I
H. N. KELLERI and H. E. HOELSCHER Department of Chemical Engineering, Johns Hopkins University, Baltimore 1 8, Md.
Development of Static Charges in a Nonconducting System How much will new synthetic materials used in hospitals and refineries increase hazards from fires and explosions sparked by static electricity? When moving liquids are involved, this may depend upon leached impurities
WHENEVER
two dissimilar materials are brought into contact and then separated, static charging occurs if one of the two materials is a poor electrical conductor. Evidence indicates that the materials must be solid or liquid (20). The charge separations, or static electricity, often can produce high voltages and a potential ignition spark wherever explosive materials are handled. Many fires and explosions are attributed to discharges of static electricity in places such as oil refineries and hospital operating rooms (7, 70). A complete discussion and summary of static electricity before 1930-including general observations, experiments, industrial hazards, and safeguards-was written by Guest (77). The present study involved charge separations a t a solid-liquid phase boundary. Previous work in this field can be categorized according to whether the liquid possessed high or low electrical conductivity. Most investigators whose studies dealt with low conductivity liquids either have not interpreted their results theoretically, or, where such attempts have been made, have attributed the charge separations to the contact potential theory (2). The apparatus and experiments of Dolezalek (7) are typical of most of these investigations. He passed high resistivity liquids, such as benzene and ether, through 1- to 2-cm. diameter metal pipes under pressure and measured the charge separations. He detected 1 Present address, Bell Telephone Laboratories, Murray Hill, N. J.
these as an electrical potential on an insulated tank into which the liquids emptied. The voltages were roughly proportional to flow rate, which was as high as 4 meters per second, corresponding approximately to a Reynolds number of 100,000. He measured up to 4000 volts with metal pipes, but only 100 volts with glass and porcelain tubes. At flow rates below 0.5 meter per second, potentials did not exceed 300 volts. Dolezalek’s findings were verified by later workers. Russig ( 7 8 ) found that minute quantities of impurities change the electrification by several thousand volts. He postulated the existence of an optimum impurity content for maximum electrification and that dectrification is zero for pure liquids. Pearson (77) also noticed the striking effect of contaminants such as water, tetraethyllead, and iron oxide on the electrification of saturated hydrocarbons. In the case of turbulent flow through a pipe line, Pearson postulated a separation of charges between the liquid and the wall when contaminants collide with the pipe wall. The liquid volume charges cause a returning current to the wall by means of turbulence, conduction, and coulombic forces. At equilibrium, when the rate of separation equals the rate of discharge, the average charge per unit volume of moving product depends upon the liquid composition and pipe-wall surface but is independent of the pumping speed. Upon discharge from the pipe into a receiving tank, the charges leak to the liquid surface and tank wall because of liquid conduct-
ance, volume charge repulsion, and turbulence. Pearson’s observed maximum charges of 1 X 10-7 coulomb per gallon of liquid agrees favorably with those reported by Silsbee (20) (3 X 10-5 coulomb per cubic meter) and MacKeown and Wouk (75) (10-7 to 10-8 ampere for flow rates of 5 to 800 gallons per minute, or the equivalent Reynolds number of 10,000 to 1,600,000). T h e latter, along with Nitka (76): measured charge separations which were directly proportional to the flow rate. Nitka conducted experiments to determine the effect of pipe diameter, length, and material. His results indicate that the pipe material makes little difference, but that small differences in smoothness have an appreciable effect on the charge; that short pipes give high charges which are only slowly increased by length, and that the charge is approximately inversely proportional to viscosity and decreases with increasing pipe diameter. The theoretical interpretation of the observed charge separations which occur in flowing conductive liquids is fairly complete in comparison to the case of nonconductive liquids. Helmholz, Gouy, Chapman, and Stern have developed the double layer theory. Any standard text on this subject includes these as well as many other referencese.g., Bikerman ( 3 ) and Butler (5). Complete reviews of the important research relating to the measurement of equilibrium streaming potentials for laminar flow of dilute aqueous solutions through cellulose, quartz, glass, silica, VOL. 49, NO. 9
SEPTEMBER 1957
1433
and alumina capillaries are available in both texts. The Helmholtz-Smoluchowski equation for calculating the zeta potential from streaming potential measurements was derived by Butler (5): Rutgers (19), and Wood (22). The equation is based upon the assumption of a very thin diffuse double layer, Poiseuillian flow within the double layer, and the validity of Poisson‘s equation. The Helmoltz-Smoluchowski equation may be expressed as follows:
It is based upon an assumed equilibrium between the current of convection, il, and the current of conduction, iz. 21
- ZKPr2
= ___
411
.
22
E.lrr2a 1
= __
(2)
(3)
Rutgers cautioned that surface conductance may become appreciable for very dilute solutions and very narrow capillaries, Wood also mentioned the possible importance of surface conductance and leakage over the outer capillary surface and measuring instrument. The effect of flow rate upon the ratio of streaming potential to pressure drop is discussed in several places. If Z is assumed constant, Equation 1 predicts that this ratio is independent of pressure. However, Ettisch and Zwanzig ( 8 ) showed that Z, as calculated with Equation 1, is dependent on flow rate at low pressures for the case of aqueous electrolyte solutions (sodium chloride) which also contain from 0 to 98.270 nonelectrolyte liquid (aliphatic alcohols), They showed that Z increases with pressure from 3 to 20 cm. of mercury, tending toward a limiting value. As the alcohol percentage was increased, the effect became more pronounced. T o explain these results, they suggested that the double layer breaks closer to the liquidsolid interface for the higher pressures and that a t low flow rates the sheared double layer reforms. Recently, Bocquet, Sliepcevich, and Bohr ( 4 ) have shown that ratio E / P is independent of flow rate, providing the flow is fully established. They measured the streaming potential for dilute sodium chloride and potassium chloride solutions in quartz, glass, Teflon, and butyl acetate tubes for a wide range of Reynolds numbers (100 to 10,000). The streaming potential was measured between the ends of the tubing and across the middle third of the tube to prove that the important criteria for application of the Helmholtz-Smoluchowski equation is fully developed flow and not whether the flow is laminar or turbulent. The objectives of this work were to study the mechanism of charge separation and the important parameters governing charge separations in liquids which flow
1434
through tubes, where both liquid and tube are relatively poor conductors. In the present work, charge developed in both the tubing and in the effluent liquid and was measured to test the validity of the double layer theory of electrokinetics for the case of flowing, nonconductive liquids. Furthermore, the theory which satisfactorily explains streaming potential measurements-i.e., the Helmholtz-Smoluchowski equation-was tested for the case of flowing hydrocarbon liquids. Further evidence is presented to resolve the question involving the variability of the zeta potential (Z)with flow rate. In this study the following charges must be considered. CHARGE GENERATION, a volume charge which is a function of the liquid and tube properties or zeta potential. CHARGE DISSIPATION due to one or all of the following: Leakage current to the grounded reservoir tank, through both liquid and tubing. Leakage current over the polystyrene insulators (proved negligible in this work) Relaxation of charges in the flowing liquid, including those between the main body of the liquid and the fixed part of the double layer, in particular as the liquid leaves the tubing. Charging of the Faraday cage capacitance. Charging of the receiving tank capacitance. Experimental Equipment
To investigate the generation of static electricity in moving liquids, heptane was passed from a reservoir tank through poly(viny1 chloride) tubing into an insulated tank. The charging of both the effluent heptane and the poly(viny1 chloride) tubing was measured as a function of the flow rate. An electrostatic voltmeter and the flow system permitted these measurements. The electrostatic voltmeter with the calibration data and curves has been described in detail ( 7 3 ) . By capacitive coupling between the voltmeter and the body under measurement, no error is introduced, as no excitation current is required. Flow System. As recommended by Henry (72): the equipment for these experiments was designed to measure electrical charge by the Faraday cage method (see diagram). The reservoir and receiving tank were each 1000-ml., stainless steel, cylindrical containers. The reservoir was placed in a gastight cylinder, 5-inch diameter, 8-inch depth, with 0.25-inch-thick walls. Oil-pumped nitrogen was fed to the cylinder through a Matheson No. 70 low-pressure regulator and provided an inert atmosphere to regulate the liquid flow. The plastic tubing passed from the reservoir through a Teflon disk with which it
INDUSTRIAL AND ENGINEERING CHEMISTRY
formed a friction. gastight seal. The tubing then coiled around a polystyrene rack within the Faraday cage, which included a regular screen box mounted within a second grounded box. The inner box, 9 X 9 inches square and 12 inches deep, was supported on the polystyrene rack. The outer box, 11.5 X 10.5 X 20 inches, completely shielded the inner insulated box and enclosed plastic tubing. Three sides of each box consisted of a double layer of 15-mesh copper screen. The fourth side of each was copper sheet. The screen not only provided shielding and permitted free circulation of air around the tubing but also reduced the capacitance of the Faraday cage to ground, thereby increasing the sensitivity of measurement. The tubing terminated a t the receiving tank assembly. Here three polystyrene supports insulated a copper tank. 5-inch diameter and 6-inch depth, from an outer grounded tank, 8-inch diameter and 10-inch depth, The outer tank completely shielded the inside tank. T o measure the charge separations between the plastic tubing and the flowing liquid, both Faraday cage and receiving tank were equipped with a 3/16inch diameter coupling rod. On the exterior end of each rod was fastened a 1.5-inch diameter copper disk which capacitively coupled with the grid pickup disk of the voltmeter. When ready for operation all equipment, including the voltmeter, was in a fixed location. Therefore, the capacity to ground of the Faraday cage, receiving tank, coupling rods, and grid pickup disks was constant. All of these components were shielded from external stray voltages. Any electrical charge on either the Faraday cage or the receiving tank induced a corresponding voltage on the grid pickup disk of the voltmeter. Throughout the entire system’the liquid came in contact only with stainless steel and plastic tubing. The plastic tubing came in contact only with polystyrene insulating supports after leaving the reservoir, where it was held at ground potential. Experimental Data
Preliminary Measurements. Determination of the receiving tank and Faraday cage capacitances permitted the heptane and poly(viny1 chloride) tubing charges to be calculated from the voltage measurements (C = Q / V ) . These capacitances were determined to be approximately 33.0 and 121.3 ppf., respectively, by use of a Type 160-A QMeter (Boonton Radio Corp.). For these measurements the electrostatic voltmeter was in position and set to a 36-pa. deflection. T o ensure absence of polarization effects, each capacitance was measured at several frequencies. T o estimate the leakage currents over
STArIC CHARGES IN NONCONDUCTING S Y S T E M 15" L e n g t h 1/5"I.D. High Pressure Regulator
M o t h e s o n No. 70 Low P r e s s u r e Regulator
/
24"Length of Polyethylene 1/8" I.D.Tubing
Polyethylene Tubing
Natvar S P 4 1 9 10x.032 W / PVC
Compartment
I
J 71 Le-Teflon
Hg
U
Meriam Unity OiI
Stainless Steel Reservoir
1
Po Iy s t y r e n e
S t o in1 e ss Steel Receiving
Insulators
~lectrostatic Val t me t e r
Tank
M anometers
Electrical charae was measured with a Faraday, cage chloride) tubina was coiledyaround a - (center riaht) in which poly(viny1 . ~. n-heptan.e throigh the tubilg polystyrene rack. Nitrogen provided an inert atmosphere for pegulating the flow, v
the polystyrene insulators and through the poly(viny1 chloride) tubing, their resistances were measured by the voltage decay method.
With no poly(viny1 chloride) tubing connected to the apparatus, the receiving tank and Faraday cage were charged by momentary contact with a power supply. The electrostatic voltmeter measured the voltage decay rates. The resistances of the polystyrene insulators were determined to be 10l6ohms. Connecting a section of poly(viny1 chloride) tubing between the receiving tank and the grounded reservoir during the receiving tank voltage decay reduced the measured resistance to approximately 5 X ohms. The poly(viny1 chloride) tubing resistance was reduced below 1013 ohms upon contact with liquid hydrocarbons. Upon continued contact of the liquid and poly(viny1 chloride) the tubing became more opaque and less flexible. As an extraction of compounding agents from the tubing was suspected, the amount of nonvolatiles in both a new and used sample of hexane was measured by a simple air evaporation experiment. The concentration was found to be zero for the new hexane, but as high as 1.7% by weight for the used hexane. The refractive index of the nonvolatile was measured. Its value of 1.4961 compares favorably with the refractive index for some commonly used plasticizers. Infrared spectroscopic tests of samples of heptane and hexane which had passed through the poly(viny1 chloride)
d
tubing also indicated appreciable contamination by plasticizer. Because of the extraction effect of hexane and heptane on the poly(viny1 chloride) tubing, various combinations of other types of plastic tubing and low conductivity liquids were investigated. The receiving tank voltages and flow rates were measured for the various combinations of liquid and tubing. In general, the results for unplasticized tubing (Kel-F and polyethylene) and pure hydrocarbon show the charge separations to be low in comparison to plasticized tubing. However, if the tubing is treated with plasticizer or plasticizer is added to the hydrocarbon, the charging tendency increases considerably. In addition to the extraction of plasticizer which continually changed the liquid properties, the extraction of plasticizer and the swelling action by the hydrocarbons reduced the electrical resistivity of the tubing. This accounted for the rapid leakage of tubing charges to the grounded reservoir tank which initially prevented a check on the equivalence of the liquid and tubing charges. After careful consideration of the previous experimental results, n-heptane and poly(viny1 chloride) tubing (with polyethylene end connections) were chosen as the best system for investigation. The following observations were important in making this decision : Polyethylene is not affected appreciably by contact with heptane, hexane, or benzene. Possessing a high electrical resistivity, the polyeth lene end connections isolate the poly&nyl chloride) so completely that equal voltages can be
measured on both the Faraday cage and receiving tank. The polyethylene inlet section also prevents contact between the poly(viny1 chloride) and the reservoir liquid. Poly(viny1 chloride) tubing yields simificantlv high electrostatic voltages in thue range of flak rates in this study. -Also its low (relative to polyethylene) electrical resistivity, which is a disadvantage in one respect, permits a fairly rapid discharge of the tubing upon contact with ground between successive runs. This is important if initial conditions for each run are to be duplicated. The use of poly(viny1 chloride) tubing with polyethylene end connections necessitated the use of a liquid whose extraction effects are low. The chosen liquid must generate relatively large charges when in contact with poly(viny1 chloride). The charge generation when passing through polyethylene end connections must be negligible. Heptane satisfied these requirements. Measurement of Data. The liquid and tubing properties control the degree of electrification at the solid-liquid interface. Two types of plasticized poly(vinyl chloride) tubing were used. Natvar SP419, 10 X .032W, medical clear poly(viny1 chloride) tubing was used for the study of length effects. The electrification of heptane was measured for 3-, 6-, 12-, and 18-foot lengths. All short samples were cut from a single 18-foot length to ensure uniform tube properties throughout the four tests. Twelve-foot lengths of Irvington Transflex poly(viny1 chloride) tubing with diameters of 0.085, 0.053, and 0.034 inch were used for determining diameter effects. This spaghetti tubing is manufactured a s wire insulation for the electrical industry. VOL. 49, NO. 9
SEPTEMBER 1957
1435
-
v)
5 0
-
70C
5
600
were measured for Reynolds numbers up to 4500. The detailed experimental measurements are available (73, 74).
In
5
-> 0
u
W
W
W
a
5
Results
50C
0
>
3
w
>
0
w 40C
2 t
? a
m
I-
0
W
n
w 30C
z
Y
z a
W
I-
W
W
a zoc V
z 2
2-
a
5:
W W V E
IOC
LT
2 C
FLOW T I M E (MINUTES)
FLOW T I M E ( M I N U T E S )
Figure 1. Typical plots showing receiving tank and Faraday cage voltage data CIS functions of time n-Heptane flowing through 18 feet of Nafvar SP419 poly(viny1 chloride) tubing
Although one sample of heptane was used for all three diameters, the three sections were cut from different rolls. T h e liquid for all tests was Phillips pure grade, 99 mole yo minimum, n-heptane. Laboratory conditions for all of these measurements were approximately 25' C. and 307, relative humidity. The major portion of data included measurements of voltage rise on the receiving tank and Faraday cage as a function of flow time for Reynolds numbers with the range of 300 to 4000. T h e poly(viny1 chloride) tubing w'a:i completely enclosed by the Faraday cage, with the exception of a short section at each end which protruded from the cage to connect with the polyethylene end sections. These sections were guided by polystyrene supports into the reservoir and to the receiving tank. The poly(viny1 chloride) and polyethylene tubings connected in friction-tight joints. While mounting, both the poly(viny1 chloride) tubing and the polystyrene developed large charges by frictional contact with each other. Because of the long time constant of polystyrene, a Tesla spark coil was employed for immediate discharge. The liquid exit was located flush with the top of the grounded shield of the receiving tank. This precaution; in addition to the low charging of the polyethylene and its high electrical resistivity, minimized the possibility of tubing-induced voltages on the receiving tank. After mounEing the tubing and positioning all equipment, the poly(viny1 chloride) tubing was discharged to ground overnight before the first test. After the meter had been warmed up, the Faraday cage and receiving tank were checked for zero voltage. Gen?rally, two trial runs were required to attain equilibrium conditions between the liquid and tubing (because of ex-
1436
traction and swelling). For each run the Faraday cage and receiving tank voltages were measured as a function of flow time at constant pressure. T o determine the flow rate, the receiving tank was weighed to the nearest 0.5 gram after each run. Frequently the voltage measurements were continued for several minutes after cessation of flow to test for the presence of leakage currents. Between two successive runs, for all but the 3-foot length and the Irvinpton tubing, the poly(viny1 chloride) tubing was grounded until the voltage of the Faraday cage decreased to zero. This guaranteed practically no tubing charge at the beginning of each run. During any one run the tubing remained continuously filled with heptane, and there was no liquid-gas interface in the tube. T o check the Helmholtz equation an accurate knowledge of the pressure drop through the tubing is required. During the experimental work the reservoir was measured. However, because of the differences in diameter between the poly(viny1 chloride) nibing and polyethylene tubing and the uneven tubing contours at the entrance, exits, and connections the pressure drop through the poly(viny1 chloride) tubing itself could not be determined from the overall pressure. T o obtain the required pressure drop data, separate experiments were made using poly(viny1 chloride) tubing of the proper diameter and with lengths varying from 6 to 21 feet. Pressure drop as a function of length was measured and these data were then used in checking the Helmholtz equation. To determine the contribution to the heptane charging by the polyethylene end sections, receiving tank voltages were measured for heptane flowing through the 2-foot polyethylene entrance section. No voltages exceeding 70 volts
INDUSTRIAL A N D ENGINEERING CHEMISTRY
As noted by Cooper ( 6 ) , a system of units for this type of study which involves electrostatics, hydrodynamics, and surface chemistry requires some compromise. Because the measurements and formulas are essentially electrical in nature and because the use of familiar electrical terms is desirable, the rationalized meter-kilogram-second system was used for all calculations. Smythe (27) has discussed the various systems of units and tabulated the necessary factors for converting from one system to another. A typical graph of the receiving tank and Faraday cage voltage data as a function of time is shown in Figure 1. In general, the points for each run form a linear plot. However, the final measurement usually falls above this line. 'This is attributed to the time required for the liquid charges to diffuse to the receiving tank wall and to a redistribution of the tubing charges over the relatively conductive poly(viny1 chloride) to provide a uniform potential. The initial and final voltages of each curve were used to compute the rate of voltage rise on the receiving tank and Faraday cage. A straight line through these two points passed through the origin. At low flow rates (Re = 500) the voltageflow time curves are nonlinear with positive slope which decreases with time of flow. A decreasing liquid level in the reservoir and, consequently, a decreasing flow rate at a constant pressure caused this effect. The rates of charging of the liquid and tubing for the higher Reynolds numbers agree within the limits of experimental accuracy (see Figure 2). This proves the negligible charging effect of the polyethylene inlet and outlet sections. There was excessive variability in the data at low flow rates when the flowing liquid did not fill the tubes completely. Also, a t the lower Reynolds numbers, the liquid in the reservoir was not exhausted during a run. When the flow was stopped by releasing the pressure, a backward flow of heptane from the tubing to the reservoir caused additional charging of the poly(viny1 chloride) tubing. Equation 2, rewritten in the MKS system, may be shown to be equivalent to the following (73): d__R - rkr2ZP" ____ (5) dt c?li Similarly! Cooper's equation ( 6 ) can be written
Equations 5 and 6, which can be proved equivalent (73). were investigated to
STATIC CHARGES IN N O N C O N D U C T I N G S Y S T E M determine if they correlate the experimental data. Both equations should be applicable if the assumption of a negligible conduction current (Equation 3) is valid. The authors believe that the low conductivity of heptane and the separation of the charged heptane from the tubing reduced the conduction current sufficiently for this assumption. Equations 5 and 6, assuming a constant zeta potential, 2, require that a plot of dR/dt us. P * / l on Cartesian paper should be a single straight line for all tube lengths. Similarly dR/dt us. (ReYu) should be linear on the same type of graph. This was not found to be the case. TVhen plotted, the data for each tube length resulted in a separate line which was markedly curved. Thus neither Equation 5 nor Equation 6 can be assumed to represent the data taken in this study with the value of the zeta potential assumed independent of flow rate. A plot of charge generation rate us. Reynolds number on logarithmic coordinates resulted in a single straight line relationship for all tube lengths within the limits of accuracy of the measurement techniques. Figure 2 is such a plot. An attempt was made to use the Helmholtz equation to explain this observed result. I t was assumed first that theie was a relaxation of liquid charges at the tubing exit and along the tube length. I t was assumed that the relaxation equation could account for a recombination of ions or charges. providing that the time dependent term in the equation may be expressed in terms of flow rate. This introduced a flow dependent term into the Helmholtz equation and permitted the zeta potential to be assumed constant in keeping with the findings of Bocquet, Sliepcevich, and Bohr ( 4 ) . A modified form of Helmholtz’ equation was derived which could be tested against the available data. Such tests were macle, and the resulting equation did not describe the experimental results. This development is discussed in detail elsewhere (73). Finally, it was assumed that the zeta potential was flow dependent, in agreement with the work of Ettisch and Zwanzig previously mentioned. The zeta potential is defined as the potential at the surface of shear between the bound layer of ions and those carried along with the flowing fluid. Increased flow rates produce larger shear forces a t the double layer. Therefore more bound ions of the diffuse layer can overcome the coulombic binding forces and be swept along with the flowing liquid. Rewriting Equation 5 and dividing both sides by W/t (the flow rate), the charge concentration in coulombs per kilogram of liquid is obtained as:
18 F t . 12 F t .
6 Ft. 18 F t .
12 F t . p!
s? x
1 0
-
IO
-
6Ft.
m m o
H Z
93 ws
o m 0
Figure 2. Charge generation rate vs. Reynolds number
I 1
I
100
1000 Re
-__
-
(7)
Assuming Poiseuille’s law, this may be written as
8k Since - is a constant, a plot of the wr2 left hand side of Equation 8 us. Reynolds number should yield a line of zero slope. However, such a plot actually produced a straight line of positive slope passing
eo
through the origin, indicating a definite linear dependence of the left side of Equation 8 on Reynolds number. Returning to Equation 5, assume Z = uRe where u is a constant of proportionality. A revised Helmholtz equation is obtained: (9)
dR P*Re - us. dt I in Figure 3 and show satisfactory agreement with Equation 9 except for the The data are plotted as
t 1 O-s
Figure 3.
P* I Re NEWTONS/METER3
Check of data with Equation 9 VOL. 49, NO. 9
SEPTEMBER 1957
1437
3-foot length of tubing. This difference was attributed to the relatively greater contribution to the liquid charge from the polyethylene inlet and outlet tubing sections for the shorter lengths of poly(viny1 chloride) tubing-Le., end effects. Using Poiseuille’s law and taking the logarithm of both sides of Equation 9, the following form was obtained: dR 4~7kv In - = in __ 2lnRe dt cwr
+
(10)
This equation predicts the observed linear log-log results in Figure 2 and in addition predicts a slope of 2. The experimental slope of Figure 2 was determined to be 2.08. The use of Poiseuille’s law in Equations 9 and 10 is obviously not justified through the transition flow range. In addition it is clearly indicated by the pressure drop-flow rate measurements that the flow was not laminar in character. The reduced radii a t the polyethylene junctions, the bends in the tubing within the Faraday cage and the entrance and exit effects are probably responsible for this. Regardless of the unknown flow conditions in the bulk liquid, the assumption of Poiseuille’s law in Equations 9 and 10 did permit a satisfactory explanation of the data. The departure from laminar flow in the fluid is probably taken care of, in part, by the constant in the assumed relationship between the zeta potential and Reynolds number. Other than this, no explanation of the good agreement between Equation 10 and the experimental data is apparent. The assumption of a variable zeta potential in Equation 9 was further verified by a determination of radius effects. According to this equation, the rate of voltage rise should be proportional to r2 for a constant flow rate. At a Reynolds number of 1000, the ratio of the rates of voltage rise for the 0.085- and 0.053-inch diameter tubings was calculated to be 2.21 as compared with a ratio of the diameters squared of 2.52. The constant of proportionality, u, was determined from the slope of Figure 3 to be 1.87 X lo-* volt. Therefore, the zeta potential for a Reynolds number of 100 equals 0.0187 volt, a value which agrees favorably with the results from Gortner’s streaming potential measurements ( 9 ) . Equation 9, which considers 2 to be dependent on flow rate, as found by Ettisch and Zwanzig ( 8 ) , and which explained the experimental data in this study, is applicable only if the current of conduction is negligible.
flow rate and independent of tubing length from 6 to 18 feet. The Helmholtz equation for the current of convection (which is equivalent to Cooper’s equation) satisfactorily explains these experimental results, providing the zeta potential is assumed to be a linear function of Reynolds number. Unlike previous investigators who studied the Helmholtz double layer theory by streaming potential measurements, the charges on both the tubing and in the effluent liquid were measured. The equivalence of these charges proved the absence of leakage currents. Further evidence was discovered to indicate that pure liquids do not electrify. The plasticizer in the tubing-or plasticizer in the heptane-is important in the development of static charges on both the liquid and the tubing. This phenomenon is unexplained but has been definitely established. The presence of a high molecular weight, polar organic molecule in the liquid or one to be leached from the plastic tubing is essential to the development of a significant charge. In any future work of this nature, special precautions should be observed to ensure fully developed flow. It would also be desirable to select a system in in which a constant contaminant concentration could be maintained. Such systems as polyethylene with benzene, heptane, or similar liquid might be used. The effect of tubing length on rate of electrification could be investigated by two methods. The tubing could be reduced until length became an important parameter; this may not be practical if the required length is small. A more practical approach would be a measurement of charge on each unit length of tubing. A series of Faraday cages along the tubing could do this. A modulator type of electrostatic voltmeter connected to a recorder would provide ideal instrumentation for such a study. The electrical resistivity of the tubing would necessarily be large to prevent equalization of charge along the tubing length. Nomenciaiwre
a
= specific conductance of liquid
c = electrical capacitance, farads
E = streaming potential F = Faraday cage voltage, negative volts
K = dielectric constant k
= absolute capacitivity
1
= tubing length
1 7 =
liquid coefficient of viscosity
Conclusions
P = pressure drop between ends of tub-
The electrification per unit weight of heptane when flowing through poly(viny1 chloride) tubing is a linear function of
p*
1438
ing pressure, Kewtons per square meter R = receiving tank voltage, positive volts
INDUSTRIAL AND ENGINEERING CHEMISTRY
=
r = tubing radius Re = Reynolds number t = time, seconds u = liquid mean velocity V, = initial voltage V , = voltage at time t W = weight of liquid flow w = liquid density X = resistance, ohms Y = Reynolds coefficient of friction Z = zeta potential Acknowledgment
The authors wish to acknowledge the generosity of the Natvar Corp. in supporting this work. The interest and contribution of R. K. Witt and F. C. Hettinger during the early stages of this work are gratefully acknowledged. Literat wre Cited
(1) Beach, R., Am. SOC..Wech. Engrs., Paper 52-A-156 (1952). ( 2 ) Beach, R.. Elec. Ene. 64, 184 (1945). (3) Bikerman, J. J., “Surface Chemistry for Industrial Research,” Academic Press, New York, 1947. (4) Bocquet, P. E., Sliepcevich, C. M., Bohr, D. F., IKD. ENG. CHEM.48, 197 (19563. ( 5 ) Butler, J. A. V., “Electrical Phenomena at Interfaces,” hfethuen BL Co.. Imndon. 1951. (6) Cooper, I+ F.,.Brzt. J. dgpl. Phys., Suppl. 2, S11 (1953). ( 7 ) Dolezalek, F., Chem. Znd. 36, 33 (1913). (8) Ettisch, G., Zwanziq. A., 2.physik Chem. A 160, 385 (1932). ( 9 ) Gortner. R. A . , Trans. Faradav SOC. 36, 63 (1940). ’ (10) Griffin, N. L.. Elec. Eng. 68, 1085 (1 ,- 0,4. 0, ),. (11) Guest, P. G., ”Static Electricity in Nature and Industry,’’ U. S. Bur. Mines, Bull. 368 (1933). (12) Henry, P. S.H., Brit. J . Appl. Phys., Suppl. 2, S6 (1953). (13) Keller, H. N., Doctor of Engineering dissertation, The Johns Hopkins University-, Baltimore, Md., 1956. (14) Keller, H. N., Hoelscher, H. E., American Documentation Institute, Auxiliarv Publications, Document No. 520f, Washington, D. C., 1957. (15) MacKeown, S. S.:Wouk, V., IND. ENG.CHEM.34, 659 (1942). (16) Nitka, H., Chem. Fabrik 14,211 (1941). (17) Pearson, J. M., Oil Gas J . 39, 140 (1940). 18) Russig, F., Chem. Ind. 36, 62 (1913). 19) Rutgers, 4.J . , Trans. Faraday SOC.36, 69 (1940). (20) Silsbee, F. B., “Static Electricity,” Natl. Bur. Standards (U. S.) No. C438 (June 10,1942). (21) Smythe, W. R., “Static and Dynamic Electricity,” page 585, McGrawHill, New York, 1950. (22) Wood, L. A , , J . Am. Chem. SOC.68,432 (1946). RECEIVED for review July 27, 1956 ACCEPTEDFebruary 15, 1957 \
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I
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