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Langmuir 1993,9, 1150-1155
Hydraulic and Electroosmotic Flow through Silica Capillaries Heyi Li and Robert J. Gale* Department of Chemistry, Louisiana State University, Baton Rouge, Louisiana 70803 Received November 20,1992. In Final Form: January 25,1993
Electrokineticeffects are of renewed interest since the emergence of new separation techniques such as micellar electrokineticcapillary chromatographyand the proepecta for a variety of soil decontamination technologies. In this study,hydraulicandelectrooemoticflowthrough silicacapillaries,50-100 pm diameters, have been determined experimentally and analyzed theoretically. Hydraulic flow follows the Poiseuille relation very well; however, with increase of the ionic strength of the fluid, the rate of electroosmoticflow decreases. Particularly, the energy consumptions are compared for hydraulic and electroosmotic flow. Resulta show that, in general, hydraulic flow is much more energy efficient than electrmmotic flow because of bulk IR losses in the latter. The classical theory for electrokinetic phenomena possibly overestimates the transfer of electrical into mechanical energy since both irreversible thermal as well as ion migration energy loases occur in the conductance of double layer ions. The physical significance of the electrokineticzeta potential based on classical theory, 1; needs to be carefully reexamined.
Introduction Capillary zone electrophoresis (CZE) and micellar electrokinetic capillary chromatography (MECC) have been growing very rapidly during this decade. This is because they offer speed and highly efficient separations, especially for macromolecules in the important area of analytical biotechnology, e.g. refs 1and 2. Also,in recent years, electrokineticsoilprocessing has been widelystudied as a practical means to remove contaminants from oils.^.^ The four major electrokineticphenomenain geotechnology are electroosmosis, streaming potential, electrophoresis, and migration (or sedimentation) p~tential.~ Electroosmosis and electrophoresisare the movement of electrolyte and charged macromolecules, respectively, due to application of an electric field. Streaming and sedimentation potentials are the generation of currents due to the movement of electrolyte under hydraulic potential and movementof charged particles under gravitational forces, respectively. Electroosmosis has been given the most attention in geotechnical engineering of the four phenomena, because of its practical value for transport of water in fine-grainedsoils and the ease by which electrical pumping can be induced in low permeability clays. It is, therefore, of considerable practical as well as theoretical interest to study the energeticsand efficienciesof hydraulic and electrokinetic flow in porous media. To simplify the experimental design, we have chosen to determine both hydraulic and electroosmoticflow velocities in cylindrical silica capillaries of diameter 50-100 Fm. Theoretical Background Considering first hydraulic flow through a single capillary,the flow rate, if laminar flow conditions exist, might be described by the Poiseuille equation, e.g. ref 6. The (1) Ghowsi, K.; Foley, J. P.; Gale, R. J. Anal. Chem. 1990, 62, 2714. (2) Ghowsi, K.; Gale, R. J. J. Chromatogr. 1991,559,95. (31 Acar, Y. B.; Alshawabkeh, A.; Gale, R. J. Proceedings of the Mediterranean Conferenceon Environmental Ceotechnology; Balkema Publishers Inc.: Rotterdam, Netherlands, 1992, p 321. (4) Gale, R. J.; Li, H.; Acar, Y. B. Soil Decontamination using ElectrokineticProcessing. In Environmental OrientedElectrochemistry; Sequeira, C . A. C., Ed.;Elsevier Science Publiehers, in press. (5) Mitchell, J. K. Fundamentals of Soil Behavior; John Wiley and Sons, Inc.: New York, 1976; pp 117 and 353-359. (6) Stulik, K.; PacAkovB, V. Electroanalytical Measurements in Flowing Liquids; John Wiley & Sons: New York, 1987; pp 36-41.
velocity of flow (cm/s) is dependent on the layer distance from the tube central axis and given by
Thus, it is a maximum at the tube axis and assumed to be zero at the wall. The total flow rate Qh (cm3/s)is given by
in which R is the capillary radius (cm), L is the length of the capillary (cm), Ap is the pressure (dyn/cm2),and q is the fluid viscosity. Figure l a (ref 6) illustrates the velocity profile of hydraulic flow through a capillary. The hydraulic force is evenly applied to the whole region of cross section of the capillary. At the tube inlet, the profile is rectangular. On passage through the tube, boundary layers develop at the walls and their thickness increases until they merge at a certain distance, x , from the inlet. The length x is called the entry region. Also, the velocity profile approaches to a steady-state laminar flow profile, the velocity in the center of the tube increases to maximum value, vm=, and the velocity at the walls is zero. The equation which is used in geotechnicalengineering to describe the hydraulic flow rate Qh in soil systems is5 Qh (4) in which k h is hydraulic conductivity and i h = (HILI the hydraulic gradient, where H is the hydraulic head pressure and L is the length of soil section. If p is the density of fluid and g is the gravitational constant, it, = ( H / L )and A = rR2;thus kh a pgR2/(87).Factors to account for the effects of porosity and tortuosity need also to be included in a practical description. There are several theories which attempt to describe the basic velocity profile of electroosmosisin a One of them most widely used for large core capillaries is
0743-7463/93/2409-1150$04.00/0 Q 1993 American Chemical Society
Langmuir, Vol. 9, No.4, 1993 1151
Flow through Silica Capillaries
I
E
'7' 2R
soil system, we obtain an equation for expressingthe flow rate due to electroosmosis
.l.
Q, = k,i,A (8) in which ie = ( E / L ) is the electrical gradient and k, is termed the coefficient of electroosmoticpermeability;the parameter k, can be found from the relation k, a -({D/ 4uq)n, where n = the porosity of soil system and A = ita cross section area. Note that these important expressions depend on the validity of the classical electrokinetictheory. Our purpose of determining the hydraulic flow through a capillaryis to comparethe hydraulic (mechanical)energy with the electric energy which causeselectrolyte flow. The hydraulicflowthrough silica capillarieshas been measured and analyzed in this paper. Also,the electroosmoticflow through the same kind of capillary has been studied. Efficiency and energy consumption are compared for the two flow types.
I
Experimental Section Figure 1. Velocity profiles obtained from (a) hydraulic (Poiseuille), and (b) electroosmotic(Helmholtz-Smoluchowski) flow.
the Helmholtz-Smoluchowski theory. In this theory, the average fluid electroomosisvelocity, u, through a capillary is u -({D/4uqWL) (5) in which D is dielectric constant of the electrolyte, q (poise or dps/cm2) is its viscosity, E is the applied electric potential, L is the length of capillary, and 2 is called the electrokineticzeta potential. Figure l b shows the velocity profile of electroosmosisthrough a capillary. The electric force is applied very near the surface (tothe electricdouble layer) at the tube wall. The large pore theory predicts a maximum flat velocity profile through most of the capillary, with zero velocity at the wall of the capillary. Earlier fundamental studies of capillary electroosmosis include those of Rutgers et al.2 Rice et al.? Koh et al.? and Ohshima et al.l0 An extensive review of the literature prior to 1974 is available.ll Schufle et al.12J3and Rutgers et al.7evaluated the total conductance of solutions in some glass capillaries. The followingformula for macroscopicconductanceproperties is given L
where R is the total resistance, L is the length of capillary, r is the capillary radius, uo is the specific conductivity in the bulk solution,and usis the swxlled specificor apparent surface conductivity. By measuring the total resistance R, uI can be calculated. The values of usare in the range of 10-5 to 10-9 S for capillaries from a few pm to 100 pm diameter, depending on the solution concentration and diameter. From eq 6, the specific surface conductivity, a two-dimensional property, can be determined
(7) Electroosmosis in a porous medium similarly can be analyzed using a capillary model. By applying eq 5 to a (7) Rutgere, A. J.; De Smet, M. Trans. Faraday SOC.1947, 43, 102. (8) Rice, C. L.; Whitehead, R. J. Phys. Chem. 1965,69,4017. (9) Koh, W.-H.; Anderson, J. L. AIChE J . 1975,21, 1176. (10) Ohshima, H.; Kondo, T.J. Colloid Interface Sci. 1990, 135 (2), 443-448. Hydrodyn. 1989, I I , 785. (11) Dukhin, S. S.; Derjaguin, B. V. Surf. Colloid Sci. 1974,7,49-272. (12) Schufle, J. A.; Yu,N.-T. J . Colloid Interface Sci. 1968,26, 395. (13) Schufle,J. A.; Huang, C.-T.;Drost-Hansen, W. J.Colloid Interface Sci. 1976, 54, 184.
Fused silica capillary (J & W deactivated fused silica capillary, Alltech Co.) was used in the studies. The diameters of capillaries were measured under a microscope (Bausch & Lomb) and by magnifying with a video camera (a CCTV camera, Model HV720u; a Philips VCR, Model VR6495AT; a Hitachi video monitor, Model VM-9001.1). T w o standard scales (2 pm X 50 divisions and 50 pm x 50 divisions) were used for calibration. Before each experiment, the capillary was flushed with deionized water (about 2 mL) or flushed with electrolyte (for the electroosmosis experiments) to equilibrate the surface. KC1 (reagent grade) was recrystallized first and dried, then 1.00 M stock solution was prepared with high-quality deionized distilled water. Dilute KC1 solutions were made from this stock. Hydraulic flow was studied for two different sizes of capillary (52 and95 pm diameters). A large glass tube (9.2 mm in diameter) was filled with water or KC1 solution and set up vertically. T w o different heights of water were used, one was total height, 122 cm, and another was half height, 62 cm. A capillary was connected to the bottom of the large glass tube and placed horizontally with a small cylinder to collect water emerging a t the end of the capillary. The amount of flow was measured by weight in hydraulic experiments. T w o different lengths of 95 pm diameter capillaries were used; one length of capillary was total length, 12.8 cm, and another half length, 6.1 cm. Also, two different lengths of 52 pm diameter capillary were used, 12.9 and 6.6 cm, respectively. Electroosmotic flow was studied in a 95 pm diameter capillary with a length of 19.3cm. The electric potential acrossthe capillary was 1500 V (HP 6515A dc power supply). The method used to measure the electroosmoticflow rate was the current-monitoring method.14 A capillary tube and cathode reservoir were filled with KCl solution a t a concentration C, and the anode reservoir was filled with KC1 solution at concentration 0.95C. With the application of an electric field across the capillary, the solution in the anode reservoir is pumped electroosmotically toward the cathode, and the conductivity in the capillary is monitored. As a consequence, the current changed during the electroosmosis operation until one complete pore volume is replaced with the lower concentration electrolyte. In order to determine the capillary surface conductances, the conductivity of KCl solution first was measured by a CDM83 conductivity meter. Then, the resistance of KC1 solution in a capillary of 95 pm diameter and 2 cm long was measured by a PAR Model 124 lock-in amplifier, using ac a t 200 Hz and a Teflon holder. While this amplifier was calibrated with knownresistors, the error was within i 2 % , using ac frequencies less than 1kHz. The reason an ac method was used is to avoid the errors due to electroosmosis of solution in the capillary. All experiments were made at the ambient laboratory temperature, 23 i 2 OC approximately. The viscosities of water and (14) Huang, X.; Gordon, M. J.; &re,
R. N. Anal. Chem. 1980,60,1837.
Li and Gale
1152 Langmuir, Vol. 9, No.4, 1993
Total n i i h t of Water
Half Height of Water
v-
0
Time (hours) Figure 2. Hydraulic flow of water and 0.05 M KCl through a capillary (95 pm diameter, 12.8 cm length): total height = 122 cm, half height = 62 cm.
. --
20
40
60
80
100
120
140
Time (hours)
Figure 4. Hydraulic flow of water through a capillary (52 pm diameter): total height = 122 cm; total length = 12.9 cm, half length = 6.6 cm. Table I. Hydraulic Flow Rate Comparison of Expbriment and Theory
140
130 120 110
test no.
-
L
0
1
2 3 4 5 6 7
10
20
30
40
50
60
70
80
90 100 110
diameter): total height of water 122 cm; total length = 12.8 cm, half length = 6.1 cm.
experimental flow rate" (mL/h) 0.613 0.023 0.605 0.009 0.718 0.007 0.307 0.003 1.527 0.005 0.0495 O.OOO8 0.116 0.003
* * ** **
theoretical flow rate (mL/h) 0.728 0.728 0.730 0.372 1.53 0.0670 0.131
Diameter of Capillary: 95 1 pm testa 1 and 2 total length of capillary, 12.8 cm; total height of water, 122 cm test 3 total length of capillary; total height of 0.05 M KCl solution, 122 cm total length of capillary; test 4 half height of water, 62 cm test 5 half length of capillary, 6.1 cm; total height of water
Time (hours)
Figure 3. Hydraulic flow of water through a capillary (95 pm
correlation" 0.9856 0.9953 0.9978 0.9976 0.9995 0.9989 0.9952
test 6 test 7
Diameter of Capillary: 52 0.7pm total length of capillary, 12.9 cm; total height of water, 122 cm half length of capillary, 6.6 cm; total height of water
0.067 M KCl were calculated using data from the CRC Handbook of Chemistry and Physics;69th ed.
" Obtained from least-squares line to linear section by Lotus 123.
Results and Discussion Hydraulic Flow Analysis. Hydraulic flow tests have been made to assessthe flow rates in capillaries by applying different pressures to different lengths of capillary. The results are shown in Figures 2-4 and are summarized in Table I. The flow rates after about 2 days are smaller than those at the beginning of the experiments, probably due to clogging of the capillary by adventitious dust or biological debris. In accordance to eq 3, the hydraulic flow rate Q h is proportional to R4. For the two different sizes of capillary used in the experiments, the ratio of the two flow rates should be close to 11.1 [(95/52)41.Comparing the experimental flow rates for the two different sizes of capillary, the agreement is reasonable, e.g. 0.61/ 0.049 = 12. Also, for a same size capillary, by increasing the height of water, the flow rate increases directly with the pressure head (Qh H). Again, reasonable agreement is observed, e.g. 122162 = 1.97(theory),0.61/0.307= 1.99 (observed). With an increase of the length of the capillary,
the flow rate decreases with the reciprocal length (Qh a l/L). For example,6.6/12.9= 0.512(theory),0.0495/0.116 = 0.427 (observed). The last column of Table I was calculated based on eq 3,and the theoretical flow rates are larger by 20% error maximum in the worst case. The reasons for smaller experimental flow rates might be due to small particles slightly clogging the capillary, electrostatic or frictional drag on the ill-defined surface of the capillary, the errors in the measurement of the capillary diameter, solvent evaporation, etc. We concludethat the classical Poiseuillemodel for flow can predict and account for the aqueous flow rates at room temperature through these silica capillaries as functions of applied pressure and radius and length of capillaries for the ranges of conditions tested. Energy Analysis of Hydraulic Flow. For an energy analysis of hydraulic flow, the potential energy, mgH, is used to cause flow, g is the gravitational constant, His the height of water, and m is mass. From the law of conservation of energy
Qc
Flow through Silica Capillaries
Langmuir, Vol. 9, No. 4, 1993 1153
also been presented by others, e.g. refs 8,9, and 16. When, for example, the double layer has an excess of cations in the solution phase and an electrical field parallel to the capillary surface is applied, a net, directional force is exerted by the cations on the liquid causing it to move. At steady state, the electrical force on a cation is assumed to be equal and opposite to the frictional slip forces within the liquid. If, however, we postulate that the electrical force is not transferred completely to mechanical energy since some of the energy may be lost in heating or eddy current effects, the equation relating velocity to applied electrical force becomes
/I
/I I/ 0.2 0.004
0.006
0.008
0.01 0
0.01 2
0.01 4
Energy Consumption/Volume (J/ml)
Figure 5. Energy consumption per volume of hydraulic flow versus flow rate.
mgH = '/2mu2+ (energy consumed)
where u is the velocity of fluid exiting the capillary and '/*mu2is the kinetic energy of the escaping fluid. So the energy consumption/flow volume, b E h , can be calculated as follows h E h = (mgH - '/2mU2)/Qht= PgH - ' / 2 ~ u=2 PgH
(J/mL) (9)
where p is the density of fluid; thus m = pV = pQht. The kinetic energy, l/zpu2is very small for this hydraulic flow and can be ignored. For example, in a 95 pm diameter, 12.8 cm length capillary, if H = 1.22 m (total height), Qh = 0.72 mL/h (theoretical flow rate), so u = 2.8 cm/s; thus J/mL and pgH = 0.012 J/mL. Hence, ' / f l u 2= 3.9 X the hydraulic energy necessary to sustain flow is that required to overcome the frictional losses and becomes h E h 0.012 J/mL. Figure 5 plots the energy consumptionper flow volume versus the hydraulic flow rates for the experiments (tests 1-4 in Table I) of a 95 pm diameter and 12.8 cm length capillary. By using the least-squares linear fitting (Lotus 123program), a straight line, with the linear regression r = 0.91, is QhE(mL/h) = (54 f 3) h E h
(J/mL)
(10)
The theoretical line predicts QhT (mL/h) = 61 h E h (J/ mL). Electroosmotic Flow Analysis. The classical Helmholtz-Smoluchowski theory of electroosmosisis considered to be applicable to those systemsin which the doublelayer thickness is small compared to the capillary diameter.6J1 Since 99.99% of the potential drop across a double layer occurs in the distance 9.2/~,where 1 / is~ the reciprocal Debye length, the actual double layer thickness will be no larger than 1pm for a le5M 1:l electrolyte and smaller at larger ionic concentration^.'^ For the capillaries and ionic strength electrolytes used in this study, it shall be assumed that large pore conditions apply. In addition to the comprehensive review of electrokinetic phenomena by Dukhin and Derjaguin," the theory has (15) Mohilner, D. M. In Electroanalytical Chemistry. A Series of Advances; Bard,A. J., Ed.;Marcel Dekber, Inc.: New York, 1966 Vol. 1, pp 247 and 318-321.
in which u, is the fluid velocity in the axial direction z,r is the capillary radial position, E, is the electric field strength, p(r) is the excess charge density at point r, 7 is the fluid viscosity, and yi is an electrical to mechanical efficiency factor for excess cation species, i. Two assumptions implicit in this theory are that the background ions consist of equal concentrations of negatively and positively charged ions whose motions result in forces which are equal and cancel and all of the excess ions are available for momentum energy transfer (i.e. the total ion excess has only species of one charge). Further, the model is strictly applicable only to dilute electrolytes since, as pointed out by Koh and Anderson9 the Debye-Hiickel theory cannot be readily applied to the doublelayer region since the region is not electroneutral. Additionally, an electrostatic drag could be created between the surface charges and the double layer excess chargee4 Table I1 and Figure 6 contain a summary of the results of electroosmotic flow measurements through silica capillaries at different KC1 concentrations. There was no excess hydraulicpressure applied. Potassiumchloride was chosen as the 1:l background electrolyte since the ionic mobilities K+ and C1- are approximately equal. As the bulk KC1 concentration is increased from 10-4 to 5 X 10-2 M,electroosmotic velocity decreased from 0.047 to 0.018 cm/s. Thus, a 500-fold change in background concentration resulted in only a 2.6-fold decrease in the electroosmotic flow rate. If we assume that the surface charge densityon the silica is constant and about a 15X reduction of the double layer thickness has occurred, then the electroosmotic flow is not a strong factor of bulk ionic strength nor double layer thickness. It is possible by calculating the bulk solution conductancein the capillary to determinethe surface conductance due to the ion excess. Some data are summarized in Table 111. With 4 orders of magnitude increase in KCl concentration, 1-1 M, the surface conductance increases by about 3 orders of magnitude. It is not known that the excess surface conductances in high ionic strength solutions are due to only cations or to both cations and anions. Schufle and Huang reported a similar trend, although their values for the KCl surface conductance in a 100-pm capillary differ somewhat from those in Table 111;e.g. M KCl(25 "C) = 12.1 x 10-7 S;10-3 M KC1 = 4.01 X le7 S;10-4 M KC1 = 2.93 X 10-8 5.13 These discrepancies may be due to differences in the surface or glass compositions, the lower values in this work perhaps indicating a less active glass surface (fewer ionic sites) or the experimental techniques (these workers used a dc electrometer for resistance measurements). The electroosmotic velocity of KCl at (16) Newman, J. S. Electrochemical Systems; Prentice-Hall, Inc.: Englewood Cliffs, NJ, 1973; Chapter 9, pp 190-207.
1154 Langmuir, Vol. 9,No. 4, 1993
Li and Gale
Table 11. Electroosmosis Velocity and Energy Consumption at Different KCl Concentrations. IO4 M 5X104M 10-3M 5 x 10-3M 10-2 M 6.8 f 0.3' 8.0 0.4 7.0 f 0.4 8.0 f 0.2 11.6 f 0.6 t b (min) 0.047 f 0.002 0.040f 0.002 0.046 f 0.003 0.040 f 0.001 0.028 f 0.001 u (cm/s) 17.5 71.7 150 680 1390 conductivityd 00 (pslcm) 0.14 0.49 0.96 4.0 8.0 Ie (rA) AEJ (J/mL) 62 261 442 2.2 x 103 6.0 x 103 AE,,P (J/mL) 19 52 61 1.8 X lo2 2.7 X lo2
5x1V2M 18.0 f 0.7 0.018f 0.001 6380 36 43 x 103 1.7 X 103
a Electroosmosis condition: E (electric potential) = 1500 V;capillary, 95 pm diameter, 19.3 cm length. Time for electrolyte moving from anode to cathode. c All errors are standard deviation of 5-15 measurements. Conductivity of bulk solution was measured with a CDM83 conductivity meter. Calculated from experimental conductance data. AE, is the total energy consumption and calculated based on eq 12. M,,,is energy on the surface conductivity.
e
E s
0.04
-
z-
5-
9
.-In 0.03 v)
b 0 2 0.02-
W
' 1'0
lo-'
1 0-'
lo-'
1 0-1
Concentrations of KCI (MI Figure 6. Electroosmosis velocity at different concentrations of KCl electrolyte (E = 1500V; capillary: 9.5pm diameter, 19.3 cm length).
M = 0.028 cm/s (with electric gradient, E/L = 78 V/cm) compared with that of M NazHP04 (Pyrex 132-pmcapillary) = 0.13cm/s (with E / L = 100V/cm), and for 0.05 M KC1 = 0.018 cm/s, whereas 0.05 M Na2HP04 = 0.087cm/s.17 Again,these values for Na2HP04 are larger than those for KC1, which may be a consequence of chemical and experimental differences, but the electroosmotic flow rate slightly decreased with increase of electrolyte concentration. These latter workers report no geometricaleffect of the cross-sectionalarea of the capillary tube under their electroosmoticflow conditionsat constant current. Energy Analysis of Electroosmotic Flow. In electroosmotic flow, most of the electric energy will be used in ionic migration and will result in PR heat. The energy consumption of electroosmosiscan be calculatedaccording to following equations: power equation: W = I V (Iis current, V is voltage) (W) energy consumption: E, = IVt (t is time) (J) energy consumption/flowvolume: AE, = IVt/Q,t = IV/Q, (J/mL) (12) Some results of energy usage are shown in Table 11. With increase of the concentration of the KC1 electrolyte, the current in the system increases and the energy for a (17) Tsuda, T.; Nomura, K.;Nakagawa, G. J. Chromatogr. 1982,248, 241. (18) Bard, A. J.; Faulkner, L. R. Electrochemical Methods, Fundamentals and Applications; John Wiley & Sons Inc.: New York, 1980, p
506.
particular flow rate increases. For example,A E e = 62J/mL for lV M KCl electrolyte, but A E e = 43 X lo3J/mL for 5X M KCl electrolyte. Overall, much more electric energy is needed than hydraulic to cause the same amount of flow. Table I1 presents also the electrical energies for flow on the basis of the excess surface conductances.They vary from about 31 % of the total electrical energy at 1V M KCl to about 4% at 5 X M KCl. Again, these surface electrical energies do not correlate linearly with the flow rates, which actually decrease despite a higher energy consumption. These energy figures are based on steady-state values for the conductances and are not adjusted for electroosmotic transport. If we make an assumption that similar mechanical energy is required to achieve equal hydraulic and electroosmotic flow rates, we will be able to estimate a value for Ti in eq 11. The efficiency parameter is clearly a function that has not been theoretically or practically established of the concentration, conductance, and the radius and charge of excess ion. Considering only the surface conductanceas providing electrical energyto cause electroosmoticflow, at 1V M KC1, Ti(C,cs,riJi) = 0.012/19 0.06% and at 5 X le2M KC1, Ti(C,cs,ri,Zi) = 0.012/(1.7 X lo3) = 0.0007%. These figures are extremely small fractions of the electricalenergy associatedwith the excess surface conductances and this clearly demonstrates that the classical model for electroosmosis is likely to be incorrect in assuming that all of the surface electrical energy is available to cause the electroosmoticflux. The energy equivalency postulate is reasonable given that in hydraulic flow, the force (pressure) is applied equally over the capillarycross-sectionalarea, whereas in electroosmotic flow the force is localized to the double layer region, seeminglya less efficient process. Further similar liquidliquid and liquid-olid frictionallosses should ensue. Since the efficiency parameters are so small, this brings into question the use of the classical electroosmotic model for deriving electrokinetic zeta potentials.
Conclusions Hydraulic flow through silica capillaries of diametera 50-100 pm closely obeyed the Poiseuille equation which assumes laminar flow. The electric energy used to cause electroosmotic flow is a very small fraction of the total electricalenergy,especially in high ionic strength solutions. With increases of the electrolyte concentration, the electroosmoticflow rate decreased slightly and the energy consumption per flow volume increased dramatically. Thus, on comparisonof hydraulic flow with electroosmotic flow, hydraulic flow needs much less energy to cause the same amount of flow. Certainly, hydraulic flow is much more energy efficient than electroosmoticflow in a 95 pm diameter capillary because in electroosmoticflow, most of the applied energy will be lost in ion migration and PR heat. The electrical energy consumed in excess surface conductance similarly is far larger than that needed for
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Langmuir, Vol. 9, No. 4, 1993 1155
Table 111. Surface Conductance Measurement of KCl Solutions in a 95-pm Silica Capillary resistance of resistance of surface conductivity of surface thickness of concentration measurement bulk solution calculation resistance conductance diffuse layer of KCl solution (M) uo (ccS/cm) R (Q) Rsb(Q) u.p (S) i / P (A) Ro" (Q) 17.5 f 0.2e 1.61 x 109 (1.12 f 0.05) x 109 3.68 X 109 1.83 X 10-8 10-4 304 lo-" 150 f 2 1.88 x 108 (1.62 f 0.06) X 108 11.7 X 108 5.74 x 10-8 96.2 10-2 1390 f 10 2.03 x 107 (1.94 f 0.02) X lo7 43.8 X lo7 1.53 X 30.4 lo-' (12.56 f 0.01) X 103 2.25 X 106 (2.16 f 0.03) X 106 54.0 X 108 1.19 X 10-8 9.6 100 (107.5 f 0.3) X lo3 2.62 X 105 (2.48 f 0.03) X lo5 46.4 X lo5 1.49 X le5 3.0 a Ro = (uorr2/L)-l, where L = 2 cm. Calculated based on: 1/R = 1/Ro + l/Rs. usis calculated according to eq 7. This column is adapted from ref 18. All errors are the standard deviation of four to eight measurements.
hydraulic flow (1000-fold or greater) and is an unknown function of the electrolyte concentration, the surface conductance, the effective ion radii, surface drag effects, etc. It must not be assumed, however, that the excess surface conductance is due solely to a single cationic species. Additionally, it is possible that the surface silica has amphoteric sites and competitive equilibria with K+, H+, C1-, and OH- ions and/or ion aggregates occurs. We have postulated that an electrical to mechanical efficiency factor is required in the classical model for electroosmosis and have presented data to support this view. Obviously, the electrokinetic zeta potential will have to be derived based on a better understanding of the magnitude of yi values and the surface species composition in the solution phase.
For real soil systems, due to clogging and consolidation of soil, etc., hydraulic flow is very inefficient, especially when the clay particle size is fractions of a micrometme However, despite the electrical energy inefficiency of electroosmosis, since its application provides a more efficient convenient pumping mechanism for fluids through contaminated clay masses than pump and treat methods, electrokinetic soil processing will continue to be of considerable interest in environmental engineering as a practical tool for soil decontamination. Acknowledgment. Mr. Heyi Li is grateful for a teaching assistantship for the Chemistry Department, Louisiana State University.
