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Electrokinetic and rheological parameters of water in a single capillary
Electrokinetic and Rheological Parameters of Water in a Single Capillary YIGAL GUR 1 Soil and Fertilizers Laboratory, Faculty of Agricultural Engineering, Technion, Haifa, Israel Received September 4, 1978; accepted February 26, 1979 An experimental setup is suggested for simultaneous studying of the streaming current and electroosmotic counterpressure phenomena in a single capillary slit. The experiments are performed with saturated AgC1 water solution at room temperature. The results of the experiments confirm previously suggested rheological theory and they are: the streaming current is a nonlinear function of the driving pressures in capillaries with high surface potentials; ~-potentials, determined from streaming current experiments, were much lower than those determined from electroosmotic pressure measurements; the difference between them decreases with decreasing surface potentials. Experimental results are used to compute values of surface potentials and rheological parameters. This is done by minimization of a suggested error function. A 93% agreement between theory and experiment is found. INTRODUCTION
The problem of the interface water rheology was solved theoretically (1). This theory arose out of an interface model, in which the ordering action of the electrical double layer was accounted for. The assumption was made that strong electrical fields of such layers have to orient water molecules in the interface region. This additional inhomogeneous orientation, being absent in the bulk, was regarded as a structural anomaly of the interface against the bulk. Interactions between oriented water dipoles lead to the establishment of additional mechanical forces, which hinder the shift of water layers in the interface. These forces were considered in the theory as an additional anomal viscosity of the interface in terms of Babchin et al. (15). The special numeric procedure was suggested (1) to evaluate the theological total current and volume flow (generalized fluxes) through a rectangular capillary slit 1 Address for correspondence: 504 Fuznas Hall, Department of Chemical Engineering, SUNY/Buffalo, Amherst, N.Y. 14226.
as functions of the external electrical field and pressure. The computed generalized fluxes were found to be almost linear, and appropriate phenomenological coefficients of the fluxes were obtained. The coefficients were used later to predict values of the electrokinetic ~-potentials in different external conditions and, in general, for different electrokinetic phenomena. As a specific effect of the rheological model, it was found that in spite of an apparent linearity of the rheological electrokinetic flows, the ~-potentials, calculated by conventional methods, may have different values. It was shown (1) that the largest difference exists between the ~-potentials that are determined from the streaming current phenomenon and from the electroosmotic pressure phenomenon, observed in the same capillary. Another specific effect of the interface rheology is that the slight nonlinearity of the relation between the streaming current and the driving pressures become significant only for sufficiently high surface potentials. When the surface potential is low, 222
0021-9797/79/140222-11 $02.00/0 Copyright © 1979 by Academic Press, Inc. All rights of reproduction in any form reserved.
Journal of Colloid and Interface Science, Vol. 72, No. 2, November 1979
WATER ELECTRORHEOLOGY PARAMETERS
Plug
,
U FIG. l. Scheme of electrokinetic investigations.
the streaming current is found to be linear even in a wide range of driving pressures. In this paper we will report the results of an experimental study of these phenomena in a series of single flat capillaries (capillary slits). The classical electroosmotic counterpressure measurements are carried out in a system consisting of a porous plug (Fig. 1) where the pressure head P is determined as a function of an applied voltage difference U. In the stationary state the electroosmotic flow is just balanced by the hydraulic flow. A modification of such a method was submitted by Rastogi and Jha (2) and successfully applied by Singb and Singb (3) for studying electrokinetic transport phenomena in porous glass filters. Unfortunately, the method (2, 3) cannot be applied for single capillary investigations because of the substantial raise in relaxation time that is needed to reach the steady state. We suggested here an electrokinetic compensation method for investigation of the electroosmotic counterpressure in a single capillary with known geometry. The method is based on the principle of a deep electronic feedback between two sequentially connected capillaries and permits the relaxation time to be reduced considerably. The streaming current as a function of pressure may be measured in the device, similar to that in Fig. 1, in which the source
223
of the voltage U is replaced by a current detector. The choice of the detector is restricted by demands of its high sensitivity and low input impedance, which results from the condition U = 0. The additional problem in streaming current measurements is the collecting electrodes. These asymmetric polarizations noted by Hunter and Alexander (4), provide additional noise current, thus decreasing the signal-to-noise factor, which is especially important for investigations in a low flow rate region. In one of the first studies of the streaming current in a single capillary, by Rutgers and de Smet (5, 6), the problem of low input impedance was solved by using a big capacitor to collect the current. The time of the capacitor's charging to a certain voltage was measured. Progress in electronics led to the development of the shunting resistance method for detecting streaming currents, which was analyzed and realized by Hurd and Hackerman (7, 8). In this method the collecting electrodes were shorted by an external resistance, whose value was much smaller than the electrolytic resistance of the capillary. A potential drop in the shunting resistance was measured by an electronic amplifier. The same method was used later by Rutgers et al. (9, 10) with an electronic voltmeter as a detector for streaming current investigations in a capillary with nonaqueous liquids. Recently a low impedance, ac, lock-on amplifier was used by Croves and Sears (11) for investigations of the altering streaming current. In the present study we used a precision electronic integrator with digital output for detection of streaming currents. The currents were determined as a result of a statistical treatment, applied to chargetime functions. Experimental data, obtained in the streaming current, and electroosmotic pressure measurements were used to compute the values of the surface potential of the capillary and to verify the rheological constants of water (1). Journal of Colloid and Interface Science, Vol. 72, No. 2, November 1979
224
YIGAL GUR EXPERIMENTAL
Pyrex tube with the B-14 cone on its end. The external part of the Pt wire was electrolytically coated with Ag and then chloridized in 0.01 N HC1 according to the procedure suggested by Ivnes and Janz (12). Bias interconnection potentials measured after an aging period of a month in a saturated AgC1 water solution were less than 0.01 mV. Capillaries. Fuzed quartz, optical grade slides, 0.15 cm thick, were cut into squares 1 x 1 cm. The plates were intensively cleaned by the following procedures: (a) washing in hot distilled water with "Teepol" detergent; (b) tetrachlorethylene vapor extraction; (c) isopropyl alcohol vapor extraction; (d) bidistilled H20 vapor extraction. The duration of each step was not less than 3 hr. The liquid drops, condensed on the plates after every operation (a)-(d), were blown off by a slight N2 jet. The cleaned plate was placed with appropriate mask (1 x 0.6 cm) in a vacuum evaporation set and two SiO~ spacers with dimension 1 cm x 0.2 cm x 1000/~ were deposited on two opposite ends of the plate's side. The thickness of the SiO2 deposit was
The experimental system. The Pyrex glass experimental system is presented in Fig. 2. Six reversible electrodes are placed at positions El-E6. Two capillary slits C~ and C2 are connected to the reservoirs Ra, R2, and R3 by means of the glass joints B-14 with Teflon sleeves. " M o n o s t a t " threading clamps were used for hermetical packing and reinforcement of all the joints. Capillary Ca is used as the streaming current generator and capillary C2 as the electroosmotic cell. Tubes T1-T3 connect the gauge with a pressure-producing system. Low-pressure gradients were obtained by producing level differences of the liquid in the 0.5-liter aspirator bottles. The differences of levels were measured with an accuracy of 0.01 cm. High-pressure gradients were produced by applying N2 pressures controlled by a precise mercury manometer having a 0.001-in. accuracy photocell registration of the Hg level. Electrodes. A platinum wire 3.5 cm long and 0.5 mm in diameter was soldered in a
Thermometer 0.01°C d i v
~gon
I,-~
~-
OS,
. . . .
'::::
-~---'ll
[] [I : : ::---:',
~----~llq,ll
o.~' I--I
II
~
H
:OO~mm
N ;ec.,v.,
Manometer *-0.001
inch
Hg
II_
_
I
Thermoisolation
&
electrostatic
screen
FIG. 2. Experimentalgauge and pressure-producing system for simultaneous streaming current and electroosmoticmeasurementsin a singlecapillary(C2).
Journal of ColloM and Interface Science,
Vol. 72, No. 2, November 1979
WATER ELECTRORHEOLOGY PARAMETERS
225
pressure-producing system were placed in a temperature-controlled room so that the temperature fluctuations in the thermostat ~.~ . Keiihley6 1 6 , , were smaller than 0.05°C. Usage of the saturated AgC1 water solution with the Ag-AgCI electrodes and intensive stirring during experiments permitted us to eliminate the concentration effects (diffusion, asymmetry polarization) as much as possible. Electronic and measuring circuits. The electronic circuit of the electrokinetic compensator for electroosmotic pressure inT3 vestigations is presented in Fig. 3. The external pressure difference P Fro. 3. Electrokineticcompensatorfor the electroosmoticcounterpressuremeasurementsin capillaryC2. generated by the pressure-producing system (Fig. 2) being applied between Ta and controlled by the quartz crystal monitor T3 (T2 is closed and disconnected) causes "Speedivac," previously calibrated by opti- a liquid hydraulic flow through system Cacal interferometer. The deposed plate was C2. This flow provides an electric charge covered with a similar nondeposed plate. transport between electrodes El-E2, which The "sandwich" was forced and glued are connected to the digital electrometer together with "Tort-Seal" cement to ob- " K e i t h l e y 616." The electrometer is tain a small capillary slit. The real height operated in the fast ampermeter mode, and of the slit was different from the separator its input resistance (105-106 1~) is less than thickness (deposited SiO2) and was deter- the electrolytic resistance of the capillary mined later by electric and hydraulic con- (-108 1~). The 1-V analog output of the ductivity measurements. electrometer is connected to the preampliAssembling. Before assembling the sys- fier Aa, whose gain can be regulated. The tem, the glass reservoirs Ra-R3 were in- output signal of A2 is proportional to the tensively washed with "Teepol" detergent streaming current in capillary Ca and is null and extracted with HzO vapor for 6-8 hr. when the flow is absent. The negative feedThe Teflon-coated stirring bars were placed back loop consists of the amplifier A2 with at the bottom of the reservoirs. The sys- _+100-V output and two electrodes E~-E6 tem R,-R3 (Fig. 2) was carefully filled which provide the electrical field in capilwith the electrolyte solution to avoid the lary C2. The A2 amplifier is operated as an possible formation of air bubbles on its glass integrator (C = 2.5 /zF, R = 100 k12) and surfaces. The electrolyte was prepared as its output voltage causes the electroosmotic saturated solution of AR-grade AgC1 in bidis- flow in the C2 capillary in opposite direction tilled water (X = 0.9 x 10.6 1~-a cm -1, to the hydraulic flow. The stationary state pH = 5.86). Small portions of solid AgC1 of the scheme is achieved in the absence were placed on the bottom of Ra-R3. Elec- of the total liquid flowthrough C1-C2 and trodes El-E6 were mounted and the whole may be submitted as an equivalence of the gauge was placed in a thermostat with the electroosmotic pressure to the external four-layer earthed electrostatic screen which pressure P. The voltage U that correprevented the system from external electro- sponds to the given P is measured by static hindrances. The thermostat with the electrodes E3-E4 connected to the highJournal of Colloid and Interface Science, Vol. 72, No. 2, November 1979
226
YIGAL GUR
®
®
© F1o. 4. Response of the compensator for two pressure pulses 0.28 and 0.25 in. Hg. Capillary's heights: C1, 4.3 /zm; C2, 6.2 /xm. Records a, b, and c were obtained in the correspondent points in Fig. 3. impedance digital voltmeter V (4600 Digital Multimeter, Dana Inc.). Figure 4 presents the dynamic response of the electrokinetic compensator on two sequential pressure pulses. The streaming current phenomenon in capillary C2 was studied by the scheme presented in Fig. 5. An external pressure difference P applied between T2 and T3 (Fig. 2) causes a charge transport through
capillary C2. This charge is registered by the "Keithley 616" digital electrometer which is operated in the fast coulometer mode so that its output is proportional to the electrical charge passed through capillary C2. Every 10 sec the Timer (Elron scaler-timer Nis 17-P) sends a strobe pulse to the isolated output/control circuit (Keithley 6162) to retrieve the digital output from the electrometer. These data (charge i
Timer
616 Electrometer
°iI,
WANG
500
Digital System
T2
FIG. 5. Digitalregistrator of the electricalcharge transport through capillaryC2. Journal of ColloM and Interface Science, Vol. 72, No. 2, November 1979
WATER ELECTRORHEOLOGY 0,00 24,
×
10,00 266,
×
20,00 500.
X Y
~0.00 737.
× Y
40,00 973,
Y
50.00 1204.
X Y
Y
Y time (see) charge (I0-I0 coul)
(A)
2,359428571-10 2,747619048-10
B A
current
,99998189 2,424740249-1! 1,870828693+01
C
correlation coefficient
E F
4,414166587-09 5,796237832-15 6. 1,418339J97-12
G H M
B
halfwidth of [he 95% confidence
interval
Fie. 6. Sample of the registrator's printout (Calculator W a n 500).
q and time t) are transmitted to the programcontrolled digital calculator (Wang 500) and stored there. After a certain number of the q(t) measurements (usually six) the linear regression analysis program is run to evaluate the mean value of the streaming current. The advantage of this method is in the high accuracy of the current determinations which is not dependent on the range of streaming current value. An example of the Wang printout with the computed current and statistical parameters is presented in Fig. 6. RESULTS OF ELECTROKINETIC EXPERIMENTS
A series of capillaries prepared as described above were filled with AgCI solution and used in the streaming current and electroosmotic pressure experiments. The capillaries were in contact with the solution
PARAMETERS
227
during the whole experimental period (about 18 months). Electrical conductivity and pH of the solution were controlled during the experiments. A slight acidization of the solution was detected as a function of time: pH = 4.3 and h = 4.5 x 10-5 ~-~-1 cm-1 had been found for the fresh prepared solution and were changed to pH = 3.1, X = 21 x 10-5 12-1 cm -1 at the end of the experimental period. Every streaming current experiment was followed by the electroosmotic pressure experiment. A time interval between these experiments did not exceed an hour. To "switch" the experimental set from one type of experiment to another, no opening or additional filling within the system was done. It enabled us to avoid external influences on the system and to observe the streaming and the electroosmotic pressure practically under the same conditions. It was found that at the beginning of the experiments, the ~-potentials of the capillaries were high and decreased slowly with time. After a period of some months, the ~-potentials reached a more or less low constant value, which did not change further.
Capillary Geometry Determinations The electrical resistance of the filled capillaries was controlled before and after every electrokinetic experiment. Electrodes E~-E6 were connected to the "Keithley 616" electrometer, operated in the fast ohmeter mode (constant current method). No changes of the resistance were found during an experimental day. To avoid possible influences of the surface conductivity and interface rheology (1), the determination of the capillary heights was done after the aging period, i.e., when ~-potentials were minimal. The electrolyte conductivity was simultaneously measured in the same temperature conditions by a standard ac bridge conductometer. The heights of the capilJournal of ColloM and Interface Science, Vol. 72, No. 2, November 1979
228
YIGAL GUR
laries calculated from these measurements were compared with those obtained from the hydraulic conductivity measurements performed in the aged capillaries (low value of the surface potentials). The hydraulic conductivity was measured by investigations of microdisplacements of a liquid meniscus in a precision bore capillary, diameter 0.33 mm, with the precautions described by Smit and Stein (13). The classical expression which results from the solution of the Navier-Stokes equation was used in calculations of h. The capillaries' heights, calculated from both methods, were significantly identical.
Rheological Behavior of the Streaming Currents The streaming current as a function of driving pressure I = I(P) was measured for high and low pressures. The reproducibility of these measurements is sufficiently high as presented in Fig. 7, where the results of
~-Potentials Typical results of the electroosmotic pressure experiments are plotted in Fig. 8. The slopes Sep of the regression line
//
o -~r _
to.
I-- o r.,r')o
taJ cr¢r-o
four experiments are plotted. The linear regression analysis was applied to obtain the slopes Sse of the I(P) lines. These slopes coincide with the L12 kinetic coefficient (1), and the difference between their values, computed for different pressure intervals, may be explained as a nonlinearity of the streaming current phenomenon, predicted by Gur and Ravina (1). The statistical t test (14) was used to find the significance of the differences in the slopes. The results of these experiments and appropriate statistical treatment are collected in Table I. The significant differences in slopes were obtained for small "fresh" capillaries. Increasing the capillary height and their aging lead to decreasing the significance in the differences.
J
°o'.oo
sb.oo lbo.oo PRESSURE
!
jT~so72o 7:m.oo e~o.oo e~o.oo (OYN/CFi o SO) • 1 0 3
FIG. 7. Streaming current in the 1.7-/~m capillary, t = 23°C. Solid line, theoretical prediction on the base of rheological theory (1). Points (+), experimental results.
Journal o f Colloid and Interface Science, Vol. 72, No. 2, November 1979
229
WATER ELECTRORHEOLOGY PARAMETERS TABLE/ Streaming CurrentPhenomenain DifferentPressureRanges a Capillary age (months)
Capillary height h (10-4 cm)
Pressure interval from Hg)
Current-pressure slope (t0 -~ esu)
Chance of difference between slopes (%)
0
1.7
10-110 550-650
1.3 1.83
>99.9
11-24 250-750
2.88 3.46
53
13-34 457-559
0.323 0.313
15
0
4.26
6
1.7
Capillary h x 0.6 x 1.0 cm, saturated AgC1solution, 23°C. U = U(P), which are proportional to the ratio L2e/L21 [see (1)] were used for computations of the ~ep-potentials according to the expression h2~~ev --
--
-
-
3~o h2,n-
-
3e0
(L21/L22)
(1/Sep),
[1]
where E0 is the dielectric constant of water. Streaming current experiments were run simultaneously in the same capillary in highpressure ranges and the slopes of lines I = I ( P ) , which are proportional to L12, were used to c o m p u t e the ~s~ potentials: C9"
7 cs.
o'
w ~ Q9~.
~o ISOc~
>4
8oOO SOoUO T88.oe 2,~OoOO s2o°8o ,~eOoOa PRESSURE ( D Y N / C I ' l o S 8 ) ~ 1 8 8
4Try0 # 4~'V0 ~se = Lie - - S s c eoah eoah
,
where 70 is viscosity, a is capillary width, and # is capillary length. Results of the ~e, and ~s~ determinations are presented in Table II. The averaged accuracy of the ~-potential determinations was + !.2 mV for ~ep and _+6.3 mV for ~c. SURFACE POTENTIAL AND RHEOLOGICAL CONSTANTS TO compare the results obtained with the theory (1) we have to k n o w the rheological constants of the water and the explicit value of the surface potential. The observed experimental data permits us to predict these values. According to Gur and Ravina (1), the slopes experimentally obtained in the present work can be expressed as functions of the next arguments: q50, f , L, B~, B2, a where 050 is surface potential, f is the viscoelectric coefficient, and L, B2, B2, a are rheological constants. We introduce now the auxilliary, positively determined function of errors F = (1 - Ssc/S*c) 2 + (1 - v~ 's c /- ~~s'c* ~ ] + ( l -- S e p / S * e p ) 2,
FIG. 8. Electroosmotic counterpressure in the 1.7-/zm capillary, t = 23°C. Solid line, rheological theory; points (x), experiment.
[2]
[3]
in which S*e is the theoretical value o f the c u r r e n t - p r e s s u r e slope in the low-pressure Journal of Colloid and Interface Science, VoL 72, No. 2, November 1979
230
YIGAL GUR T A B L E II ~-Potentials, E v a l u a t e d from S t r e a m i n g Current E x p e r i m e n t s (~¢) and from E l e c t r o o s m o t i c Counterpressure Measurements (~J~
Capillaryage (months)
pH of solution
Capillaryheight (10-4 em)
0
4.3
1.7 4.16 4.3 6.2 6.4
6
3.3
1.7 4.16
13
3.1
1.7 4.16
-L~z (10-6 esu)
~sc (mV)
L22/L2~ (10-~ esu)
--63.2 --62.1 --62.9 --61.5 --62.8
0.756 4.02 4.38 9.24 10.2
3.20 6.13
-- 14.2 -- 11.0
7.48 74.8
-- 15.4 --9.2
1.84 3.22
--8.1 --5.8
22.5 82.9
--5.1 --8.3
14.4 34.5 36.2 51.0 53.2
(~ (mV)
-- 152 -- 171 --168 -- 165 --159
Capillary h × 0.6 × 1.0 cm, s a t u r a t e d AgC1 solution, 23°C.
region, S~* is the theoretical value of the minimization. The value F = 0.13 was obcurrent-pressure slope in the high-pressure tained for the next values of the variables: region, S*p is the theoretical value of the 4)0 = -150 m V ; f = 9.18 x 10-7; L = 300; voltage-pressure slope in the electro- B1 = 8.058 x 10-3; B2 = 0.333; ot = 0.01. osmotic pressure experiments, and S~c, The experimental results (points) are comS'sc, Sep are appropriate experimental values. pared with the theoretical predictions (solid From the reasons pointed out above, the lines) of the streaming current and electrofunction F may be treated as a function of osmotic pressure in Figs. 7 and 8. several variables ~b0,f , L, B1, B2, a. It is clear that the variables may be determined DISCUSSION by a minimization of the F-function. The The differences between ~-potentials minimal value of the function may be a measured in low ionic strength electrolytes criteria of the theory-to-experiment coinciby electroosmotic and streaming systems dence. have been reported over the years (5, 16). We minimized the F-function in the These studies dealt only with two types of present work by the conjugate directions electrokinetic experiments: electroosmosis procedure, suggested by Powell (14). The (~eo) and streaming potentials (~sp) investigaslopes S*e and S~* were computed accordtions. The anomalous differences between ing to the procedure described previously ~eo and ~so were obtained (16) for con(1). For the third term S*p the necessary ductivity grade water, but were the result tangential field for a given pressure was of experimental errors. In a more careful determined from the total flux condition: study, submitted later by Rutgers and de Smet 0 = J(U,P). [41 (5), the equivalence for ~eo and ~o was obThe tabulated function U(P), which corre- tained and most scientists tend to believe sponded to the condition of Eq. [4], was that all electrokinetic systems used for deused further in the linear regression analysis termining of the ~-potentials are fundamentally equivalent. to find the value S*p. The equality ~eo = ~sp is equivalent to the Experimental data obtained for " f r e s h " 1.7 x 10-4 cm capillary were used in the general principle of the theory of irreversiJournal of Colloid and Interface Science, Vol. 72, No. 2, November 1979
WATER ELECTRORHEOLOGY PARAMETERS H
=
17000
T
=
E3
E
=
0
B
-
1CN
e = I0~
2
8YN/CN.50
P = 10~t
¢
DYNtCM.58
+
P = I0~/
6
DrNICM.50
x
P = IO~m
8
O~N/CM.SQ
R
C
5P =
°
149
MV
7 CD
EL~-
>-
o
>$ a~ Ix_ --
0o00
1
0o02
0°03
D~ST~NC£
0°05
0°07
OoOB
< C N ) ~ 1 0 -s
FIG. 9. Distributions of the effective viscosity near the capillary wall computed according to the rheological theory (1) with found values of the rheological parameters.
ble processes: the Onsager's symmetry of the phenomenological coefficients on linearized transport equations (17), as was carefully discussed by Miller (18). The rheological theory of ~-potentials, raised by Gur and Ravina (1), does not contradict this principle and, as a consequence, predicts the same values for ~eo, ~p, and ~se, but makes them sensitive to the deformation rate distribution in the interface. This distribution is significantly different for streaming phenomena and for a stationary case of the electroosmotic pressure phenomenon. As a result of this difference, g~c and ~ep have different values, as was predicted (1) and observed experimentally in the present work. The increase of the ~-potentials with an increase in the deformation rates in interfaces, experimentally observed here in streaming experiments, must be taken into account when one compares electrokinetic results obtained in different capillaries. The variations of
231
the ~-potential as a function of the hydronium ion concentration (pH) in aqueous solutions-silica systems was studied experimentally by Wiese et al. (19). It is interesting to compare their results, obtained for 10-4-10 -3 M K N 0 3 with the ~se, measured by us in saturated AgC1 solution. The isoelectric point (pI) derived from our results is pH = 2.99 --_ 0.03 which agrees satisfactorily with the pI pH = 2.5 ___ 0.2 obtained by Wiese et al. (19) and falls within values, recorded in the literature (20), for quartz and SiO2 sols and gels. The difference of about pH = 0.5 may result from differences in streaming conditions. The streaming experiments of Wiese et al. (19) were performed in a vitreous silica capillary of 0.76-mm diameter, i.e., with higher deformation rates than realized here. According to the theory (1) ~-potentials, measured in high deformation conditions, must be much higher (in absolute values) than registered in our capillary, which respectively may lead to a decrease of the pI obtained. The surface potential estimated from the Nerust equation (21, 22): 49s = 2 . 3 0 3 ( k T / e ) ( p H p i - pH)
[5]
has a value qSs = -105.8 mV (23°C, ApH = 1.8). Levine and Smith (23) analyzed the validity of the Nerust equation for an oxide/ aqueous electrolyte interface. They found that Eq. [5] is valid for the micropotential of the surface ~bs which may be expressed as the macropotential 4~0 of the electrical double layer and a self-atmosphere potential to due to the disturbance in the mean distribution of surrounding ions caused by the presence of the ion at the given position: 6s = 4~0 + to.
[6]
The qS0 = - 150 mV, estimated from the experiments, gives for the self-atmosphere potential to = 44.2 inV. Figure 9 presents the distribution of the effective viscosity in the capillary h = 1.7 /xm computed with the obtained values of Journal of Colloid and Interface Science, Vol. 72, No. 2, November 1979
232
YIGAL GUR
the rheological constants and ~b0 = -150 inV. The three-region model of the viscosity distribution, suggested by Gur and Ravina (1), is not changed with the obtained values of the rheological parameters. ACKNOWLEDGMENTS This United (BSF), debted
research was supported by a grant from the States-Israel Binational Science Foundation Jerusalem, Israel. The author is deeply into Referee II, for his constructive criticism. REFERENCES
1. Gur, Y., and Ravina, I., J. Colloid Interface Sci., in press. 2. Rastogi, R. P., and Jha, K. M., J. Phys. Chem. 70, 1017 (1966). 3. Singb, K., and Singb, J., Colloid Polim. Sci. 255, 379 (1977). 4. Hunter, R. J., and Alexander, A. E,, J, Colloid Sci. 17, 781 (1962). 5. Rutgers, A. J., and de Smet, M., Trans. Faraday Soc. 43, 102 (1947). 6. Rutgers, A. J., and de Smet, M., Trans. Faraday Soc. 48, 635 (1952). 7. Hurd, R. M., and Hackerman, N., J. Electrochem. Soc. 102, 594 (1955).
Journalof Colloidand InterfaceScience, Vol.72, No. 2, November1979
8. Hurd, R. M., and Hackerman, N., J. Electrochem. Soc. 103, 316 (1956). 9. Rutgers, A. J., de Smet, M., and de Myer, G., Trans. Faraday Soc. 53, 393 (1957). 10. Rutgers, A. J., de Smet, M., and Rigola, W., J. Colloid Sci. 14, 330 (1959). 11. Croves, J. M., and Sears, A. R., J. Colloid Interface Sci. 53, 83 (1975). 12. Ivnes, D. J. G., and Janz, G. J., "Reference Electrodes." Academic Press, New York, 1961. 13. Smit, W., and Stein, H. N., J. Colloid Interface Sci. 60, 299 (1977). 14. Powell, M. J. D., Computer J. 7, 155 (1964). 15. Babchin, A. J., Piliavin, M. A., and Levich, V. G., J. Colloid Interface Sci. 57, 1 (1976). 16. Du Bois, R., and Roberts, A. H., J. Phys. Chem. 40, 543 (1936). 17. De Groot, S. R., and Mazur, P., "Non-equilibrium Thermodynamics." North-Holland, Amsterdam, 1963. 18. Miller, D. G., Chem. Rev. 60, 15 (1960). 19. Wiese, G. R., James, R. O., and Healy, T. W., Disc. Faraday Soc. 52, 302 (1971). 20. Parks, G. A., Chem. Rev. 65, 177 (1965). 21. Berube, Y. G., and De-Bruyn, P. L., J. Colloid Interface Sci. 27, 305 (1968). 22. Hunter, R. J., and Wright, H. J. L., J. Colloid Interface Sci. 37, 564 (1971). 23. Levine, S., and Smith, A. L., Disc. Faraday Soc. 52, 290 (1971).
The problem of the interface water rheology was solved theoretically (1). This theory arose out of an interface model, in which the ordering action of the electrical double layer was accounted for. The assumption was made that strong electrical fields of such layers have to orient water molecules in the interface region. This additional inhomogeneous orientation, being absent in the bulk, was regarded as a structural anomaly of the interface against the bulk. Interactions between oriented water dipoles lead to the establishment of additional mechanical forces, which hinder the shift of water layers in the interface. These forces were considered in the theory as an additional anomal viscosity of the interface in terms of Babchin et al. (15). The special numeric procedure was suggested (1) to evaluate the theological total current and volume flow (generalized fluxes) through a rectangular capillary slit 1 Address for correspondence: 504 Fuznas Hall, Department of Chemical Engineering, SUNY/Buffalo, Amherst, N.Y. 14226.
as functions of the external electrical field and pressure. The computed generalized fluxes were found to be almost linear, and appropriate phenomenological coefficients of the fluxes were obtained. The coefficients were used later to predict values of the electrokinetic ~-potentials in different external conditions and, in general, for different electrokinetic phenomena. As a specific effect of the rheological model, it was found that in spite of an apparent linearity of the rheological electrokinetic flows, the ~-potentials, calculated by conventional methods, may have different values. It was shown (1) that the largest difference exists between the ~-potentials that are determined from the streaming current phenomenon and from the electroosmotic pressure phenomenon, observed in the same capillary. Another specific effect of the interface rheology is that the slight nonlinearity of the relation between the streaming current and the driving pressures become significant only for sufficiently high surface potentials. When the surface potential is low, 222
0021-9797/79/140222-11 $02.00/0 Copyright © 1979 by Academic Press, Inc. All rights of reproduction in any form reserved.
Journal of Colloid and Interface Science, Vol. 72, No. 2, November 1979
WATER ELECTRORHEOLOGY PARAMETERS
Plug
,
U FIG. l. Scheme of electrokinetic investigations.
the streaming current is found to be linear even in a wide range of driving pressures. In this paper we will report the results of an experimental study of these phenomena in a series of single flat capillaries (capillary slits). The classical electroosmotic counterpressure measurements are carried out in a system consisting of a porous plug (Fig. 1) where the pressure head P is determined as a function of an applied voltage difference U. In the stationary state the electroosmotic flow is just balanced by the hydraulic flow. A modification of such a method was submitted by Rastogi and Jha (2) and successfully applied by Singb and Singb (3) for studying electrokinetic transport phenomena in porous glass filters. Unfortunately, the method (2, 3) cannot be applied for single capillary investigations because of the substantial raise in relaxation time that is needed to reach the steady state. We suggested here an electrokinetic compensation method for investigation of the electroosmotic counterpressure in a single capillary with known geometry. The method is based on the principle of a deep electronic feedback between two sequentially connected capillaries and permits the relaxation time to be reduced considerably. The streaming current as a function of pressure may be measured in the device, similar to that in Fig. 1, in which the source
223
of the voltage U is replaced by a current detector. The choice of the detector is restricted by demands of its high sensitivity and low input impedance, which results from the condition U = 0. The additional problem in streaming current measurements is the collecting electrodes. These asymmetric polarizations noted by Hunter and Alexander (4), provide additional noise current, thus decreasing the signal-to-noise factor, which is especially important for investigations in a low flow rate region. In one of the first studies of the streaming current in a single capillary, by Rutgers and de Smet (5, 6), the problem of low input impedance was solved by using a big capacitor to collect the current. The time of the capacitor's charging to a certain voltage was measured. Progress in electronics led to the development of the shunting resistance method for detecting streaming currents, which was analyzed and realized by Hurd and Hackerman (7, 8). In this method the collecting electrodes were shorted by an external resistance, whose value was much smaller than the electrolytic resistance of the capillary. A potential drop in the shunting resistance was measured by an electronic amplifier. The same method was used later by Rutgers et al. (9, 10) with an electronic voltmeter as a detector for streaming current investigations in a capillary with nonaqueous liquids. Recently a low impedance, ac, lock-on amplifier was used by Croves and Sears (11) for investigations of the altering streaming current. In the present study we used a precision electronic integrator with digital output for detection of streaming currents. The currents were determined as a result of a statistical treatment, applied to chargetime functions. Experimental data, obtained in the streaming current, and electroosmotic pressure measurements were used to compute the values of the surface potential of the capillary and to verify the rheological constants of water (1). Journal of Colloid and Interface Science, Vol. 72, No. 2, November 1979
224
YIGAL GUR EXPERIMENTAL
Pyrex tube with the B-14 cone on its end. The external part of the Pt wire was electrolytically coated with Ag and then chloridized in 0.01 N HC1 according to the procedure suggested by Ivnes and Janz (12). Bias interconnection potentials measured after an aging period of a month in a saturated AgC1 water solution were less than 0.01 mV. Capillaries. Fuzed quartz, optical grade slides, 0.15 cm thick, were cut into squares 1 x 1 cm. The plates were intensively cleaned by the following procedures: (a) washing in hot distilled water with "Teepol" detergent; (b) tetrachlorethylene vapor extraction; (c) isopropyl alcohol vapor extraction; (d) bidistilled H20 vapor extraction. The duration of each step was not less than 3 hr. The liquid drops, condensed on the plates after every operation (a)-(d), were blown off by a slight N2 jet. The cleaned plate was placed with appropriate mask (1 x 0.6 cm) in a vacuum evaporation set and two SiO~ spacers with dimension 1 cm x 0.2 cm x 1000/~ were deposited on two opposite ends of the plate's side. The thickness of the SiO2 deposit was
The experimental system. The Pyrex glass experimental system is presented in Fig. 2. Six reversible electrodes are placed at positions El-E6. Two capillary slits C~ and C2 are connected to the reservoirs Ra, R2, and R3 by means of the glass joints B-14 with Teflon sleeves. " M o n o s t a t " threading clamps were used for hermetical packing and reinforcement of all the joints. Capillary Ca is used as the streaming current generator and capillary C2 as the electroosmotic cell. Tubes T1-T3 connect the gauge with a pressure-producing system. Low-pressure gradients were obtained by producing level differences of the liquid in the 0.5-liter aspirator bottles. The differences of levels were measured with an accuracy of 0.01 cm. High-pressure gradients were produced by applying N2 pressures controlled by a precise mercury manometer having a 0.001-in. accuracy photocell registration of the Hg level. Electrodes. A platinum wire 3.5 cm long and 0.5 mm in diameter was soldered in a
Thermometer 0.01°C d i v
~gon
I,-~
~-
OS,
. . . .
'::::
-~---'ll
[] [I : : ::---:',
~----~llq,ll
o.~' I--I
II
~
H
:OO~mm
N ;ec.,v.,
Manometer *-0.001
inch
Hg
II_
_
I
Thermoisolation
&
electrostatic
screen
FIG. 2. Experimentalgauge and pressure-producing system for simultaneous streaming current and electroosmoticmeasurementsin a singlecapillary(C2).
Journal of ColloM and Interface Science,
Vol. 72, No. 2, November 1979
WATER ELECTRORHEOLOGY PARAMETERS
225
pressure-producing system were placed in a temperature-controlled room so that the temperature fluctuations in the thermostat ~.~ . Keiihley6 1 6 , , were smaller than 0.05°C. Usage of the saturated AgC1 water solution with the Ag-AgCI electrodes and intensive stirring during experiments permitted us to eliminate the concentration effects (diffusion, asymmetry polarization) as much as possible. Electronic and measuring circuits. The electronic circuit of the electrokinetic compensator for electroosmotic pressure inT3 vestigations is presented in Fig. 3. The external pressure difference P Fro. 3. Electrokineticcompensatorfor the electroosmoticcounterpressuremeasurementsin capillaryC2. generated by the pressure-producing system (Fig. 2) being applied between Ta and controlled by the quartz crystal monitor T3 (T2 is closed and disconnected) causes "Speedivac," previously calibrated by opti- a liquid hydraulic flow through system Cacal interferometer. The deposed plate was C2. This flow provides an electric charge covered with a similar nondeposed plate. transport between electrodes El-E2, which The "sandwich" was forced and glued are connected to the digital electrometer together with "Tort-Seal" cement to ob- " K e i t h l e y 616." The electrometer is tain a small capillary slit. The real height operated in the fast ampermeter mode, and of the slit was different from the separator its input resistance (105-106 1~) is less than thickness (deposited SiO2) and was deter- the electrolytic resistance of the capillary mined later by electric and hydraulic con- (-108 1~). The 1-V analog output of the ductivity measurements. electrometer is connected to the preampliAssembling. Before assembling the sys- fier Aa, whose gain can be regulated. The tem, the glass reservoirs Ra-R3 were in- output signal of A2 is proportional to the tensively washed with "Teepol" detergent streaming current in capillary Ca and is null and extracted with HzO vapor for 6-8 hr. when the flow is absent. The negative feedThe Teflon-coated stirring bars were placed back loop consists of the amplifier A2 with at the bottom of the reservoirs. The sys- _+100-V output and two electrodes E~-E6 tem R,-R3 (Fig. 2) was carefully filled which provide the electrical field in capilwith the electrolyte solution to avoid the lary C2. The A2 amplifier is operated as an possible formation of air bubbles on its glass integrator (C = 2.5 /zF, R = 100 k12) and surfaces. The electrolyte was prepared as its output voltage causes the electroosmotic saturated solution of AR-grade AgC1 in bidis- flow in the C2 capillary in opposite direction tilled water (X = 0.9 x 10.6 1~-a cm -1, to the hydraulic flow. The stationary state pH = 5.86). Small portions of solid AgC1 of the scheme is achieved in the absence were placed on the bottom of Ra-R3. Elec- of the total liquid flowthrough C1-C2 and trodes El-E6 were mounted and the whole may be submitted as an equivalence of the gauge was placed in a thermostat with the electroosmotic pressure to the external four-layer earthed electrostatic screen which pressure P. The voltage U that correprevented the system from external electro- sponds to the given P is measured by static hindrances. The thermostat with the electrodes E3-E4 connected to the highJournal of Colloid and Interface Science, Vol. 72, No. 2, November 1979
226
YIGAL GUR
®
®
© F1o. 4. Response of the compensator for two pressure pulses 0.28 and 0.25 in. Hg. Capillary's heights: C1, 4.3 /zm; C2, 6.2 /xm. Records a, b, and c were obtained in the correspondent points in Fig. 3. impedance digital voltmeter V (4600 Digital Multimeter, Dana Inc.). Figure 4 presents the dynamic response of the electrokinetic compensator on two sequential pressure pulses. The streaming current phenomenon in capillary C2 was studied by the scheme presented in Fig. 5. An external pressure difference P applied between T2 and T3 (Fig. 2) causes a charge transport through
capillary C2. This charge is registered by the "Keithley 616" digital electrometer which is operated in the fast coulometer mode so that its output is proportional to the electrical charge passed through capillary C2. Every 10 sec the Timer (Elron scaler-timer Nis 17-P) sends a strobe pulse to the isolated output/control circuit (Keithley 6162) to retrieve the digital output from the electrometer. These data (charge i
Timer
616 Electrometer
°iI,
WANG
500
Digital System
T2
FIG. 5. Digitalregistrator of the electricalcharge transport through capillaryC2. Journal of ColloM and Interface Science, Vol. 72, No. 2, November 1979
WATER ELECTRORHEOLOGY 0,00 24,
×
10,00 266,
×
20,00 500.
X Y
~0.00 737.
× Y
40,00 973,
Y
50.00 1204.
X Y
Y
Y time (see) charge (I0-I0 coul)
(A)
2,359428571-10 2,747619048-10
B A
current
,99998189 2,424740249-1! 1,870828693+01
C
correlation coefficient
E F
4,414166587-09 5,796237832-15 6. 1,418339J97-12
G H M
B
halfwidth of [he 95% confidence
interval
Fie. 6. Sample of the registrator's printout (Calculator W a n 500).
q and time t) are transmitted to the programcontrolled digital calculator (Wang 500) and stored there. After a certain number of the q(t) measurements (usually six) the linear regression analysis program is run to evaluate the mean value of the streaming current. The advantage of this method is in the high accuracy of the current determinations which is not dependent on the range of streaming current value. An example of the Wang printout with the computed current and statistical parameters is presented in Fig. 6. RESULTS OF ELECTROKINETIC EXPERIMENTS
A series of capillaries prepared as described above were filled with AgCI solution and used in the streaming current and electroosmotic pressure experiments. The capillaries were in contact with the solution
PARAMETERS
227
during the whole experimental period (about 18 months). Electrical conductivity and pH of the solution were controlled during the experiments. A slight acidization of the solution was detected as a function of time: pH = 4.3 and h = 4.5 x 10-5 ~-~-1 cm-1 had been found for the fresh prepared solution and were changed to pH = 3.1, X = 21 x 10-5 12-1 cm -1 at the end of the experimental period. Every streaming current experiment was followed by the electroosmotic pressure experiment. A time interval between these experiments did not exceed an hour. To "switch" the experimental set from one type of experiment to another, no opening or additional filling within the system was done. It enabled us to avoid external influences on the system and to observe the streaming and the electroosmotic pressure practically under the same conditions. It was found that at the beginning of the experiments, the ~-potentials of the capillaries were high and decreased slowly with time. After a period of some months, the ~-potentials reached a more or less low constant value, which did not change further.
Capillary Geometry Determinations The electrical resistance of the filled capillaries was controlled before and after every electrokinetic experiment. Electrodes E~-E6 were connected to the "Keithley 616" electrometer, operated in the fast ohmeter mode (constant current method). No changes of the resistance were found during an experimental day. To avoid possible influences of the surface conductivity and interface rheology (1), the determination of the capillary heights was done after the aging period, i.e., when ~-potentials were minimal. The electrolyte conductivity was simultaneously measured in the same temperature conditions by a standard ac bridge conductometer. The heights of the capilJournal of ColloM and Interface Science, Vol. 72, No. 2, November 1979
228
YIGAL GUR
laries calculated from these measurements were compared with those obtained from the hydraulic conductivity measurements performed in the aged capillaries (low value of the surface potentials). The hydraulic conductivity was measured by investigations of microdisplacements of a liquid meniscus in a precision bore capillary, diameter 0.33 mm, with the precautions described by Smit and Stein (13). The classical expression which results from the solution of the Navier-Stokes equation was used in calculations of h. The capillaries' heights, calculated from both methods, were significantly identical.
Rheological Behavior of the Streaming Currents The streaming current as a function of driving pressure I = I(P) was measured for high and low pressures. The reproducibility of these measurements is sufficiently high as presented in Fig. 7, where the results of
~-Potentials Typical results of the electroosmotic pressure experiments are plotted in Fig. 8. The slopes Sep of the regression line
//
o -~r _
to.
I-- o r.,r')o
taJ cr¢r-o
four experiments are plotted. The linear regression analysis was applied to obtain the slopes Sse of the I(P) lines. These slopes coincide with the L12 kinetic coefficient (1), and the difference between their values, computed for different pressure intervals, may be explained as a nonlinearity of the streaming current phenomenon, predicted by Gur and Ravina (1). The statistical t test (14) was used to find the significance of the differences in the slopes. The results of these experiments and appropriate statistical treatment are collected in Table I. The significant differences in slopes were obtained for small "fresh" capillaries. Increasing the capillary height and their aging lead to decreasing the significance in the differences.
J
°o'.oo
sb.oo lbo.oo PRESSURE
!
jT~so72o 7:m.oo e~o.oo e~o.oo (OYN/CFi o SO) • 1 0 3
FIG. 7. Streaming current in the 1.7-/~m capillary, t = 23°C. Solid line, theoretical prediction on the base of rheological theory (1). Points (+), experimental results.
Journal o f Colloid and Interface Science, Vol. 72, No. 2, November 1979
229
WATER ELECTRORHEOLOGY PARAMETERS TABLE/ Streaming CurrentPhenomenain DifferentPressureRanges a Capillary age (months)
Capillary height h (10-4 cm)
Pressure interval from Hg)
Current-pressure slope (t0 -~ esu)
Chance of difference between slopes (%)
0
1.7
10-110 550-650
1.3 1.83
>99.9
11-24 250-750
2.88 3.46
53
13-34 457-559
0.323 0.313
15
0
4.26
6
1.7
Capillary h x 0.6 x 1.0 cm, saturated AgC1solution, 23°C. U = U(P), which are proportional to the ratio L2e/L21 [see (1)] were used for computations of the ~ep-potentials according to the expression h2~~ev --
--
-
-
3~o h2,n-
-
3e0
(L21/L22)
(1/Sep),
[1]
where E0 is the dielectric constant of water. Streaming current experiments were run simultaneously in the same capillary in highpressure ranges and the slopes of lines I = I ( P ) , which are proportional to L12, were used to c o m p u t e the ~s~ potentials: C9"
7 cs.
o'
w ~ Q9~.
~o ISOc~
>4
8oOO SOoUO T88.oe 2,~OoOO s2o°8o ,~eOoOa PRESSURE ( D Y N / C I ' l o S 8 ) ~ 1 8 8
4Try0 # 4~'V0 ~se = Lie - - S s c eoah eoah
,
where 70 is viscosity, a is capillary width, and # is capillary length. Results of the ~e, and ~s~ determinations are presented in Table II. The averaged accuracy of the ~-potential determinations was + !.2 mV for ~ep and _+6.3 mV for ~c. SURFACE POTENTIAL AND RHEOLOGICAL CONSTANTS TO compare the results obtained with the theory (1) we have to k n o w the rheological constants of the water and the explicit value of the surface potential. The observed experimental data permits us to predict these values. According to Gur and Ravina (1), the slopes experimentally obtained in the present work can be expressed as functions of the next arguments: q50, f , L, B~, B2, a where 050 is surface potential, f is the viscoelectric coefficient, and L, B2, B2, a are rheological constants. We introduce now the auxilliary, positively determined function of errors F = (1 - Ssc/S*c) 2 + (1 - v~ 's c /- ~~s'c* ~ ] + ( l -- S e p / S * e p ) 2,
FIG. 8. Electroosmotic counterpressure in the 1.7-/zm capillary, t = 23°C. Solid line, rheological theory; points (x), experiment.
[2]
[3]
in which S*e is the theoretical value o f the c u r r e n t - p r e s s u r e slope in the low-pressure Journal of Colloid and Interface Science, VoL 72, No. 2, November 1979
230
YIGAL GUR T A B L E II ~-Potentials, E v a l u a t e d from S t r e a m i n g Current E x p e r i m e n t s (~¢) and from E l e c t r o o s m o t i c Counterpressure Measurements (~J~
Capillaryage (months)
pH of solution
Capillaryheight (10-4 em)
0
4.3
1.7 4.16 4.3 6.2 6.4
6
3.3
1.7 4.16
13
3.1
1.7 4.16
-L~z (10-6 esu)
~sc (mV)
L22/L2~ (10-~ esu)
--63.2 --62.1 --62.9 --61.5 --62.8
0.756 4.02 4.38 9.24 10.2
3.20 6.13
-- 14.2 -- 11.0
7.48 74.8
-- 15.4 --9.2
1.84 3.22
--8.1 --5.8
22.5 82.9
--5.1 --8.3
14.4 34.5 36.2 51.0 53.2
(~ (mV)
-- 152 -- 171 --168 -- 165 --159
Capillary h × 0.6 × 1.0 cm, s a t u r a t e d AgC1 solution, 23°C.
region, S~* is the theoretical value of the minimization. The value F = 0.13 was obcurrent-pressure slope in the high-pressure tained for the next values of the variables: region, S*p is the theoretical value of the 4)0 = -150 m V ; f = 9.18 x 10-7; L = 300; voltage-pressure slope in the electro- B1 = 8.058 x 10-3; B2 = 0.333; ot = 0.01. osmotic pressure experiments, and S~c, The experimental results (points) are comS'sc, Sep are appropriate experimental values. pared with the theoretical predictions (solid From the reasons pointed out above, the lines) of the streaming current and electrofunction F may be treated as a function of osmotic pressure in Figs. 7 and 8. several variables ~b0,f , L, B1, B2, a. It is clear that the variables may be determined DISCUSSION by a minimization of the F-function. The The differences between ~-potentials minimal value of the function may be a measured in low ionic strength electrolytes criteria of the theory-to-experiment coinciby electroosmotic and streaming systems dence. have been reported over the years (5, 16). We minimized the F-function in the These studies dealt only with two types of present work by the conjugate directions electrokinetic experiments: electroosmosis procedure, suggested by Powell (14). The (~eo) and streaming potentials (~sp) investigaslopes S*e and S~* were computed accordtions. The anomalous differences between ing to the procedure described previously ~eo and ~so were obtained (16) for con(1). For the third term S*p the necessary ductivity grade water, but were the result tangential field for a given pressure was of experimental errors. In a more careful determined from the total flux condition: study, submitted later by Rutgers and de Smet 0 = J(U,P). [41 (5), the equivalence for ~eo and ~o was obThe tabulated function U(P), which corre- tained and most scientists tend to believe sponded to the condition of Eq. [4], was that all electrokinetic systems used for deused further in the linear regression analysis termining of the ~-potentials are fundamentally equivalent. to find the value S*p. The equality ~eo = ~sp is equivalent to the Experimental data obtained for " f r e s h " 1.7 x 10-4 cm capillary were used in the general principle of the theory of irreversiJournal of Colloid and Interface Science, Vol. 72, No. 2, November 1979
WATER ELECTRORHEOLOGY PARAMETERS H
=
17000
T
=
E3
E
=
0
B
-
1CN
e = I0~
2
8YN/CN.50
P = 10~t
¢
DYNtCM.58
+
P = I0~/
6
DrNICM.50
x
P = IO~m
8
O~N/CM.SQ
R
C
5P =
°
149
MV
7 CD
EL~-
>-
o
>$ a~ Ix_ --
0o00
1
0o02
0°03
D~ST~NC£
0°05
0°07
OoOB
< C N ) ~ 1 0 -s
FIG. 9. Distributions of the effective viscosity near the capillary wall computed according to the rheological theory (1) with found values of the rheological parameters.
ble processes: the Onsager's symmetry of the phenomenological coefficients on linearized transport equations (17), as was carefully discussed by Miller (18). The rheological theory of ~-potentials, raised by Gur and Ravina (1), does not contradict this principle and, as a consequence, predicts the same values for ~eo, ~p, and ~se, but makes them sensitive to the deformation rate distribution in the interface. This distribution is significantly different for streaming phenomena and for a stationary case of the electroosmotic pressure phenomenon. As a result of this difference, g~c and ~ep have different values, as was predicted (1) and observed experimentally in the present work. The increase of the ~-potentials with an increase in the deformation rates in interfaces, experimentally observed here in streaming experiments, must be taken into account when one compares electrokinetic results obtained in different capillaries. The variations of
231
the ~-potential as a function of the hydronium ion concentration (pH) in aqueous solutions-silica systems was studied experimentally by Wiese et al. (19). It is interesting to compare their results, obtained for 10-4-10 -3 M K N 0 3 with the ~se, measured by us in saturated AgC1 solution. The isoelectric point (pI) derived from our results is pH = 2.99 --_ 0.03 which agrees satisfactorily with the pI pH = 2.5 ___ 0.2 obtained by Wiese et al. (19) and falls within values, recorded in the literature (20), for quartz and SiO2 sols and gels. The difference of about pH = 0.5 may result from differences in streaming conditions. The streaming experiments of Wiese et al. (19) were performed in a vitreous silica capillary of 0.76-mm diameter, i.e., with higher deformation rates than realized here. According to the theory (1) ~-potentials, measured in high deformation conditions, must be much higher (in absolute values) than registered in our capillary, which respectively may lead to a decrease of the pI obtained. The surface potential estimated from the Nerust equation (21, 22): 49s = 2 . 3 0 3 ( k T / e ) ( p H p i - pH)
[5]
has a value qSs = -105.8 mV (23°C, ApH = 1.8). Levine and Smith (23) analyzed the validity of the Nerust equation for an oxide/ aqueous electrolyte interface. They found that Eq. [5] is valid for the micropotential of the surface ~bs which may be expressed as the macropotential 4~0 of the electrical double layer and a self-atmosphere potential to due to the disturbance in the mean distribution of surrounding ions caused by the presence of the ion at the given position: 6s = 4~0 + to.
[6]
The qS0 = - 150 mV, estimated from the experiments, gives for the self-atmosphere potential to = 44.2 inV. Figure 9 presents the distribution of the effective viscosity in the capillary h = 1.7 /xm computed with the obtained values of Journal of Colloid and Interface Science, Vol. 72, No. 2, November 1979
232
YIGAL GUR
the rheological constants and ~b0 = -150 inV. The three-region model of the viscosity distribution, suggested by Gur and Ravina (1), is not changed with the obtained values of the rheological parameters. ACKNOWLEDGMENTS This United (BSF), debted
research was supported by a grant from the States-Israel Binational Science Foundation Jerusalem, Israel. The author is deeply into Referee II, for his constructive criticism. REFERENCES
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Journalof Colloidand InterfaceScience, Vol.72, No. 2, November1979
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