where R12 stands for the value of R at 12 ppm concentration of PVME. From Eqs. [10] and [11] we can write
TABLEI
R12 = 2R6 - R0.
Values of the P h e n o m e n o l o g i c a l Coefficients L~,, L,2, L21, L22, and the E l e c t r i c a l R e s i s t a n c e at Various C o n c e n t r a t i o n s of P V M E
The value of R~2 computed from Eq. [i2] using the experimentally determined values of Ro and R6 (Table I), comes out to be equal to 0.495 × 106 ohm which matches very well with the experimentally determined value (Table I). This clearly indicates the formation of multilayers of the liquid membrane at surfactant concentrations higher than the CMC. According to the liquid membrane hypothesis (2-4), partial liquid membranes
Concentration of PVME (pprn) LH x 107 m 3 N - ' sec -~ L,2 × 106 m A J - ' L~, x 106 m A J - ' L22 × l0 S o h m - ' m -2 Resistance × 10 ~ ohm
0
3
6
12
0.486 0.936 0.925 2.36
0.38 0.63 0.62 2.33
0.246 0.44 0.45 2.23
0.212 0.37 0.36 2.14
0.445
0.45
0.47
0.49
[12]
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286
SRIVASTAVA AND YADAV
exist below and c o m p l e t e liquid m e m b r a n e s at or a b o v e the critical micelle concentration o f the surfactant. Utilizing the analysis for mosaic m e m b r a n e s (9-11) it is possible to estimate f r o m the transport data r e p o r t e d in this p a p e r (Figs. 2 - 5 ) , the fraction o f the total a r e a of the supporting m e m b r a n e , c o v e r e d with the liquid m e m b r a n e , at concentrations lower than the CMC. F o r this let us consider the hydraulic permeability data (Fig. 2) corresponding to P V M E concentrations equal to 0, 3, and 6 ppm. F o r simplicity of calculation we will focus attention only on the linear region o f the curves (Fig. 2). Since at concentrations l o w e r than the C M C the supporting m e m brane is only partially c o v e r e d with the liquid m e m b r a n e , the w a t e r flux for such a case would be given by the equation (A s + A C ) J v = L l l S A S A p + LI~CAC(Ap - AP0)
[13]
which on transformation can be rewritten as Jv :
[ t l l S ( A s A SA ) +c
+ LnC(AsA--~-Ac)]AP - Ln c
( ×
Ac As + Ac
) APo,
[14]
w h e r e the superscripts S and C stand for the supporting m e m b r a n e and the supporting m e m b r a n e c o v e r e d with the liquid m e m brane, respectively, and A represents the area of the m e m b r a n e denoted by the superscripts. Llx s and Lllc r e p r e s e n t the values o f La~ denoted b y the superscripts. Since at 6 p p m (the C M C value) concentration of P V M E the supporting m e m b r a n e is fully c o v e r e d with the liquid m e m b r a n e it is logical to expect that at 3 p p m concentration the fraction of the total area c o v e r e d with the liquid m e m b r a n e will be equal to half. Thus the slope o f the straight line
Journal of Colloid and Interface Science, Vol. 69, No. 2, April 1979
part of the Jv versus flap curve for 3 p p m concentration of P V M E (Fig. 2) should be equal to ((Lll s + LuC)/2), where Lla s and Lll c, respectively, are values of the slopes corresponding to 0 and 6 p p m concentrations of P V M E . Value of the slope thus computed c o m e s out to be equal to 0.366 × 10 -7 which m a t c h e s with the experimental value o f La~ for 3 p p m concentration of P V M E (Table I). Similar conclusions can be arrived at f r o m the analysis of the electro-osmotic velocity and streaming current data. ACKNOWLEDGMENTS This work forms a part of the project sponsored by the Indian Council of Agricultural Research New Delhi. We are grateful to Professor N. Lakshminarayaniah of Thomas Jefferson UniverSity, Philadelphia, Pa., for the generous gift of poly(vinyl methyl ether). REFERENCES 1. Martin, F., private communication to R. Kesting, March 1963. See also: Hwang, S. T., and Kammermeyer, K., "Membranes in Separation," Chap. VIII, p. 173. Wiley, New York, 1975. 2. Kesting, R., Vincent, A., and Eberlin, J., OSW R&D Report No. 117, Aug. 1964. 3. Kesting, R. "Reverse osmosis process using surfactant feed additives," OSW, Patent application SAL 830, Nov. 3, 1965. 4. Kesting, R., Subcasky, W. J., and Paton, J. D., J. Colloid Interface Sci. 28, 156 (1968). 5. Srivastava, R. C., and Abraham, M. G., J. Colloid Interface Sci. 57, 58 (1976). 6. Srivastava, R. C., and Avasthi, P. K., Kolloid Z. Z. Polym. 250, 253 (1972). 7. Srivastava, R. C., and Avasthi, P. K., J. Hydrol. 20, 37 (1973). 8. Katchalsky, A., and Curran, P. F., "NonEquilibrium Thermodynamics in Biophysics," p. 244. Harvard Univ. Press, Cambridge, Mass., 1965. 9. Spiegler, K. S., and Kedem, O., Desalination 1, 311 (1966). 10. Sherwood, T. K., Brain, P. L. T., and Fischer, R. E., Ind. Eng. Chem. Fundam. 6, 2 (1967). 11. Harris, F. L., Humphreys, G. B., and Spiegler, K. S., in "Membrane Separation Processes," (P. Meares, Ed.), Chap. 4. Elsevier, Amsterdam/New York, 1976.