Langmuir 1992,8, 1342-1346
1342
Permeabilities of Unsupported Ceramic Membranes of Alumina Mary J. Gieselmannt Water Chemistry Program, University of Wisconsin, Madison, Wisconsin 53706 Received April 15, 1991. I n Final Form: September 10, 1991 Most models for hydrodynamic permeability predict that the flow of an aqueous solution through a membrane that bears an electrostatic charge on the pore walls will be retarded when compared to the flow through uncharged pores under otherwise identical conditions. The prediction of flow retardation is based on the concept of a spontaneously generatedstreaming potential and subsequent electroosmotic backflow. To test the models, two types of unsupported membranes of alumina (A1203) were prepared which differed in composition, microstructure, and pore size (3.5- and 14.1-nmradii). The data from electrophoretic mobility titrations performed on ground membranes establishedthat the isoelectric point was pH 9.5-10.0 and that the electrostatic charge was fully developed at pH I7.0. However, the hydrodynamic permeabilities measured at pH values of 4,7, and 10 were not significantly different from each other for either type of membrane. Electroosmotic permeabilitieswere also much lower than predicted from the classic Smoluchowski equations. The results are consistent with the permeabilitymodels that correct the Smoluchowski equations for overlap of the electrical double layers which occurs in small pores (i.e., Kr 5 5).
Introduction A major concern of many industrial processes is the separation, concentration, and purification of the product and waste streams. The appeal of membranes for component separation is primarily based on the potential for conserving energy and, thereby, reducing costs. Ceramic membranes can be used in situations where organic membranes would fail due to the better resistance of the inorganic materials to (1)high pressures, (2) high temperatures, (3) mechanical wear, (4) organic solvents and other harsh chemical environments, ( 5 ) microbial attack, and (6) ionizing radiation. It is generally accepted that the electrostatic charge on the pore wall influences the permeability, selectivity, and fouling characteristics of a membrane. The use of oxide membranes with aqueous feed streams is further complicated because oxides have constant-potential surfaces (H30+ is a potential-determining ion) and the hydroxyl groups on the surface are amphoteric. As a result, both the sign and the magnitude of the charge on the pore wall of oxide membranes are a function of the composition of the solid (e.g., alumina or silica) as well as the pH and ionic strength of the feed stream. The main focus of the research described in this paper is the relationship between the hydrodynamic permeability of alumina membranes to aqueous electrolytesolutions and the electrostatic charge on the pore wall. One of the difficulties in studying transport phenomena in porous media is that a primary driving force can generate secondary driving forces which, in turn, affect the fluxes of solvent, solutes, and electrical current. For example, if a pressure gradient is used to drive a solution through a membrane, then filtration may occur. The accumulation of rejected solutes at the upstream face generates a gradient in chemical potential which results in osmosis, diffusion, and possibly a membrane potential. These complications were avoided in the present study by using alumina membranes with such large pores that no filtration occurred. However, when any solution is pressure-driven through a charged pore, a streaming potential is generated which, in turn, produces an electroosmotic backflow. This t
Current address: Dow Chemical Co., Midland, MI 48674.
0743-7463192f 2408-1342$03.00/0
retardation of the net flux in the forward direction is known as the primary electroviscous effect.’ Darcy’s law, which is one of the simplest models that describes hydrodynamic permeability, is given by dV K A P -=dt 7L where dV/dt is the volumetric flow rate or flux, K is the permeability constant, AP is the pressure drop across the membrane, and 9 and L are the viscosity of the solution and length of the pore channel, respectively. Poiseuille’s equation for a straight cylindrical pore and the KozenyCarman equation for media with a complex structure of interconnected porosity are also commonly used to describe hydrodynamic permeability. The three equations mentioned above do not deal specifically with the effects of electrostatic charge. Consequently, it is helpful to consider a set of phenomenological equations of the type utilized in the analysis of the thermodynamics of irreversible pr0cesses.~-5
J, = L,, AP + L12AE + L,,
Ap
I L,, AP+ L,, AE + L,, Ap
(2)
J , = L,, AP+ L,, AE+ L,, Ap These equations couple the volumetric flux of volume (primarily solvent) (&), electrical current (I),and solute flux (J,)to the driving forces of pressure (AP), electrostatic potential (A@, and chemical potential ( A p ) via nine phenomenological coefficients (Lij). In the absence of electrostatic and chemical potential differences, the hydrodynamic permeability can be related to the coefficient (1) Hunter, R. J. Zeta Potential in Colloid Science -Principles and Applications; Academic Press: New York, 1981. (2) Devereux, 0. F. Topics in Metallurgical Thermodynamics; WileyInterscience: New York, 1983. (3) Starzak, M. E. The Physical Chemistry of Membranes; Academic Press: New York, 1984. (4)Pusch, W. Desalination 1986,59, 105. ( 5 ) van der Put, A. Ph.D. Thesis, Landbouwhogeschool te Wageningen, The Netherlands, 1980.
0 1992 American Chemical Society
Langmuir, Vol. 8, No. 5, 1992 1343
Unsupported Ceramic Membranes of Alumina
(3)
This equation assumes that either the solid surface is electrically neutral or that the membrane has been shortcircuited to eliminate the streaming potential. If short-circuiting electrodes are not present and if the membrane pores are charged, then the decreased hydraulic permeability is given by = L”[ 1-
&]
(4)
where the expression in brackets is called the electroviscous retardation factor.5 The second term inside the brackets is related to the streaming current and the streaming potential. The various interaction coefficients can be measured experimentally. However, because the model is not predictive, it would be necessary to determine the coefficients for each solution/membrane combination. In an attempt to make eq 4 predictive, Khilar6used the classicSmoluchowski equations for streaming current ( I d and potential (Est).
where t is the permittivity, {is the zeta potential, k, and k, are the bulk and surface conductivities, respectively, and r is the pore radius. The retardation of the flow due to the primary electroviscous effect was then modeled as a decrease in the permeability constant in Darcy’s law. This treatment led to the following expression for the ratio of flow in an uncharged pore to the flow in the same pore when there is an electrostatic charge on the pore wall.
Since the Smoluchowski equations were used, this model is restricted to low { potentials and situations where the pore radius, r, is large when compared to the thickness of the diffuse part of the double layer, K-’, Le., to cases where Kr > 300.’ Under these circumstances, however, the electroosmotic backflow is insignificant and the value of the second term in the brackets in eq 6 is negligible. Rice and Whitehead7 also derived an expression to predict the interaction between electrostatic charge on the pore wall and the hydrodynamic permeability of the pore. Their use of the linearized form of the PoissonBoltzmann equation restricts the proper application of their model to situations were the { potential is low. However, the Smoluchowski equations were corrected for small values of Kr and especially for the secondary electroviscous effect due to the overlap of the electrical double layers which occurs under conditions where Kr < 5-10.’ The flow retardation was not modeled as a decrease in the permeability constant, as was done in eq 6, but as an increase in the apparent viscosity. According to this model, when the ratios of apparent to actual viscosities were calculated for different potentials, the ratios showed maxima when plotted against K r (at Kr = 2.2). The ratios tended to 1in the limits of both large and small values of Kr. The magnitudes of the viscosity ratios increased with the {potential but were significantly lower than the values calculated according to the model of Khilars under ~
~
~
~~~
(6) Khilar, K. C. Ind. Eng. Chem. Fundam. 1983,22,214. (7) Rice, C. L.; Whitehead, R. J.Phys. Chem. 1965, 69,4017.
comparable conditions. However, when Kr is very large, the correction factors cancel out and the equation of Rice and Whitehead reduces to a form nearly identical to that of Khilar. Finally, Levine et alS8took an approach similar to that of Rice and Whitehead.I However, they introduced a factor F that corrects Smoluchowski’s equation for high surface potentials (+a) and reduces. the electroosmotic velocity to zero as Kr 0. F, which has values between 0 and 1,also depends upon the properties of the electrolyte. Levine et al. also employed a second correction factor, G, which was defined as the ratio of the mean electrostatic potential across the pore to the {potential. G also depends on Kr and and, like F, varies between 0 and 1. By introducing the parameters F and G, Levine et al. corrected for high potentials and both the primary and secondary electroviscous effects. Their expression for the ratio of the apparent viscosity (va) to the actual viscosity (9) is given by
-
c
. -1
(7)
where 0* depends on the properties of the electrolyte, but not its concentration. Like the model of Rice and Whitehead? when eq 7 from Levine et al.8 is plotted against Kr, the viscosity ratios exhibit maxima at intermediate values of Kr but tend to 1when Kr is either very small or very large. The two models differ, however, when plotted against the potential. In this case, the viscosity ratios from eq 7 show maxima at intermediate potentials but tend to 1in the limits of very high or very low potentials. In contrast, the viscosityratios calculated according the Rice and Whitehead rise monotonically with potential. The two models predict nearly identical flow retardations a t low potentials. But a t high potentials > 100mV) ,the model of Levine et al. predicts much lower flow retardations than that of Rice and Whitehead. At all potentials, the models of Levine et al. and Rice and Whitehead predict much lower flow retardations than that of KhilarG described earlier. The goal of the research reported here was to test the last three models described above by comparing the permeabilities of unsupported alumina membranes under conditions were the pore walls are charged and uncharged.
Materials and Methods The unsupported alumina membranes used in the following experiments were prepared by sol-gel processing as described in detail elsewhere? Twotypes of membranes,designated‘mediumpore” and “small-pore”,were studied. Both types were shaped like disks with a diameter of ca. 3.5 cm and a thickness of ca. 200 pm. The medium-pore membranes were made of a-Al203 with a microstructure composed of micrometer-sized grains with a great deal of intragranular porosity. These membraneshad pores with a modal radius of 14.1 nm and 24% porosity. The smallpore membranes were composed of transition aluminas. The microstructure was a random packing of spheroidal-shaped aggregates,each ca. 50 nm in diameter. The modal pore radius was 3.5 nm with a total porosity of 32 % . The electrophoreticmobilitydata were collectedusing a System 3000 automated electrokinetics analyzer (PenKemInc.,Bedford Hills, NY). The suspensions used in the electrophoretic titrations were prepared from powders made by hand grinding membranes in a mortar and pestle of synthetic sapphire (Diamonite Products, Shreve, OH) to minimize contamination. A sample of the powder was added to an aliquot of the electrolyte (8)Levine,&; Marriott, J. R.;Neale, G.;Epstein,N.J.Colloidlnterface Sci. 1975, 52, 136. (9) Gieselmann, M. J. Ph.D. Thesis, University of Wisconsin, Madison, WI, 1991.
Gieselmann
1344 Langmuir, Vol. 8, No. 5, 1992
m
d
d
A - Opening through which pressure i s a p p l i e d t o t h e upstream s o l u t i o n r e s e r v o i r . B - Capped opening f o r f i l l i n g and emptying t h e solution reservoir. C - Solution reservoir. D - S l i d i n g c o l l a r t o hold the 2 solution r e s e r v o i r s and t h e membrane h o l d e r t o g e t h e r . E - O-ring. F - H o l d e r f o r ceramic membrane. G - Barbed f i t t i n g t h a t connects t h e t u b i n g between t h e downstream s o l u t i o n r e s e r v o i r and t h e graduated c a p i l l a r y p i p e t t e used t o measure t h e v o l u m e t r i c f l o w r a t e .
Figure 1. Diagram of one of the cells used in the permeability measurements. A ceramic membrane is shown attached to the membrane holder. solution. The suspension was sonicated with occasionalshaking for 10 min, and then the larger particles were allowed to settle for a few minutes. The remaining suspension was transferred to a wide mouth poly(methy1pentene) jar used for the titrations. Electrolyte solution was added to give a final solids concentration of 100-200 mg/L. Although preliminary experiments showed that C02 did not adsorb to the alumina particles, the titrations were peformed with the sample under a N2 atmosphere to avoid pH drift due to the absorption of COz into basic solutions. The alumina samples were aged for 2.5 h at a pH value below 5. (Aging up to 5 weeks did not alter the results.) Three titrations were performed on each type of alumina powder. The ionic strengths of the suspensions in each set were 1E-3 M, 1E-2 M, and 1E-1 M in KC1. The titrations were performed by adding aliquots of stock KOH solutions until the final pH was greater thin 12. (The KOH and KC1 were both from Aldrich Chemical Co., Milwaukee, WI.) Mobilities of the particles were measured from at least two portions on the suspension at each pH. Data from at least 15 different pH values were collected during each titration. In general, the titrations were performed quickly, i.e., in less than 3 h. A diagram of one of the cells used to measure hydrodynamic permeabilities is shown in Figure 1. A cylinder of Nz gas was employed to apply pressure to the liquid on the upstream side of the membrane. The pressure was measured by means of a Baratron Type 122A absolute pressure gauge connected to a PDR-D-1 power supply/digital readout (MKS Instruments, Inc., Andover, MA). All of the tubing, stopcocks, valves, and connectors between the nitrogen tank and the permeability cell were made of Teflon PFA (Galtek fittings from Fluoroware, Inc., Chaska, MN). The cell, collars, and membrane holders were fabricated of acrylic materials while the O-rings and washers were made of Viton (E.I. duPont de Nemours & Co., Wilmington, DE). Each ceramic membrane was attached to a membrane holder by means of a ring of silicone rubber sealant. A constant temperature of 25.0 0.2 OC was maintained by submerging the cell and graduated pipet into a water bath (Lauda Model RC-20 refrigerated bath with a Model T-2 immersion circulator, Brinkmann Instruments Inc., Westbury, NY). In a typical measurement of hydrodynamic permeability, the test solution of a specific pH and ionic strength (see Tables I and I1 for the actual values) was prepared and degassed for at least 5 min by means of a sonicator and partial vacuum obtained from
*
Table I. Summary of Hydrodynamic Permeability Data for Alumina Membranes with a Nominal Modal Pore Radius of 14.1 nm test solution average permeability,a rL/(min-atm) test solution water ratio pH [KCll, M 4.0 1E-4 8.03 8.16 0.98 4.0 1E-4 7.38 7.21 1.02 4.0 1E-3 9.44 9.79 0.97 9.53 4.0 1E-3 0.96 9.98 4.0 1E-2 1.02 9.57 9.41 1.01 9.86 4.0 1E-2 9.78 8.43 1.04 7.0 1E-2 8.10 1.02 9.27 9.13 1E-2 7.0 1.02 9.44 9.22 7.0 1E-2 7.17 0.99 7.29 10.0 1E-3 6.71 10.0 1E-3 6.76 0.99 10.2b 1E-2 8.53 1.00 8.51 7.97 10.2 1E-2 0.96 7.66 11.0 1E-2 8.62 0.91 7.85 11.0 1E-2 7.23 7.79 0.93 a Permeabilities for each solution were determined at three different applied pressures in the range 0.35-0.65 atm. The initial pH of the test solutions was 10.22. After completion of the measurement,the pH of the solution in the cell reservoirs was 10.15. This difference is not considered significant. Table 11. Summary of Hydrodynamic Permeability Data for Alumina Membranes with a Nominal Modal Pore Radius of 3.5 nm test solution permeability ratio test solution water PH [KCll, M 1.16 7.0 1E-1 0.342 0.294 1.02 7.0 1E-1 0.392 0.385 0.298 0.286 7.0 1E-2 1.04 0.380 0.387 7.0 1E-2 0.98 10.0 1E-3 0.281 0.302 0.93 10.0 1E-3 0.99 0.287 0.290 10.0 1E-3 0.357 0.97 0.367 0.350 0.353 10.0 1E-3 1.01 11.0 1E-2 0.235 0.278 0.85 11.0 1E-2 0.321 0.367 0.87 Permeabilities for each solution were determined at a single applied pressure of ca. 1.0 atm. a water aspirator. The solution was then maintained under a Nz atmosphere to prevent the reabsorption of C02. The cell reservoirs were rinsed twice with the solution and then filled and capped, with the entire rinsing and filling procedure taking less that 5 midcell. The pores of the membranes were then flushed with the new solution by the application of a pressure drop across the membrane higher than any pressure used in the subsequent permeability measurements. A t least 150 rL of solution wae flushed through the membranes (ca. 5 times the effective pore volume of the membranes). After this flushing procedure, the actual permeability measurements were performed. The entire procedure was then repeated using degassed water as a reference liquid. The cell shown in Figure 1 was also employed in the electroosmotic permeability studies. Reversible Ag/AgCl electrodes were positioned in the cell reservoirs through the end openings (ports B in Figure 1). The electrodeswere prepared by a standard electrolysis procedure from pieces of silver wire (1-mm diameter, 99.9%,from Aldrich, Milwaukee, WI). During both the electrode preparation and the actual permeability measurementa,the direct current was supplied by a Model 224 programmable current source and monitored by a Model 197 autoranging microvolt digital multimeter (both from Keithley Instruments, Inc., Cleveland, OH). Measurements of pH were performed with a Ross sure-flow combination electrode (model 81-72)and a Model 701A digital pH/mV meter (both from Orion Research Inc., Boston, MA). Sonications of solutions and suspensions were performed in a Model 1200R-1 ultrasonic cleaner (Branson Ultrasonics Corp., Danbury, CT). All reagenta were analytical grade or better and were used
Langmuir, Vol. 8, No. 5, 1992 1345
Unsupported Ceramic Membranes of Alumina 150
-
3 ’ a
f
s
TM IE AP
-0
25
(MIN)
PERM
so
75
TM IE
100
12s
150
(MINI
Figure 2. Pressure-driven flow of water through a mediumpore membrane (top) and a small-pore membrane (bottom) as a function of time. without further purification. Solutions were made from high resistivity water (1.8E7Q-cm)produced by feeding water first through a reverse-osmosisfilter and then through a Milli-Qwater purification system (Millipore Corp., Bedford, MA).
Results and Discussion The results of the electrophoretic mobility titrations indicated that the isoelectric point (IEP) of the powders from both types of membranes was pH 9.5-10.0. For pH < 7.0,the mobilities remained constant at their maximum values of 4.0 and 3.OE-8 m2/(V*s)for the medium- and small-pore membranes, respectively. potentials of 52 and 39 mV were calculated according to O’Brien and Whitelo for the two mobility values, respectively. A particle radius of 1 pm and [KC11 = 1E-2 M (i.e., Kr = 330) were used in the calculations. Figure 2 contains data cn the volumetric flow of water under a pressure gradient as a function of time. The data for the medium-pore membrane (Figure 2, top) are extremely linear (coefficients of determination 20.999) and pass through the origin. The average permeability of water for this membrane is 7.97 f 0.17 pL/(min.atm). Similar data for a small-poremembrane (Figure 2, bottom) exhibit more scatter. At the lowest pressure applied, the data were linear from the start of the test. However, as the pressure gradient across the membrane was increased, the permeability of the membrane was initially high and then declined to a steady value during the first l/2 h of the test. As a result, the straight lines used to calculate the permeabilities at the two higher pressures do not pass through the origin. Nevertheless, the coefficients of determination for the three lines in Figure 2, bottom, are 20.996. The average permeability of water for this smallpore membrane was 0.356 f 0.027 pL/(min-atm). Table I summarizes the permeability data for mediumpore membranes obtained using different aqueous solutions. Combinations of four different pH values and three different concentrations of KC1 were tested. Although (10)O’Brien, R. W.;White, L.R. J . Chem. SOC.,Faraday Trans. 2 1978, 74, 1607.
the data on the porosities and pore size distributions of these membranes are quite reproducible, the thicknesses and effective membrane areas varied by as much as 10%. To eliminate the effectsof variability between membranes, the permeabilities to the test solution and a standard solution (i.e., pure water) were measured on the same day. The ratio of these two permeabilities is presented in the last column of the table. On the basis of the electrophoretic data, the IEP of the pore walls was 95-10 and the walls were fully charged at pH 4 and 7. However, the permeability ratios for all of the test solutions with pH values of 4, 7, and 10 vary between 0.96 and 1.04; Le., they are not very different from 1.0. Finally, the test solutions with a pH of 11 had relative permeabilities through the medium-pore alumina membranes that were the lowest of all solutions tested. At present, there is no explanation as to why a pH 11 test solution should move through the pores so much more slowly than water. Table I1 contains a summary of corresponding data for small-pore membranes. The permeability of the first solution tested (pH 7) is ca. 16% higher than that of water. However, this increase in permeability was not observed in the other three trials at pH 7. Hence, the first entry is probably an artifact. The four entries for the test solution with pH 10 also do not show ratios very different from 1.0. The flux of the pH 11 test solution appears to be significantly and consistently lower than that of water; Le., the permeability ratios are 0.85 and 0.87. As with the permeability data for the medium-pore membranes at the same pH, this result cannot presently be explained. The electrophoretic data for the medium-pore membranes in contact with acidic solutionsyielded a {potential of 52 mV. Khilar’sg model predicts a permeability ratio of 1.58 (assuming a surface conductivity of the pore liquid of 1E-9/Q) while the model of Levine et predicts a ratio of 51.1 for Kr = 4.65 (for 1E-2 M KC1). Although the difference in the values predicted by the two models is not large, the data in Table I are consistent with the model of Levine et al. For small-pore membranes, with a tpotential of 39 mV for a fully charged surface (Le., pH I7), Khilar’s6model predicts a permeability ratio of 5.85. On the other hand, the model of Levine et aL8 predicts a permeability ratio for Kr = 1.16 (Le., [KC11 = 1E-2 M) of
